=============
API Reference
=============

Introduction
------------

This chapter is the reference manual for MuJoCo. It is generated from the header files included with MuJoCo, but also
contains additional text not available in the headers.

.. _Type:

Type definitions
----------------

.. _tyPrimitive:

Primitive types
^^^^^^^^^^^^^^^

MuJoCo defines a large number of primitive types described here. Except for :ref:`mjtNum` and
:ref:`mjtByte`, all other primitive types are C enums used to define various integer constants. Note that the
rest of the API does not use these enum types directly. Instead it uses ints, and only the documentation/comments state
that certain ints correspond to certain enum types. This is because we want the API to be compiler-independent, and the
C standard does not dictate how many bytes must be used to represent an enum type. Nevertheless we recommend using these
types when calling the API functions (and letting the compiler do the enum-to-int type cast).

.. _mjtNum:

mjtNum
~~~~~~

.. code-block:: C

   #ifdef mjUSEDOUBLE
       typedef double mjtNum;
   #else
       typedef float mjtNum;
   #endif

| Defined in `mjtnum.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjtnum.h>`_

| This is the floating-point type used throughout the simulator. If the symbol ``mjUSEDOUBLE`` is defined in
  ``mjmodel.h``, this type is defined as ``double``, otherwise it is defined as ``float``. Currently only the
  double-precision version of MuJoCo is distributed, although the entire code base works with single-precision as well.
  We may release the single-precision version in the future for efficiency reasons, but the double-precision version
  will always be available. Thus it is safe to write user code assuming double precision. However, our preference is to
  write code that works with either single or double precision. To this end we provide math utility functions that are
  always defined with the correct floating-point type.

| Note that changing ``mjUSEDOUBLE`` in ``mjtnum.h`` will not change how the library was compiled, and instead will
  result in numerous link errors. In general, the header files distributed with precompiled MuJoCo should never be
  changed by the user.

.. _mjtByte:

mjtByte
~~~~~~~

.. code-block:: C

   typedef unsigned char mjtByte;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Byte type used to represent boolean variables.

.. _mjtDisableBit:

mjtDisableBit
~~~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtDisableBit
   {
       mjDSBL_CONSTRAINT   = 1<<0,     // entire constraint solver
       mjDSBL_EQUALITY     = 1<<1,     // equality constraints
       mjDSBL_FRICTIONLOSS = 1<<2,     // joint and tendon frictionloss constraints
       mjDSBL_LIMIT        = 1<<3,     // joint and tendon limit constraints
       mjDSBL_CONTACT      = 1<<4,     // contact constraints
       mjDSBL_PASSIVE      = 1<<5,     // passive forces
       mjDSBL_GRAVITY      = 1<<6,     // gravitational forces
       mjDSBL_CLAMPCTRL    = 1<<7,     // clamp control to specified range
       mjDSBL_WARMSTART    = 1<<8,     // warmstart constraint solver
       mjDSBL_FILTERPARENT = 1<<9,     // remove collisions with parent body
       mjDSBL_ACTUATION    = 1<<10,    // apply actuation forces
       mjDSBL_REFSAFE      = 1<<11,    // integrator safety: make ref[0]>=2*timestep
       mjDSBL_SENSOR       = 1<<12,    // sensors

       mjNDISABLE          = 13        // number of disable flags
   } mjtDisableBit;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Constants which are powers of 2. They are used as bitmasks for the field ``disableflags`` of :ref:`mjOption`.
  At runtime this field is ``m->opt.disableflags``. The number of these constants is given by ``mjNDISABLE`` which is
  also the length of the global string array :ref:`mjDISABLESTRING` with text descriptions of these
  flags.

.. _mjtEnableBit:

mjtEnableBit
~~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtEnableBit
   {
       mjENBL_OVERRIDE     = 1<<0,     // override contact parameters
       mjENBL_ENERGY       = 1<<1,     // energy computation
       mjENBL_FWDINV       = 1<<2,     // compare forward and inverse dynamics
       mjENBL_SENSORNOISE  = 1<<3,     // add noise to sensor data

                                       // experimental features:
       mjENBL_MULTICCD     = 1<<30,    // multi-point convex collision detection

       mjNENABLE           = 5         // number of enable flags
   } mjtEnableBit;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Constants which are powers of 2. They are used as bitmasks for the field ``enableflags`` of :ref:`mjOption`.
  At runtime this field is ``m->opt.enableflags``. The number of these constants is given by ``mjNENABLE`` which is also
  the length of the global string array :ref:`mjENABLESTRING` with text descriptions of these flags.

.. _mjtJoint:

mjtJoint
~~~~~~~~

.. code-block:: C

   typedef enum _mjtJoint
   {
       mjJNT_FREE          = 0,        // global position and orientation (quat)       (7)
       mjJNT_BALL,                     // orientation (quat) relative to parent        (4)
       mjJNT_SLIDE,                    // sliding distance along body-fixed axis       (1)
       mjJNT_HINGE                     // rotation angle (rad) around body-fixed axis  (1)
   } mjtJoint;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Primitive joint types. These values are used in ``m->jnt_type``. The numbers in the comments indicate how many
  positional coordinates each joint type has. Note that ball joints and rotational components of free joints are
  represented as unit quaternions - which have 4 positional coordinates but 3 degrees of freedom each.

.. _mjtGeom:

mjtGeom
~~~~~~~

.. code-block:: C

   typedef enum _mjtGeom
   {
       // regular geom types
       mjGEOM_PLANE        = 0,        // plane
       mjGEOM_HFIELD,                  // height field
       mjGEOM_SPHERE,                  // sphere
       mjGEOM_CAPSULE,                 // capsule
       mjGEOM_ELLIPSOID,               // ellipsoid
       mjGEOM_CYLINDER,                // cylinder
       mjGEOM_BOX,                     // box
       mjGEOM_MESH,                    // mesh

       mjNGEOMTYPES,                   // number of regular geom types

       // rendering-only geom types: not used in mjModel, not counted in mjNGEOMTYPES
       mjGEOM_ARROW        = 100,      // arrow
       mjGEOM_ARROW1,                  // arrow without wedges
       mjGEOM_ARROW2,                  // arrow in both directions
       mjGEOM_LINE,                    // line
       mjGEOM_SKIN,                    // skin
       mjGEOM_LABEL,                   // text label

       mjGEOM_NONE         = 1001      // missing geom type
   } mjtGeom;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Geometric types supported by MuJoCo. The first group are "official" geom types that can be used in the model. The
  second group are geom types that cannot be used in the model but are used by the visualizer to add decorative
  elements. These values are used in ``m->geom_type`` and ``m->site_type``.

.. _mjtCamLight:

mjtCamLight
~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtCamLight
   {
       mjCAMLIGHT_FIXED    = 0,        // pos and rot fixed in body
       mjCAMLIGHT_TRACK,               // pos tracks body, rot fixed in global
       mjCAMLIGHT_TRACKCOM,            // pos tracks subtree com, rot fixed in body
       mjCAMLIGHT_TARGETBODY,          // pos fixed in body, rot tracks target body
       mjCAMLIGHT_TARGETBODYCOM        // pos fixed in body, rot tracks target subtree com
   } mjtCamLight;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Dynamic modes for cameras and lights, specifying how the camera/light position and orientation are computed. These
  values are used in ``m->cam_mode`` and ``m->light_mode``.

.. _mjtTexture:

mjtTexture
~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtTexture
   {
       mjTEXTURE_2D        = 0,        // 2d texture, suitable for planes and hfields
       mjTEXTURE_CUBE,                 // cube texture, suitable for all other geom types
       mjTEXTURE_SKYBOX                // cube texture used as skybox
   } mjtTexture;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Texture types, specifying how the texture will be mapped. These values are used in ``m->tex_type``.

.. _mjtIntegrator:

mjtIntegrator
~~~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtIntegrator         // integrator mode
   {
       mjINT_EULER         = 0,        // semi-implicit Euler
       mjINT_RK4                       // 4th-order Runge Kutta
       mjINT_IMPLICIT                  // implicit in velocity
   } mjtIntegrator;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Numerical integrator types. These values are used in ``m->opt.integrator``.

.. _mjtCollision:

mjtCollision
~~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtCollision          // collision mode for selecting geom pairs
   {
       mjCOL_ALL           = 0,        // test precomputed and dynamic pairs
       mjCOL_PAIR,                     // test predefined pairs only
       mjCOL_DYNAMIC                   // test dynamic pairs only
   } mjtCollision;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Collision modes specifying how candidate geom pairs are generated for near-phase collision checking. These values are
  used in ``m->opt.collision``.

.. _mjtCone:

mjtCone
~~~~~~~

.. code-block:: C

   typedef enum _mjtCone               // type of friction cone
   {
       mjCONE_PYRAMIDAL     = 0,       // pyramidal
       mjCONE_ELLIPTIC                 // elliptic
   } mjtCone;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Available friction cone types. These values are used in ``m->opt.cone``.

.. _mjtJacobian:

mjtJacobian
~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtJacobian           // type of constraint Jacobian
   {
       mjJAC_DENSE          = 0,       // dense
       mjJAC_SPARSE,                   // sparse
       mjJAC_AUTO                      // dense if nv<=60, sparse otherwise
   } mjtJacobian;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Available Jacobian types. These values are used in ``m->opt.jacobian``.

.. _mjtSolver:

mjtSolver
~~~~~~~~~

.. code-block:: C

   typedef enum _mjtSolver             // constraint solver algorithm
   {
       mjSOL_PGS            = 0,       // PGS    (dual)
       mjSOL_CG,                       // CG     (primal)
       mjSOL_NEWTON                    // Newton (primal)
   } mjtSolver;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Available constraint solver algorithms. These values are used in ``m->opt.solver``.

.. _mjtEq:

mjtEq
~~~~~

.. code-block:: C

   typedef enum _mjtEq
   {
       mjEQ_CONNECT        = 0,        // connect two bodies at a point (ball joint)
       mjEQ_WELD,                      // fix relative position and orientation of two bodies
       mjEQ_JOINT,                     // couple the values of two scalar joints with cubic
       mjEQ_TENDON,                    // couple the lengths of two tendons with cubic
       mjEQ_DISTANCE                   // unsupported, will cause an error if used
   } mjtEq;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Equality constraint types. These values are used in ``m->eq_type``.

.. _mjtWrap:

mjtWrap
~~~~~~~

.. code-block:: C

   typedef enum _mjtWrap
   {
       mjWRAP_NONE         = 0,        // null object
       mjWRAP_JOINT,                   // constant moment arm
       mjWRAP_PULLEY,                  // pulley used to split tendon
       mjWRAP_SITE,                    // pass through site
       mjWRAP_SPHERE,                  // wrap around sphere
       mjWRAP_CYLINDER                 // wrap around (infinite) cylinder
   } mjtWrap;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Tendon wrapping object types. These values are used in ``m->wrap_type``.

.. _mjtTrn:

mjtTrn
~~~~~~

.. code-block:: C

   typedef enum _mjtTrn
   {
       mjTRN_JOINT         = 0,        // force on joint
       mjTRN_JOINTINPARENT,            // force on joint, expressed in parent frame
       mjTRN_SLIDERCRANK,              // force via slider-crank linkage
       mjTRN_TENDON,                   // force on tendon
       mjTRN_SITE,                     // force on site

       mjTRN_UNDEFINED     = 1000      // undefined transmission type
   } mjtTrn;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Actuator transmission types. These values are used in ``m->actuator_trntype``.

.. _mjtDyn:

mjtDyn
~~~~~~

.. code-block:: C

   typedef enum _mjtDyn
   {
       mjDYN_NONE          = 0,        // no internal dynamics; ctrl specifies force
       mjDYN_INTEGRATOR,               // integrator: da/dt = u
       mjDYN_FILTER,                   // linear filter: da/dt = (u-a) / tau
       mjDYN_MUSCLE,                   // piece-wise linear filter with two time constants
       mjDYN_USER                      // user-defined dynamics type
   } mjtDyn;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Actuator dynamics types. These values are used in ``m->actuator_dyntype``.

.. _mjtGain:

mjtGain
~~~~~~~

.. code-block:: C

   typedef enum _mjtGain
   {
       mjGAIN_FIXED        = 0,        // fixed gain
       mjGAIN_AFFINE,                  // const + kp*length + kv*velocity
       mjGAIN_MUSCLE,                  // muscle FLV curve computed by mju_muscleGain()
       mjGAIN_USER                     // user-defined gain type
   } mjtGain;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Actuator gain types. These values are used in ``m->actuator_gaintype``.

.. _mjtBias:

mjtBias
~~~~~~~

.. code-block:: C

   typedef enum _mjtBias
   {
       mjBIAS_NONE         = 0,        // no bias
       mjBIAS_AFFINE,                  // const + kp*length + kv*velocity
       mjBIAS_MUSCLE,                  // muscle passive force computed by mju_muscleBias()
       mjBIAS_USER                     // user-defined bias type
   } mjtBias;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Actuator bias types. These values are used in ``m->actuator_biastype``.

.. _mjtObj:

mjtObj
~~~~~~

.. code-block:: C

   typedef enum _mjtObj
   {
       mjOBJ_UNKNOWN       = 0,        // unknown object type
       mjOBJ_BODY,                     // body
       mjOBJ_XBODY,                    // body, used to access regular frame instead of i-frame
       mjOBJ_JOINT,                    // joint
       mjOBJ_DOF,                      // dof
       mjOBJ_GEOM,                     // geom
       mjOBJ_SITE,                     // site
       mjOBJ_CAMERA,                   // camera
       mjOBJ_LIGHT,                    // light
       mjOBJ_MESH,                     // mesh
       mjOBJ_SKIN,                     // skin
       mjOBJ_HFIELD,                   // heightfield
       mjOBJ_TEXTURE,                  // texture
       mjOBJ_MATERIAL,                 // material for rendering
       mjOBJ_PAIR,                     // geom pair to include
       mjOBJ_EXCLUDE,                  // body pair to exclude
       mjOBJ_EQUALITY,                 // equality constraint
       mjOBJ_TENDON,                   // tendon
       mjOBJ_ACTUATOR,                 // actuator
       mjOBJ_SENSOR,                   // sensor
       mjOBJ_NUMERIC,                  // numeric
       mjOBJ_TEXT,                     // text
       mjOBJ_TUPLE,                    // tuple
       mjOBJ_KEY                       // keyframe
   } mjtObj;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| MuJoCo object types. These values are used in the support functions :ref:`mj_name2id` and
  :ref:`mj_id2name` to convert between object names and integer ids.

.. _mjtConstraint:

mjtConstraint
~~~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtConstraint
   {
       mjCNSTR_EQUALITY    = 0,        // equality constraint
       mjCNSTR_FRICTION_DOF,           // dof friction
       mjCNSTR_FRICTION_TENDON,        // tendon friction
       mjCNSTR_LIMIT_JOINT,            // joint limit
       mjCNSTR_LIMIT_TENDON,           // tendon limit
       mjCNSTR_CONTACT_FRICTIONLESS,   // frictionless contact
       mjCNSTR_CONTACT_PYRAMIDAL,      // frictional contact, pyramidal friction cone
       mjCNSTR_CONTACT_ELLIPTIC        // frictional contact, elliptic friction cone
   } mjtConstraint;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Constraint types. These values are not used in mjModel, but are used in the mjData field ``d->efc_type`` when the list
  of active constraints is constructed at each simulation time step.

.. _mjtConstraintState:

mjtConstraintState
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtConstraintState
   {
       mjCNSTRSTATE_SATISFIED = 0,     // constraint satisfied, zero cost (limit, contact)
       mjCNSTRSTATE_QUADRATIC,         // quadratic cost (equality, friction, limit, contact)
       mjCNSTRSTATE_LINEARNEG,         // linear cost, negative side (friction)
       mjCNSTRSTATE_LINEARPOS,         // linear cost, positive side (friction)
       mjCNSTRSTATE_CONE               // squared distance to cone cost (elliptic contact)
   } mjtConstraintState;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| These values are used by the solver internally to keep track of the constraint states.

.. _mjtSensor:

mjtSensor
~~~~~~~~~

.. code-block:: C

   typedef enum _mjtSensor             // type of sensor
   {
       // common robotic sensors, attached to a site
       mjSENS_TOUCH        = 0,        // scalar contact normal forces summed over sensor zone
       mjSENS_ACCELEROMETER,           // 3D linear acceleration, in local frame
       mjSENS_VELOCIMETER,             // 3D linear velocity, in local frame
       mjSENS_GYRO,                    // 3D angular velocity, in local frame
       mjSENS_FORCE,                   // 3D force between site's body and its parent body
       mjSENS_TORQUE,                  // 3D torque between site's body and its parent body
       mjSENS_MAGNETOMETER,            // 3D magnetometer
       mjSENS_RANGEFINDER,             // scalar distance to nearest geom or site along z-axis

       // sensors related to scalar joints, tendons, actuators
       mjSENS_JOINTPOS,                // scalar joint position (hinge and slide only)
       mjSENS_JOINTVEL,                // scalar joint velocity (hinge and slide only)
       mjSENS_TENDONPOS,               // scalar tendon position
       mjSENS_TENDONVEL,               // scalar tendon velocity
       mjSENS_ACTUATORPOS,             // scalar actuator position
       mjSENS_ACTUATORVEL,             // scalar actuator velocity
       mjSENS_ACTUATORFRC,             // scalar actuator force

       // sensors related to ball joints
       mjSENS_BALLQUAT,                // 4D ball joint quaternion
       mjSENS_BALLANGVEL,              // 3D ball joint angular velocity

       // joint and tendon limit sensors, in constraint space
       mjSENS_JOINTLIMITPOS,           // joint limit distance-margin
       mjSENS_JOINTLIMITVEL,           // joint limit velocity
       mjSENS_JOINTLIMITFRC,           // joint limit force
       mjSENS_TENDONLIMITPOS,          // tendon limit distance-margin
       mjSENS_TENDONLIMITVEL,          // tendon limit velocity
       mjSENS_TENDONLIMITFRC,          // tendon limit force

       // sensors attached to an object with spatial frame: (x)body, geom, site, camera
       mjSENS_FRAMEPOS,                // 3D position
       mjSENS_FRAMEQUAT,               // 4D unit quaternion orientation
       mjSENS_FRAMEXAXIS,              // 3D unit vector: x-axis of object's frame
       mjSENS_FRAMEYAXIS,              // 3D unit vector: y-axis of object's frame
       mjSENS_FRAMEZAXIS,              // 3D unit vector: z-axis of object's frame
       mjSENS_FRAMELINVEL,             // 3D linear velocity
       mjSENS_FRAMEANGVEL,             // 3D angular velocity
       mjSENS_FRAMELINACC,             // 3D linear acceleration
       mjSENS_FRAMEANGACC,             // 3D angular acceleration

       // sensors related to kinematic subtrees; attached to a body (which is the subtree root)
       mjSENS_SUBTREECOM,              // 3D center of mass of subtree
       mjSENS_SUBTREELINVEL,           // 3D linear velocity of subtree
       mjSENS_SUBTREEANGMOM,           // 3D angular momentum of subtree

       // user-defined sensor
       mjSENS_USER                     // sensor data provided by mjcb_sensor callback
   } mjtSensor;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| Sensor types. These values are used in ``m->sensor_type``.

.. _mjtStage:

mjtStage
~~~~~~~~

.. code-block:: C

   typedef enum _mjtStage
   {
       mjSTAGE_NONE        = 0,        // no computations
       mjSTAGE_POS,                    // position-dependent computations
       mjSTAGE_VEL,                    // velocity-dependent computations
       mjSTAGE_ACC                     // acceleration/force-dependent computations
   } mjtStage;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| These are the compute stages for the skipstage parameters of :ref:`mj_forwardSkip` and
  :ref:`mj_inverseSkip`.

.. _mjtDataType:

mjtDataType
~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtDataType           // data type for sensors
   {
       mjDATATYPE_REAL     = 0,        // real values, no constraints
       mjDATATYPE_POSITIVE,            // positive values; 0 or negative: inactive
       mjDATATYPE_AXIS,                // 3D unit vector
       mjDATATYPE_QUATERNION           // unit quaternion
   } mjtDataType;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| These are the possible sensor data types, used in ``mjData.sensor_datatype``.

.. _mjtWarning:

mjtWarning
~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtWarning            // warning types
   {
       mjWARN_INERTIA      = 0,        // (near) singular inertia matrix
       mjWARN_CONTACTFULL,             // too many contacts in contact list
       mjWARN_CNSTRFULL,               // too many constraints
       mjWARN_VGEOMFULL,               // too many visual geoms
       mjWARN_BADQPOS,                 // bad number in qpos
       mjWARN_BADQVEL,                 // bad number in qvel
       mjWARN_BADQACC,                 // bad number in qacc
       mjWARN_BADCTRL,                 // bad number in ctrl

       mjNWARNING                      // number of warnings
   } mjtWarning;

| Defined in `mjdata.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`_

| Warning types. The number of warning types is given by ``mjNWARNING`` which is also the length of the array
  ``mjData.warning``.

.. _mjtTimer:

mjtTimer
~~~~~~~~

.. code-block:: C

   typedef enum _mjtTimer
   {
       // main api
       mjTIMER_STEP        = 0,        // step
       mjTIMER_FORWARD,                // forward
       mjTIMER_INVERSE,                // inverse

       // breakdown of step/forward
       mjTIMER_POSITION,               // fwdPosition
       mjTIMER_VELOCITY,               // fwdVelocity
       mjTIMER_ACTUATION,              // fwdActuation
       mjTIMER_ACCELERATION,           // fwdAcceleration
       mjTIMER_CONSTRAINT,             // fwdConstraint

       // breakdown of fwdPosition
       mjTIMER_POS_KINEMATICS,         // kinematics, com, tendon, transmission
       mjTIMER_POS_INERTIA,            // inertia computations
       mjTIMER_POS_COLLISION,          // collision detection
       mjTIMER_POS_MAKE,               // make constraints
       mjTIMER_POS_PROJECT,            // project constraints

       mjNTIMER                        // number of timers
   } mjtTimer;

| Defined in `mjdata.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`_

| Timer types. The number of timer types is given by ``mjNTIMER`` which is also the length of the array
  ``mjData.timer``, as well as the length of the string array :ref:`mjTIMERSTRING` with timer names.

.. _mjtCatBit:

mjtCatBit
~~~~~~~~~

.. code-block:: C

   typedef enum _mjtCatBit
   {
       mjCAT_STATIC        = 1,        // model elements in body 0
       mjCAT_DYNAMIC       = 2,        // model elements in all other bodies
       mjCAT_DECOR         = 4,        // decorative geoms
       mjCAT_ALL           = 7         // select all categories
   } mjtCatBit;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These are the available categories of geoms in the abstract visualizer. The bitmask can be used in the function
  :ref:`mjr_render` to specify which categories should be rendered.

.. _mjtMouse:

mjtMouse
~~~~~~~~

.. code-block:: C

   typedef enum _mjtMouse
   {
       mjMOUSE_NONE         = 0,       // no action
       mjMOUSE_ROTATE_V,               // rotate, vertical plane
       mjMOUSE_ROTATE_H,               // rotate, horizontal plane
       mjMOUSE_MOVE_V,                 // move, vertical plane
       mjMOUSE_MOVE_H,                 // move, horizontal plane
       mjMOUSE_ZOOM,                   // zoom
       mjMOUSE_SELECT                  // selection
   } mjtMouse;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These are the mouse actions that the abstract visualizer recognizes. It is up to the user to intercept mouse events
  and translate them into these actions, as illustrated in ``simulate.cc``.

.. _mjtPertBit:

mjtPertBit
~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtPertBit
   {
       mjPERT_TRANSLATE    = 1,        // translation
       mjPERT_ROTATE       = 2         // rotation
   } mjtPertBit;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These bitmasks enable the translational and rotational components of the mouse perturbation. For the regular mouse,
  only one can be enabled at a time. For the 3D mouse (SpaceNavigator) both can be enabled simultaneously. They are used
  in ``mjvPerturb.active``.

.. _mjtCamera:

mjtCamera
~~~~~~~~~

.. code-block:: C

   typedef enum _mjtCamera
   {
       mjCAMERA_FREE        = 0,       // free camera
       mjCAMERA_TRACKING,              // tracking camera; uses trackbodyid
       mjCAMERA_FIXED,                 // fixed camera; uses fixedcamid
       mjCAMERA_USER                   // user is responsible for setting OpenGL camera
   } mjtCamera;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These are the possible camera types, used in ``mjvCamera.type``.

.. _mjtLabel:

mjtLabel
~~~~~~~~

.. code-block:: C

   typedef enum _mjtLabel
   {
       mjLABEL_NONE        = 0,        // nothing
       mjLABEL_BODY,                   // body labels
       mjLABEL_JOINT,                  // joint labels
       mjLABEL_GEOM,                   // geom labels
       mjLABEL_SITE,                   // site labels
       mjLABEL_CAMERA,                 // camera labels
       mjLABEL_LIGHT,                  // light labels
       mjLABEL_TENDON,                 // tendon labels
       mjLABEL_ACTUATOR,               // actuator labels
       mjLABEL_CONSTRAINT,             // constraint labels
       mjLABEL_SKIN,                   // skin labels
       mjLABEL_SELECTION,              // selected object
       mjLABEL_SELPNT,                 // coordinates of selection point
       mjLABEL_CONTACTFORCE,           // magnitude of contact force

       mjNLABEL                        // number of label types
   } mjtLabel;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These are the abstract visualization elements that can have text labels. Used in ``mjvOption.label``.

.. _mjtFrame:

mjtFrame
~~~~~~~~

.. code-block:: C

   typedef enum _mjtFrame
   {
       mjFRAME_NONE        = 0,        // no frames
       mjFRAME_BODY,                   // body frames
       mjFRAME_GEOM,                   // geom frames
       mjFRAME_SITE,                   // site frames
       mjFRAME_CAMERA,                 // camera frames
       mjFRAME_LIGHT,                  // light frames
       mjFRAME_WORLD,                  // world frame

       mjNFRAME                        // number of visualization frames
   } mjtFrame;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These are the MuJoCo objects whose spatial frames can be rendered. Used in ``mjvOption.frame``.

.. _mjtVisFlag:

mjtVisFlag
~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtVisFlag
   {
       mjVIS_CONVEXHULL    = 0,        // mesh convex hull
       mjVIS_TEXTURE,                  // textures
       mjVIS_JOINT,                    // joints
       mjVIS_ACTUATOR,                 // actuators
       mjVIS_CAMERA,                   // cameras
       mjVIS_LIGHT,                    // lights
       mjVIS_TENDON,                   // tendons
       mjVIS_RANGEFINDER,              // rangefinder sensors
       mjVIS_CONSTRAINT,               // point constraints
       mjVIS_INERTIA,                  // equivalent inertia boxes
       mjVIS_SCLINERTIA,               // scale equivalent inertia boxes with mass
       mjVIS_PERTFORCE,                // perturbation force
       mjVIS_PERTOBJ,                  // perturbation object
       mjVIS_CONTACTPOINT,             // contact points
       mjVIS_CONTACTFORCE,             // contact force
       mjVIS_CONTACTSPLIT,             // split contact force into normal and tanget
       mjVIS_TRANSPARENT,              // make dynamic geoms more transparent
       mjVIS_AUTOCONNECT,              // auto connect joints and body coms
       mjVIS_COM,                      // center of mass
       mjVIS_SELECT,                   // selection point
       mjVIS_STATIC,                   // static bodies
       mjVIS_SKIN,                     // skin

       mjNVISFLAG                      // number of visualization flags
   } mjtVisFlag;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These are indices in the array ``mjvOption.flags``, whose elements enable/disable the visualization of the
  corresponding model or decoration element.

.. _mjtRndFlag:

mjtRndFlag
~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtRndFlag
   {
       mjRND_SHADOW        = 0,        // shadows
       mjRND_WIREFRAME,                // wireframe
       mjRND_REFLECTION,               // reflections
       mjRND_ADDITIVE,                 // additive transparency
       mjRND_SKYBOX,                   // skybox
       mjRND_FOG,                      // fog
       mjRND_HAZE,                     // haze
       mjRND_SEGMENT,                  // segmentation with random color
       mjRND_IDCOLOR,                  // segmentation with segid+1 color
       mjRND_CULL_FACE,                // cull backward faces

       mjNRNDFLAG                      // number of rendering flags
   } mjtRndFlag;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These are indices in the array ``mjvScene.flags``, whose elements enable/disable OpenGL rendering effects.

.. _mjtStereo:

mjtStereo
~~~~~~~~~

.. code-block:: C

   typedef enum _mjtStereo
   {
       mjSTEREO_NONE       = 0,        // no stereo; use left eye only
       mjSTEREO_QUADBUFFERED,          // quad buffered; revert to side-by-side if no hardware support
       mjSTEREO_SIDEBYSIDE             // side-by-side
   } mjtStereo;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| These are the possible stereo rendering types. They are used in ``mjvScene.stereo``.

.. _mjtGridPos:

mjtGridPos
~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtGridPos
   {
       mjGRID_TOPLEFT      = 0,        // top left
       mjGRID_TOPRIGHT,                // top right
       mjGRID_BOTTOMLEFT,              // bottom left
       mjGRID_BOTTOMRIGHT              // bottom right
   } mjtGridPos;

| Defined in `mjrender.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjrender.h>`_

| These are the possible grid positions for text overlays. They are used as an argument to the function
  :ref:`mjr_overlay`.

.. _mjtFramebuffer:

mjtFramebuffer
~~~~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtFramebuffer
   {
       mjFB_WINDOW         = 0,        // default/window buffer
       mjFB_OFFSCREEN                  // offscreen buffer
   } mjtFramebuffer;

| Defined in `mjrender.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjrender.h>`_

| These are the possible framebuffers. They are used as an argument to the function :ref:`mjr_setBuffer`.

.. _mjtFontScale:

mjtFontScale
~~~~~~~~~~~~

.. code-block:: C

   typedef enum _mjtFontScale
   {
       mjFONTSCALE_50      = 50,       // 50% scale, suitable for low-res rendering
       mjFONTSCALE_100     = 100,      // normal scale, suitable in the absence of DPI scaling
       mjFONTSCALE_150     = 150,      // 150% scale
       mjFONTSCALE_200     = 200,      // 200% scale
       mjFONTSCALE_250     = 250,      // 250% scale
       mjFONTSCALE_300     = 300       // 300% scale
   } mjtFontScale;

| Defined in `mjrender.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjrender.h>`_

| These are the possible font sizes. The fonts are predefined bitmaps stored in the dynamic library at three different
  sizes.

.. _mjtFont:

mjtFont
~~~~~~~

.. code-block:: C

   typedef enum _mjtFont
   {
       mjFONT_NORMAL       = 0,        // normal font
       mjFONT_SHADOW,                  // normal font with shadow (for higher contrast)
       mjFONT_BIG                      // big font (for user alerts)
   } mjtFont;

| Defined in `mjrender.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjrender.h>`_

| These are the possible font types.

.. _mjtButton:

mjtButton
~~~~~~~~~

.. code-block:: C

   typedef enum _mjtButton         // mouse button
   {
       mjBUTTON_NONE = 0,          // no button
       mjBUTTON_LEFT,              // left button
       mjBUTTON_RIGHT,             // right button
       mjBUTTON_MIDDLE             // middle button
   } mjtButton;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| Mouse button IDs used in the UI framework.

.. _mjtEvent:

mjtEvent
~~~~~~~~

.. code-block:: C

   typedef enum _mjtEvent          // mouse and keyboard event type
   {
       mjEVENT_NONE = 0,           // no event
       mjEVENT_MOVE,               // mouse move
       mjEVENT_PRESS,              // mouse button press
       mjEVENT_RELEASE,            // mouse button release
       mjEVENT_SCROLL,             // scroll
       mjEVENT_KEY,                // key press
       mjEVENT_RESIZE              // resize
   } mjtEvent;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| Event types used in the UI framework.

.. _mjtItem:

mjtItem
~~~~~~~

.. code-block:: C

   typedef enum _mjtItem           // UI item type
   {
       mjITEM_END = -2,            // end of definition list (not an item)
       mjITEM_SECTION = -1,        // section (not an item)
       mjITEM_SEPARATOR = 0,       // separator
       mjITEM_STATIC,              // static text
       mjITEM_BUTTON,              // button

       // the rest have data pointer
       mjITEM_CHECKINT,            // check box, int value
       mjITEM_CHECKBYTE,           // check box, mjtByte value
       mjITEM_RADIO,               // radio group
       mjITEM_SELECT,              // selection box
       mjITEM_SLIDERINT,           // slider, int value
       mjITEM_SLIDERNUM,           // slider, mjtNum value
       mjITEM_EDITINT,             // editable array, int values
       mjITEM_EDITNUM,             // editable array, mjtNum values
       mjITEM_EDITTXT,             // editable text

       mjNITEM                     // number of item types
   } mjtItem;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| Item types used in the UI framework.

.. _tyFunction:

Function types
^^^^^^^^^^^^^^

MuJoCo callbacks have corresponding function types. They are defined in `mjdata.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`_ and in
`mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_. The actual callback functions are documented later.

.. _mjfGeneric:

mjfGeneric
~~~~~~~~~~

.. code-block:: C

   typedef void (*mjfGeneric)(const mjModel* m, mjData* d);

This is the function type of the callbacks :ref:`mjcb_passive` and :ref:`mjcb_control`.

.. _mjfConFilt:

mjfConFilt
~~~~~~~~~~

.. code-block:: C

   typedef int (*mjfConFilt)(const mjModel* m, mjData* d, int geom1, int geom2);

This is the function type of the callback :ref:`mjcb_contactfilter`. The return value is 1: discard,
0: proceed with collision check.

.. _mjfSensor:

mjfSensor
~~~~~~~~~

.. code-block:: C

   typedef void (*mjfSensor)(const mjModel* m, mjData* d, int stage);

This is the function type of the callback :ref:`mjcb_sensor`.

.. _mjfTime:

mjfTime
~~~~~~~

.. code-block:: C

   typedef mjtNum (*mjfTime)(void);

This is the function type of the callback :ref:`mjcb_time`.

.. _mjfAct:

mjfAct
~~~~~~

.. code-block:: C

   typedef mjtNum (*mjfAct)(const mjModel* m, const mjData* d, int id);

This is the function type of the callbacks :ref:`mjcb_act_dyn`, :ref:`mjcb_act_gain` and
:ref:`mjcb_act_bias`.

.. _mjfCollision:

mjfCollision
~~~~~~~~~~~~

.. code-block:: C

   typedef int (*mjfCollision)(const mjModel* m, const mjData* d,
                               mjContact* con, int g1, int g2, mjtNum margin);

This is the function type of the callbacks in the collision table :ref:`mjCOLLISIONFUNC`.

.. _mjfItemEnable:

mjfItemEnable
~~~~~~~~~~~~~

.. code-block:: C

   typedef int (*mjfItemEnable)(int category, void* data);

This is the function type of the predicate function used by the UI framework to determine if each item is enabled or
disabled.

.. _tyStructure:

Data structures
^^^^^^^^^^^^^^^

MuJoCo uses several data structures shown below. They are taken directly from the header files which contain comments
for each field.

.. _mjVFS:

mjVFS
~~~~~

.. code-block:: C

   struct _mjVFS                       // virtual file system for loading from memory
   {
       int   nfile;                    // number of files present
       char  filename[mjMAXVFS][mjMAXVFSNAME]; // file name without path
       int   filesize[mjMAXVFS];       // file size in bytes
       void* filedata[mjMAXVFS];       // buffer with file data
   };
   typedef struct _mjVFS mjVFS;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| This is the data structure with the virtual file system. It can only be constructed programmatically, and does not
  have an analog in MJCF.

.. _mjOption:

mjOption
~~~~~~~~

.. code-block:: C

   struct _mjOption                    // physics options
   {
       // timing parameters
       mjtNum timestep;                // timestep
       mjtNum apirate;                 // update rate for remote API (Hz)

       // solver parameters
       mjtNum impratio;                // ratio of friction-to-normal contact impedance
       mjtNum tolerance;               // main solver tolerance
       mjtNum noslip_tolerance;        // noslip solver tolerance
       mjtNum mpr_tolerance;           // MPR solver tolerance

       // physical constants
       mjtNum gravity[3];              // gravitational acceleration
       mjtNum wind[3];                 // wind (for lift, drag and viscosity)
       mjtNum magnetic[3];             // global magnetic flux
       mjtNum density;                 // density of medium
       mjtNum viscosity;               // viscosity of medium

       // override contact solver parameters (if enabled)
       mjtNum o_margin;                // margin
       mjtNum o_solref[mjNREF];        // solref
       mjtNum o_solimp[mjNIMP];        // solimp

       // discrete settings
       int integrator;                 // integration mode (mjtIntegrator)
       int collision;                  // collision mode (mjtCollision)
       int cone;                       // type of friction cone (mjtCone)
       int jacobian;                   // type of Jacobian (mjtJacobian)
       int solver;                     // solver algorithm (mjtSolver)
       int iterations;                 // maximum number of main solver iterations
       int noslip_iterations;          // maximum number of noslip solver iterations
       int mpr_iterations;             // maximum number of MPR solver iterations
       int disableflags;               // bit flags for disabling standard features
       int enableflags;                // bit flags for enabling optional features
   };
   typedef struct _mjOption mjOption;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| This is the data structure with simulation options. It corresponds to the MJCF element
  :ref:`option <option>`. One instance of it is embedded in mjModel.

.. _mjVisual:

mjVisual
~~~~~~~~

.. code-block:: C

   struct _mjVisual                    // visualization options
   {
       struct                          // global parameters
       {
           float fovy;                 // y-field of view for free camera (degrees)
           float ipd;                  // inter-pupilary distance for free camera
           float linewidth;            // line width for wireframe and ray rendering
           float glow;                 // glow coefficient for selected body
           int offwidth;               // width of offscreen buffer
           int offheight;              // height of offscreen buffer
       } global;

       struct                          // rendering quality
       {
           int   shadowsize;           // size of shadowmap texture
           int   offsamples;           // number of multisamples for offscreen rendering
           int   numslices;            // number of slices for builtin geom drawing
           int   numstacks;            // number of stacks for builtin geom drawing
           int   numquads;             // number of quads for box rendering
       } quality;

       struct                          // head light
       {
           float ambient[3];           // ambient rgb (alpha=1)
           float diffuse[3];           // diffuse rgb (alpha=1)
           float specular[3];          // specular rgb (alpha=1)
           int   active;               // is headlight active
       } headlight;

       struct                          // mapping
       {
           float stiffness;            // mouse perturbation stiffness (space->force)
           float stiffnessrot;         // mouse perturbation stiffness (space->torque)
           float force;                // from force units to space units
           float torque;               // from torque units to space units
           float alpha;                // scale geom alphas when transparency is enabled
           float fogstart;             // OpenGL fog starts at fogstart * mjModel.stat.extent
           float fogend;               // OpenGL fog ends at fogend * mjModel.stat.extent
           float znear;                // near clipping plane = znear * mjModel.stat.extent
           float zfar;                 // far clipping plane = zfar * mjModel.stat.extent
           float haze;                 // haze ratio
           float shadowclip;           // directional light: shadowclip * mjModel.stat.extent
           float shadowscale;          // spot light: shadowscale * light.cutoff
           float actuatortendon;       // scale tendon width
       } map;

       struct                          // scale of decor elements relative to mean body size
       {
           float forcewidth;           // width of force arrow
           float contactwidth;         // contact width
           float contactheight;        // contact height
           float connect;              // autoconnect capsule width
           float com;                  // com radius
           float camera;               // camera object
           float light;                // light object
           float selectpoint;          // selection point
           float jointlength;          // joint length
           float jointwidth;           // joint width
           float actuatorlength;       // actuator length
           float actuatorwidth;        // actuator width
           float framelength;          // bodyframe axis length
           float framewidth;           // bodyframe axis width
           float constraint;           // constraint width
           float slidercrank;          // slidercrank width
       } scale;

       struct                          // color of decor elements
       {
           float fog[4];               // fog
           float haze[4];              // haze
           float force[4];             // external force
           float inertia[4];           // inertia box
           float joint[4];             // joint
           float actuator[4];          // actuator, neutral
           float actuatornegative[4];  // actuator, negative limit
           float actuatorpositive[4];  // actuator, positive limit
           float com[4];               // center of mass
           float camera[4];            // camera object
           float light[4];             // light object
           float selectpoint[4];       // selection point
           float connect[4];           // auto connect
           float contactpoint[4];      // contact point
           float contactforce[4];      // contact force
           float contactfriction[4];   // contact friction force
           float contacttorque[4];     // contact torque
           float contactgap[4];        // contact point in gap
           float rangefinder[4];       // rangefinder ray
           float constraint[4];        // constraint
           float slidercrank[4];       // slidercrank
           float crankbroken[4];       // used when crank must be stretched/broken
       } rgba;
   };
   typedef struct _mjVisual mjVisual;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| This is the data structure with abstract visualization options. It corresponds to the MJCF element
  :ref:`visual <visual>`. One instance of it is embedded in mjModel.

.. _mjStatistic:

mjStatistic
~~~~~~~~~~~

.. code-block:: C

   struct _mjStatistic                 // model statistics (in qpos0)
   {
       mjtNum meaninertia;             // mean diagonal inertia
       mjtNum meanmass;                // mean body mass
       mjtNum meansize;                // mean body size
       mjtNum extent;                  // spatial extent
       mjtNum center[3];               // center of model
   };
   typedef struct _mjStatistic mjStatistic;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| This is the data structure with model statistics precomputed by the compiler or set by the user. It corresponds to the
  MJCF element :ref:`statistic <statistic>`. One instance of it is embedded in mjModel.

.. _mjModel:

mjModel
~~~~~~~

.. code-block:: C

   struct _mjModel
   {
       // ------------------------------- sizes

       // sizes needed at mjModel construction
       int nq;                         // number of generalized coordinates = dim(qpos)
       int nv;                         // number of degrees of freedom = dim(qvel)
       int nu;                         // number of actuators/controls = dim(ctrl)
       int na;                         // number of activation states = dim(act)
       int nbody;                      // number of bodies
       int njnt;                       // number of joints
       int ngeom;                      // number of geoms
       int nsite;                      // number of sites
       int ncam;                       // number of cameras
       int nlight;                     // number of lights
       int nmesh;                      // number of meshes
       int nmeshvert;                  // number of vertices in all meshes
       int nmeshtexvert;               // number of vertices with texcoords in all meshes
       int nmeshface;                  // number of triangular faces in all meshes
       int nmeshgraph;                 // number of ints in mesh auxiliary data
       int nskin;                      // number of skins
       int nskinvert;                  // number of vertices in all skins
       int nskintexvert;               // number of vertiex with texcoords in all skins
       int nskinface;                  // number of triangular faces in all skins
       int nskinbone;                  // number of bones in all skins
       int nskinbonevert;              // number of vertices in all skin bones
       int nhfield;                    // number of heightfields
       int nhfielddata;                // number of data points in all heightfields
       int ntex;                       // number of textures
       int ntexdata;                   // number of bytes in texture rgb data
       int nmat;                       // number of materials
       int npair;                      // number of predefined geom pairs
       int nexclude;                   // number of excluded geom pairs
       int neq;                        // number of equality constraints
       int ntendon;                    // number of tendons
       int nwrap;                      // number of wrap objects in all tendon paths
       int nsensor;                    // number of sensors
       int nnumeric;                   // number of numeric custom fields
       int nnumericdata;               // number of mjtNums in all numeric fields
       int ntext;                      // number of text custom fields
       int ntextdata;                  // number of mjtBytes in all text fields
       int ntuple;                     // number of tuple custom fields
       int ntupledata;                 // number of objects in all tuple fields
       int nkey;                       // number of keyframes
       int nmocap;                     // number of mocap bodies
       int nuser_body;                 // number of mjtNums in body_user
       int nuser_jnt;                  // number of mjtNums in jnt_user
       int nuser_geom;                 // number of mjtNums in geom_user
       int nuser_site;                 // number of mjtNums in site_user
       int nuser_cam;                  // number of mjtNums in cam_user
       int nuser_tendon;               // number of mjtNums in tendon_user
       int nuser_actuator;             // number of mjtNums in actuator_user
       int nuser_sensor;               // number of mjtNums in sensor_user
       int nnames;                     // number of chars in all names

       // sizes set after mjModel construction (only affect mjData)
       int nM;                         // number of non-zeros in sparse inertia matrix
       int nemax;                      // number of potential equality-constraint rows
       int njmax;                      // number of available rows in constraint Jacobian
       int nconmax;                    // number of potential contacts in contact list
       int nstack;                     // number of fields in mjData stack
       int nuserdata;                  // number of extra fields in mjData
       int nsensordata;                // number of fields in sensor data vector

       int nbuffer;                    // number of bytes in buffer

       // ------------------------------- options and statistics

       mjOption opt;                   // physics options
       mjVisual vis;                   // visualization options
       mjStatistic stat;               // model statistics

       // ------------------------------- buffers

       // main buffer
       void*     buffer;               // main buffer; all pointers point in it    (nbuffer)

       // default generalized coordinates
       mjtNum*   qpos0;                // qpos values at default pose              (nq x 1)
       mjtNum*   qpos_spring;          // reference pose for springs               (nq x 1)

       // bodies
       int*      body_parentid;        // id of body's parent                      (nbody x 1)
       int*      body_rootid;          // id of root above body                    (nbody x 1)
       int*      body_weldid;          // id of body that this body is welded to   (nbody x 1)
       int*      body_mocapid;         // id of mocap data; -1: none               (nbody x 1)
       int*      body_jntnum;          // number of joints for this body           (nbody x 1)
       int*      body_jntadr;          // start addr of joints; -1: no joints      (nbody x 1)
       int*      body_dofnum;          // number of motion degrees of freedom      (nbody x 1)
       int*      body_dofadr;          // start addr of dofs; -1: no dofs          (nbody x 1)
       int*      body_geomnum;         // number of geoms                          (nbody x 1)
       int*      body_geomadr;         // start addr of geoms; -1: no geoms        (nbody x 1)
       mjtByte*  body_simple;          // body is simple (has diagonal M)          (nbody x 1)
       mjtByte*  body_sameframe;       // inertial frame is same as body frame     (nbody x 1)
       mjtNum*   body_pos;             // position offset rel. to parent body      (nbody x 3)
       mjtNum*   body_quat;            // orientation offset rel. to parent body   (nbody x 4)
       mjtNum*   body_ipos;            // local position of center of mass         (nbody x 3)
       mjtNum*   body_iquat;           // local orientation of inertia ellipsoid   (nbody x 4)
       mjtNum*   body_mass;            // mass                                     (nbody x 1)
       mjtNum*   body_subtreemass;     // mass of subtree starting at this body    (nbody x 1)
       mjtNum*   body_inertia;         // diagonal inertia in ipos/iquat frame     (nbody x 3)
       mjtNum*   body_invweight0;      // mean inv inert in qpos0 (trn, rot)       (nbody x 2)
       mjtNum*   body_user;            // user data                                (nbody x nuser_body)

       // joints
       int*      jnt_type;             // type of joint (mjtJoint)                 (njnt x 1)
       int*      jnt_qposadr;          // start addr in 'qpos' for joint's data    (njnt x 1)
       int*      jnt_dofadr;           // start addr in 'qvel' for joint's data    (njnt x 1)
       int*      jnt_bodyid;           // id of joint's body                       (njnt x 1)
       int*      jnt_group;            // group for visibility                     (njnt x 1)
       mjtByte*  jnt_limited;          // does joint have limits                   (njnt x 1)
       mjtNum*   jnt_solref;           // constraint solver reference: limit       (njnt x mjNREF)
       mjtNum*   jnt_solimp;           // constraint solver impedance: limit       (njnt x mjNIMP)
       mjtNum*   jnt_pos;              // local anchor position                    (njnt x 3)
       mjtNum*   jnt_axis;             // local joint axis                         (njnt x 3)
       mjtNum*   jnt_stiffness;        // stiffness coefficient                    (njnt x 1)
       mjtNum*   jnt_range;            // joint limits                             (njnt x 2)
       mjtNum*   jnt_margin;           // min distance for limit detection         (njnt x 1)
       mjtNum*   jnt_user;             // user data                                (njnt x nuser_jnt)

       // dofs
       int*      dof_bodyid;           // id of dof's body                         (nv x 1)
       int*      dof_jntid;            // id of dof's joint                        (nv x 1)
       int*      dof_parentid;         // id of dof's parent; -1: none             (nv x 1)
       int*      dof_Madr;             // dof address in M-diagonal                (nv x 1)
       int*      dof_simplenum;        // number of consecutive simple dofs        (nv x 1)
       mjtNum*   dof_solref;           // constraint solver reference:frictionloss (nv x mjNREF)
       mjtNum*   dof_solimp;           // constraint solver impedance:frictionloss (nv x mjNIMP)
       mjtNum*   dof_frictionloss;     // dof friction loss                        (nv x 1)
       mjtNum*   dof_armature;         // dof armature inertia/mass                (nv x 1)
       mjtNum*   dof_damping;          // damping coefficient                      (nv x 1)
       mjtNum*   dof_invweight0;       // diag. inverse inertia in qpos0           (nv x 1)
       mjtNum*   dof_M0;               // diag. inertia in qpos0                   (nv x 1)

       // geoms
       int*      geom_type;            // geometric type (mjtGeom)                 (ngeom x 1)
       int*      geom_contype;         // geom contact type                        (ngeom x 1)
       int*      geom_conaffinity;     // geom contact affinity                    (ngeom x 1)
       int*      geom_condim;          // contact dimensionality (1, 3, 4, 6)      (ngeom x 1)
       int*      geom_bodyid;          // id of geom's body                        (ngeom x 1)
       int*      geom_dataid;          // id of geom's mesh/hfield (-1: none)      (ngeom x 1)
       int*      geom_matid;           // material id for rendering                (ngeom x 1)
       int*      geom_group;           // group for visibility                     (ngeom x 1)
       int*      geom_priority;        // geom contact priority                    (ngeom x 1)
       mjtByte*  geom_sameframe;       // same as body frame (1) or iframe (2)     (ngeom x 1)
       mjtNum*   geom_solmix;          // mixing coef for solref/imp in geom pair  (ngeom x 1)
       mjtNum*   geom_solref;          // constraint solver reference: contact     (ngeom x mjNREF)
       mjtNum*   geom_solimp;          // constraint solver impedance: contact     (ngeom x mjNIMP)
       mjtNum*   geom_size;            // geom-specific size parameters            (ngeom x 3)
       mjtNum*   geom_rbound;          // radius of bounding sphere                (ngeom x 1)
       mjtNum*   geom_pos;             // local position offset rel. to body       (ngeom x 3)
       mjtNum*   geom_quat;            // local orientation offset rel. to body    (ngeom x 4)
       mjtNum*   geom_friction;        // friction for (slide, spin, roll)         (ngeom x 3)
       mjtNum*   geom_margin;          // detect contact if dist<margin            (ngeom x 1)
       mjtNum*   geom_gap;             // include in solver if dist<margin-gap     (ngeom x 1)
       mjtNum*   geom_fluid;           // fluid interaction parameters             (ngeom x mjNFLUID)
       mjtNum*   geom_user;            // user data                                (ngeom x nuser_geom)
       float*    geom_rgba;            // rgba when material is omitted            (ngeom x 4)

       // sites
       int*      site_type;            // geom type for rendering (mjtGeom)        (nsite x 1)
       int*      site_bodyid;          // id of site's body                        (nsite x 1)
       int*      site_matid;           // material id for rendering                (nsite x 1)
       int*      site_group;           // group for visibility                     (nsite x 1)
       mjtByte*  site_sameframe;       // same as body frame (1) or iframe (2)     (nsite x 1)
       mjtNum*   site_size;            // geom size for rendering                  (nsite x 3)
       mjtNum*   site_pos;             // local position offset rel. to body       (nsite x 3)
       mjtNum*   site_quat;            // local orientation offset rel. to body    (nsite x 4)
       mjtNum*   site_user;            // user data                                (nsite x nuser_site)
       float*    site_rgba;            // rgba when material is omitted            (nsite x 4)

       // cameras
       int*      cam_mode;             // camera tracking mode (mjtCamLight)       (ncam x 1)
       int*      cam_bodyid;           // id of camera's body                      (ncam x 1)
       int*      cam_targetbodyid;     // id of targeted body; -1: none            (ncam x 1)
       mjtNum*   cam_pos;              // position rel. to body frame              (ncam x 3)
       mjtNum*   cam_quat;             // orientation rel. to body frame           (ncam x 4)
       mjtNum*   cam_poscom0;          // global position rel. to sub-com in qpos0 (ncam x 3)
       mjtNum*   cam_pos0;             // global position rel. to body in qpos0    (ncam x 3)
       mjtNum*   cam_mat0;             // global orientation in qpos0              (ncam x 9)
       mjtNum*   cam_fovy;             // y-field of view (deg)                    (ncam x 1)
       mjtNum*   cam_ipd;              // inter-pupilary distance                  (ncam x 1)
       mjtNum*   cam_user;             // user data                                (ncam x nuser_cam)

       // lights
       int*      light_mode;           // light tracking mode (mjtCamLight)        (nlight x 1)
       int*      light_bodyid;         // id of light's body                       (nlight x 1)
       int*      light_targetbodyid;   // id of targeted body; -1: none            (nlight x 1)
       mjtByte*  light_directional;    // directional light                        (nlight x 1)
       mjtByte*  light_castshadow;     // does light cast shadows                  (nlight x 1)
       mjtByte*  light_active;         // is light on                              (nlight x 1)
       mjtNum*   light_pos;            // position rel. to body frame              (nlight x 3)
       mjtNum*   light_dir;            // direction rel. to body frame             (nlight x 3)
       mjtNum*   light_poscom0;        // global position rel. to sub-com in qpos0 (nlight x 3)
       mjtNum*   light_pos0;           // global position rel. to body in qpos0    (nlight x 3)
       mjtNum*   light_dir0;           // global direction in qpos0                (nlight x 3)
       float*    light_attenuation;    // OpenGL attenuation (quadratic model)     (nlight x 3)
       float*    light_cutoff;         // OpenGL cutoff                            (nlight x 1)
       float*    light_exponent;       // OpenGL exponent                          (nlight x 1)
       float*    light_ambient;        // ambient rgb (alpha=1)                    (nlight x 3)
       float*    light_diffuse;        // diffuse rgb (alpha=1)                    (nlight x 3)
       float*    light_specular;       // specular rgb (alpha=1)                   (nlight x 3)

       // meshes
       int*      mesh_vertadr;         // first vertex address                     (nmesh x 1)
       int*      mesh_vertnum;         // number of vertices                       (nmesh x 1)
       int*      mesh_texcoordadr;     // texcoord data address; -1: no texcoord   (nmesh x 1)
       int*      mesh_faceadr;         // first face address                       (nmesh x 1)
       int*      mesh_facenum;         // number of faces                          (nmesh x 1)
       int*      mesh_graphadr;        // graph data address; -1: no graph         (nmesh x 1)
       float*    mesh_vert;            // vertex positions for all meshes          (nmeshvert x 3)
       float*    mesh_normal;          // vertex normals for all meshes            (nmeshvert x 3)
       float*    mesh_texcoord;        // vertex texcoords for all meshes          (nmeshtexvert x 2)
       int*      mesh_face;            // triangle face data                       (nmeshface x 3)
       int*      mesh_graph;           // convex graph data                        (nmeshgraph x 1)

       // skins
       int*      skin_matid;           // skin material id; -1: none               (nskin x 1)
       float*    skin_rgba;            // skin rgba                                (nskin x 4)
       float*    skin_inflate;         // inflate skin in normal direction         (nskin x 1)
       int*      skin_vertadr;         // first vertex address                     (nskin x 1)
       int*      skin_vertnum;         // number of vertices                       (nskin x 1)
       int*      skin_texcoordadr;     // texcoord data address; -1: no texcoord   (nskin x 1)
       int*      skin_faceadr;         // first face address                       (nskin x 1)
       int*      skin_facenum;         // number of faces                          (nskin x 1)
       int*      skin_boneadr;         // first bone in skin                       (nskin x 1)
       int*      skin_bonenum;         // number of bones in skin                  (nskin x 1)
       float*    skin_vert;            // vertex positions for all skin meshes     (nskinvert x 3)
       float*    skin_texcoord;        // vertex texcoords for all skin meshes     (nskintexvert x 2)
       int*      skin_face;            // triangle faces for all skin meshes       (nskinface x 3)
       int*      skin_bonevertadr;     // first vertex in each bone                (nskinbone x 1)
       int*      skin_bonevertnum;     // number of vertices in each bone          (nskinbone x 1)
       float*    skin_bonebindpos;     // bind pos of each bone                    (nskinbone x 3)
       float*    skin_bonebindquat;    // bind quat of each bone                   (nskinbone x 4)
       int*      skin_bonebodyid;      // body id of each bone                     (nskinbone x 1)
       int*      skin_bonevertid;      // mesh ids of vertices in each bone        (nskinbonevert x 1)
       float*    skin_bonevertweight;  // weights of vertices in each bone         (nskinbonevert x 1)

       // height fields
       mjtNum*   hfield_size;          // (x, y, z_top, z_bottom)                  (nhfield x 4)
       int*      hfield_nrow;          // number of rows in grid                   (nhfield x 1)
       int*      hfield_ncol;          // number of columns in grid                (nhfield x 1)
       int*      hfield_adr;           // address in hfield_data                   (nhfield x 1)
       float*    hfield_data;          // elevation data                           (nhfielddata x 1)

       // textures
       int*      tex_type;             // texture type (mjtTexture)                (ntex x 1)
       int*      tex_height;           // number of rows in texture image          (ntex x 1)
       int*      tex_width;            // number of columns in texture image       (ntex x 1)
       int*      tex_adr;              // address in rgb                           (ntex x 1)
       mjtByte*  tex_rgb;              // rgb (alpha = 1)                          (ntexdata x 1)

       // materials
       int*      mat_texid;            // texture id; -1: none                     (nmat x 1)
       mjtByte*  mat_texuniform;       // make texture cube uniform                (nmat x 1)
       float*    mat_texrepeat;        // texture repetition for 2d mapping        (nmat x 2)
       float*    mat_emission;         // emission (x rgb)                         (nmat x 1)
       float*    mat_specular;         // specular (x white)                       (nmat x 1)
       float*    mat_shininess;        // shininess coef                           (nmat x 1)
       float*    mat_reflectance;      // reflectance (0: disable)                 (nmat x 1)
       float*    mat_rgba;             // rgba                                     (nmat x 4)

       // predefined geom pairs for collision detection; has precedence over exclude
       int*      pair_dim;             // contact dimensionality                   (npair x 1)
       int*      pair_geom1;           // id of geom1                              (npair x 1)
       int*      pair_geom2;           // id of geom2                              (npair x 1)
       int*      pair_signature;       // (body1+1)<<16 + body2+1                  (npair x 1)
       mjtNum*   pair_solref;          // constraint solver reference: contact     (npair x mjNREF)
       mjtNum*   pair_solimp;          // constraint solver impedance: contact     (npair x mjNIMP)
       mjtNum*   pair_margin;          // detect contact if dist<margin            (npair x 1)
       mjtNum*   pair_gap;             // include in solver if dist<margin-gap     (npair x 1)
       mjtNum*   pair_friction;        // tangent1, 2, spin, roll1, 2              (npair x 5)

       // excluded body pairs for collision detection
       int*      exclude_signature;    // (body1+1)<<16 + body2+1                  (nexclude x 1)

       // equality constraints
       int*      eq_type;              // constraint type (mjtEq)                  (neq x 1)
       int*      eq_obj1id;            // id of object 1                           (neq x 1)
       int*      eq_obj2id;            // id of object 2                           (neq x 1)
       mjtByte*  eq_active;            // enable/disable constraint                (neq x 1)
       mjtNum*   eq_solref;            // constraint solver reference              (neq x mjNREF)
       mjtNum*   eq_solimp;            // constraint solver impedance              (neq x mjNIMP)
       mjtNum*   eq_data;              // numeric data for constraint              (neq x mjNEQDATA)

       // tendons
       int*      tendon_adr;           // address of first object in tendon's path (ntendon x 1)
       int*      tendon_num;           // number of objects in tendon's path       (ntendon x 1)
       int*      tendon_matid;         // material id for rendering                (ntendon x 1)
       int*      tendon_group;         // group for visibility                     (ntendon x 1)
       mjtByte*  tendon_limited;       // does tendon have length limits           (ntendon x 1)
       mjtNum*   tendon_width;         // width for rendering                      (ntendon x 1)
       mjtNum*   tendon_solref_lim;    // constraint solver reference: limit       (ntendon x mjNREF)
       mjtNum*   tendon_solimp_lim;    // constraint solver impedance: limit       (ntendon x mjNIMP)
       mjtNum*   tendon_solref_fri;    // constraint solver reference: friction    (ntendon x mjNREF)
       mjtNum*   tendon_solimp_fri;    // constraint solver impedance: friction    (ntendon x mjNIMP)
       mjtNum*   tendon_range;         // tendon length limits                     (ntendon x 2)
       mjtNum*   tendon_margin;        // min distance for limit detection         (ntendon x 1)
       mjtNum*   tendon_stiffness;     // stiffness coefficient                    (ntendon x 1)
       mjtNum*   tendon_damping;       // damping coefficient                      (ntendon x 1)
       mjtNum*   tendon_frictionloss;  // loss due to friction                     (ntendon x 1)
       mjtNum*   tendon_lengthspring;  // tendon length in qpos_spring             (ntendon x 1)
       mjtNum*   tendon_length0;       // tendon length in qpos0                   (ntendon x 1)
       mjtNum*   tendon_invweight0;    // inv. weight in qpos0                     (ntendon x 1)
       mjtNum*   tendon_user;          // user data                                (ntendon x nuser_tendon)
       float*    tendon_rgba;          // rgba when material is omitted            (ntendon x 4)

       // list of all wrap objects in tendon paths
       int*      wrap_type;            // wrap object type (mjtWrap)               (nwrap x 1)
       int*      wrap_objid;           // object id: geom, site, joint             (nwrap x 1)
       mjtNum*   wrap_prm;             // divisor, joint coef, or site id          (nwrap x 1)

       // actuators
       int*      actuator_trntype;     // transmission type (mjtTrn)               (nu x 1)
       int*      actuator_dyntype;     // dynamics type (mjtDyn)                   (nu x 1)
       int*      actuator_gaintype;    // gain type (mjtGain)                      (nu x 1)
       int*      actuator_biastype;    // bias type (mjtBias)                      (nu x 1)
       int*      actuator_trnid;       // transmission id: joint, tendon, site     (nu x 2)
       int*      actuator_group;       // group for visibility                     (nu x 1)
       mjtByte*  actuator_ctrllimited; // is control limited                       (nu x 1)
       mjtByte*  actuator_forcelimited;// is force limited                         (nu x 1)
       mjtNum*   actuator_dynprm;      // dynamics parameters                      (nu x mjNDYN)
       mjtNum*   actuator_gainprm;     // gain parameters                          (nu x mjNGAIN)
       mjtNum*   actuator_biasprm;     // bias parameters                          (nu x mjNBIAS)
       mjtNum*   actuator_ctrlrange;   // range of controls                        (nu x 2)
       mjtNum*   actuator_forcerange;  // range of forces                          (nu x 2)
       mjtNum*   actuator_gear;        // scale length and transmitted force       (nu x 6)
       mjtNum*   actuator_cranklength; // crank length for slider-crank            (nu x 1)
       mjtNum*   actuator_acc0;        // acceleration from unit force in qpos0    (nu x 1)
       mjtNum*   actuator_length0;     // actuator length in qpos0                 (nu x 1)
       mjtNum*   actuator_lengthrange; // feasible actuator length range           (nu x 2)
       mjtNum*   actuator_user;        // user data                                (nu x nuser_actuator)

       // sensors
       int*      sensor_type;          // sensor type (mjtSensor)                  (nsensor x 1)
       int*      sensor_datatype;      // numeric data type (mjtDataType)          (nsensor x 1)
       int*      sensor_needstage;     // required compute stage (mjtStage)        (nsensor x 1)
       int*      sensor_objtype;       // type of sensorized object (mjtObj)       (nsensor x 1)
       int*      sensor_objid;         // id of sensorized object                  (nsensor x 1)
       int*      sensor_reftype;       // type of reference frame (mjtObj)         (nsensor x 1)
       int*      sensor_refid;         // id of reference frame; -1: global frame  (nsensor x 1)
       int*      sensor_dim;           // number of scalar outputs                 (nsensor x 1)
       int*      sensor_adr;           // address in sensor array                  (nsensor x 1)
       mjtNum*   sensor_cutoff;        // cutoff for real and positive; 0: ignore  (nsensor x 1)
       mjtNum*   sensor_noise;         // noise standard deviation                 (nsensor x 1)
       mjtNum*   sensor_user;          // user data                                (nsensor x nuser_sensor)

       // custom numeric fields
       int*      numeric_adr;          // address of field in numeric_data         (nnumeric x 1)
       int*      numeric_size;         // size of numeric field                    (nnumeric x 1)
       mjtNum*   numeric_data;         // array of all numeric fields              (nnumericdata x 1)

       // custom text fields
       int*      text_adr;             // address of text in text_data             (ntext x 1)
       int*      text_size;            // size of text field (strlen+1)            (ntext x 1)
       char*     text_data;            // array of all text fields (0-terminated)  (ntextdata x 1)

       // custom tuple fields
       int*      tuple_adr;            // address of text in text_data             (ntuple x 1)
       int*      tuple_size;           // number of objects in tuple               (ntuple x 1)
       int*      tuple_objtype;        // array of object types in all tuples      (ntupledata x 1)
       int*      tuple_objid;          // array of object ids in all tuples        (ntupledata x 1)
       mjtNum*   tuple_objprm;         // array of object params in all tuples     (ntupledata x 1)

       // keyframes
       mjtNum*   key_time;             // key time                                 (nkey x 1)
       mjtNum*   key_qpos;             // key position                             (nkey x nq)
       mjtNum*   key_qvel;             // key velocity                             (nkey x nv)
       mjtNum*   key_act;              // key activation                           (nkey x na)
       mjtNum*   key_mpos;             // key mocap position                       (nkey x 3*nmocap)
       mjtNum*   key_mquat;            // key mocap quaternion                     (nkey x 4*nmocap)
       mjtNum*   key_ctrl;             // key control                              (nkey x nu)

       // names
       int*      name_bodyadr;         // body name pointers                       (nbody x 1)
       int*      name_jntadr;          // joint name pointers                      (njnt x 1)
       int*      name_geomadr;         // geom name pointers                       (ngeom x 1)
       int*      name_siteadr;         // site name pointers                       (nsite x 1)
       int*      name_camadr;          // camera name pointers                     (ncam x 1)
       int*      name_lightadr;        // light name pointers                      (nlight x 1)
       int*      name_meshadr;         // mesh name pointers                       (nmesh x 1)
       int*      name_skinadr;         // skin name pointers                       (nskin x 1)
       int*      name_hfieldadr;       // hfield name pointers                     (nhfield x 1)
       int*      name_texadr;          // texture name pointers                    (ntex x 1)
       int*      name_matadr;          // material name pointers                   (nmat x 1)
       int*      name_pairadr;         // geom pair name pointers                  (npair x 1)
       int*      name_excludeadr;      // exclude name pointers                    (nexclude x 1)
       int*      name_eqadr;           // equality constraint name pointers        (neq x 1)
       int*      name_tendonadr;       // tendon name pointers                     (ntendon x 1)
       int*      name_actuatoradr;     // actuator name pointers                   (nu x 1)
       int*      name_sensoradr;       // sensor name pointers                     (nsensor x 1)
       int*      name_numericadr;      // numeric name pointers                    (nnumeric x 1)
       int*      name_textadr;         // text name pointers                       (ntext x 1)
       int*      name_tupleadr;        // tuple name pointers                      (ntuple x 1)
       int*      name_keyadr;          // keyframe name pointers                   (nkey x 1)
       char*     names;                // names of all objects, 0-terminated       (nnames x 1)
   };
   typedef struct _mjModel mjModel;

| Defined in `mjmodel.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjmodel.h>`_

| This is the main data structure holding the MuJoCo model. It is treated as constant by the simulator.

.. _mjContact:

mjContact
~~~~~~~~~

.. code-block:: C

   struct _mjContact                   // result of collision detection functions
   {
       // contact parameters set by geom-specific collision detector
       mjtNum dist;                    // distance between nearest points; neg: penetration
       mjtNum pos[3];                  // position of contact point: midpoint between geoms
       mjtNum frame[9];                // normal is in [0-2]

       // contact parameters set by mj_collideGeoms
       mjtNum includemargin;           // include if dist<includemargin=margin-gap
       mjtNum friction[5];             // tangent1, 2, spin, roll1, 2
       mjtNum solref[mjNREF];          // constraint solver reference
       mjtNum solimp[mjNIMP];          // constraint solver impedance

       // internal storage used by solver
       mjtNum mu;                      // friction of regularized cone, set by mj_makeR
       mjtNum H[36];                   // cone Hessian, set by mj_updateConstraint

       // contact descriptors set by mj_collideGeoms
       int dim;                        // contact space dimensionality: 1, 3, 4 or 6
       int geom1;                      // id of geom 1
       int geom2;                      // id of geom 2

       // flag set by mj_fuseContact or mj_instantianteEquality
       int exclude;                    // 0: include, 1: in gap, 2: fused, 3: equality

       // address computed by mj_instantiateContact
       int efc_address;                // address in efc; -1: not included, -2-i: distance constraint i
   };
   typedef struct _mjContact mjContact;

| Defined in `mjdata.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`_

| This is the data structure holding information about one contact. ``mjData.contact`` is a preallocated array of
  mjContact data structures, populated at runtime with the contacts found by the collision detector. Additional contact
  information is then filled-in by the simulator.

.. _mjWarningStat:

mjWarningStat
~~~~~~~~~~~~~

.. code-block:: C

   struct _mjWarningStat               // warning statistics
   {
       int lastinfo;                   // info from last warning
       int number;                     // how many times was warning raised
   };
   typedef struct _mjWarningStat mjWarningStat;

| Defined in `mjdata.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`_

| This is the data structure holding information about one warning type. ``mjData.warning`` is a preallocated array of
  mjWarningStat data structures, one for each warning type.

.. _mjTimerStat:

mjTimerStat
~~~~~~~~~~~

.. code-block:: C

   struct _mjTimerStat                 // timer statistics
   {
       mjtNum duration;                // cumulative duration
       int number;                     // how many times was timer called
   };
   typedef struct _mjTimerStat mjTimerStat;

| Defined in `mjdata.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`_

| This is the data structure holding information about one timer. ``mjData.timer`` is a preallocated array of
  mjTimerStat data structures, one for each timer type.

.. _mjSolverStat:

mjSolverStat
~~~~~~~~~~~~

.. code-block:: C

   struct _mjSolverStat                // per-iteration solver statistics
   {
       mjtNum improvement;             // cost reduction, scaled by 1/trace(M(qpos0))
       mjtNum gradient;                // gradient norm (primal only, scaled)
       mjtNum lineslope;               // slope in linesearch
       int nactive;                    // number of active constraints
       int nchange;                    // number of constraint state changes
       int neval;                      // number of cost evaluations in line search
       int nupdate;                    // number of Cholesky updates in line search
   };
   typedef struct _mjSolverStat mjSolverStat;

| Defined in `mjdata.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`_

| This is the data structure holding information about one solver iteration. ``mjData.solver`` is a preallocated array
  of mjSolverStat data structures, one for each iteration of the solver, up to a maximum of mjNSOLVER. The actual number
  of solver iterations is given by ``mjData.solver_iter``.

.. _mjData:

mjData
~~~~~~

.. code-block:: C

   struct _mjData
   {
       // constant sizes
       int nstack;                     // number of mjtNums that can fit in stack
       int nbuffer;                    // size of main buffer in bytes

       // stack pointer
       int pstack;                     // first available mjtNum address in stack

       // memory utilization stats
       int maxuse_stack;               // maximum stack allocation
       int maxuse_con;                 // maximum number of contacts
       int maxuse_efc;                 // maximum number of scalar constraints

       // diagnostics
       mjWarningStat warning[mjNWARNING]; // warning statistics
       mjTimerStat timer[mjNTIMER];       // timer statistics
       mjSolverStat solver[mjNSOLVER];    // solver statistics per iteration
       int solver_iter;                // number of solver iterations
       int solver_nnz;                 // number of non-zeros in Hessian or efc_AR
       mjtNum solver_fwdinv[2];        // forward-inverse comparison: qfrc, efc

       // variable sizes
       int ne;                         // number of equality constraints
       int nf;                         // number of friction constraints
       int nefc;                       // number of constraints
       int ncon;                       // number of detected contacts

       // global properties
       mjtNum time;                    // simulation time
       mjtNum energy[2];               // potential, kinetic energy

       //-------------------------------- end of info header

       // buffers
       void*     buffer;               // main buffer; all pointers point in it    (nbuffer bytes)
       mjtNum*   stack;                // stack buffer                             (nstack mjtNums)

       //-------------------------------- main inputs and outputs of the computation

       // state
       mjtNum*   qpos;                 // position                                 (nq x 1)
       mjtNum*   qvel;                 // velocity                                 (nv x 1)
       mjtNum*   act;                  // actuator activation                      (na x 1)
       mjtNum*   qacc_warmstart;       // acceleration used for warmstart          (nv x 1)

       // control
       mjtNum*   ctrl;                 // control                                  (nu x 1)
       mjtNum*   qfrc_applied;         // applied generalized force                (nv x 1)
       mjtNum*   xfrc_applied;         // applied Cartesian force/torque           (nbody x 6)

       // mocap data
       mjtNum*  mocap_pos;             // positions of mocap bodies                (nmocap x 3)
       mjtNum*  mocap_quat;            // orientations of mocap bodies             (nmocap x 4)

       // dynamics
       mjtNum*   qacc;                 // acceleration                             (nv x 1)
       mjtNum*   act_dot;              // time-derivative of actuator activation   (na x 1)

       // user data
       mjtNum*   userdata;              // user data, not touched by engine        (nuserdata x 1)

       // sensors
       mjtNum*   sensordata;            // sensor data array                       (nsensordata x 1)

       //-------------------------------- POSITION dependent

       // computed by mj_fwdPosition/mj_kinematics
       mjtNum*   xpos;                 // Cartesian position of body frame         (nbody x 3)
       mjtNum*   xquat;                // Cartesian orientation of body frame      (nbody x 4)
       mjtNum*   xmat;                 // Cartesian orientation of body frame      (nbody x 9)
       mjtNum*   xipos;                // Cartesian position of body com           (nbody x 3)
       mjtNum*   ximat;                // Cartesian orientation of body inertia    (nbody x 9)
       mjtNum*   xanchor;              // Cartesian position of joint anchor       (njnt x 3)
       mjtNum*   xaxis;                // Cartesian joint axis                     (njnt x 3)
       mjtNum*   geom_xpos;            // Cartesian geom position                  (ngeom x 3)
       mjtNum*   geom_xmat;            // Cartesian geom orientation               (ngeom x 9)
       mjtNum*   site_xpos;            // Cartesian site position                  (nsite x 3)
       mjtNum*   site_xmat;            // Cartesian site orientation               (nsite x 9)
       mjtNum*   cam_xpos;             // Cartesian camera position                (ncam x 3)
       mjtNum*   cam_xmat;             // Cartesian camera orientation             (ncam x 9)
       mjtNum*   light_xpos;           // Cartesian light position                 (nlight x 3)
       mjtNum*   light_xdir;           // Cartesian light direction                (nlight x 3)

       // computed by mj_fwdPosition/mj_comPos
       mjtNum*   subtree_com;          // center of mass of each subtree           (nbody x 3)
       mjtNum*   cdof;                 // com-based motion axis of each dof        (nv x 6)
       mjtNum*   cinert;               // com-based body inertia and mass          (nbody x 10)

       // computed by mj_fwdPosition/mj_tendon
       int*      ten_wrapadr;          // start address of tendon's path           (ntendon x 1)
       int*      ten_wrapnum;          // number of wrap points in path            (ntendon x 1)
       int*      ten_J_rownnz;         // number of non-zeros in Jacobian row      (ntendon x 1)
       int*      ten_J_rowadr;         // row start address in colind array        (ntendon x 1)
       int*      ten_J_colind;         // column indices in sparse Jacobian        (ntendon x nv)
       mjtNum*   ten_length;           // tendon lengths                           (ntendon x 1)
       mjtNum*   ten_J;                // tendon Jacobian                          (ntendon x nv)
       int*      wrap_obj;             // geom id; -1: site; -2: pulley            (nwrap*2 x 1)
       mjtNum*   wrap_xpos;            // Cartesian 3D points in all path          (nwrap*2 x 3)

       // computed by mj_fwdPosition/mj_transmission
       mjtNum*   actuator_length;      // actuator lengths                         (nu x 1)
       mjtNum*   actuator_moment;      // actuator moments                         (nu x nv)

       // computed by mj_fwdPosition/mj_crb
       mjtNum*   crb;                  // com-based composite inertia and mass     (nbody x 10)
       mjtNum*   qM;                   // total inertia                            (nM x 1)

       // computed by mj_fwdPosition/mj_factorM
       mjtNum*   qLD;                  // L'*D*L factorization of M                (nM x 1)
       mjtNum*   qLDiagInv;            // 1/diag(D)                                (nv x 1)
       mjtNum*   qLDiagSqrtInv;        // 1/sqrt(diag(D))                          (nv x 1)

       // computed by mj_fwdPosition/mj_collision
       mjContact* contact;             // list of all detected contacts            (nconmax x 1)

       // computed by mj_fwdPosition/mj_makeConstraint
       int*      efc_type;             // constraint type (mjtConstraint)          (njmax x 1)
       int*      efc_id;               // id of object of specified type           (njmax x 1)
       int*      efc_J_rownnz;         // number of non-zeros in Jacobian row      (njmax x 1)
       int*      efc_J_rowadr;         // row start address in colind array        (njmax x 1)
       int*      efc_J_rowsuper;       // number of subsequent rows in supernode   (njmax x 1)
       int*      efc_J_colind;         // column indices in Jacobian               (njmax x nv)
       int*      efc_JT_rownnz;        // number of non-zeros in Jacobian row    T (nv x 1)
       int*      efc_JT_rowadr;        // row start address in colind array      T (nv x 1)
       int*      efc_JT_rowsuper;      // number of subsequent rows in supernode T (nv x 1)
       int*      efc_JT_colind;        // column indices in Jacobian             T (nv x njmax)
       mjtNum*   efc_J;                // constraint Jacobian                      (njmax x nv)
       mjtNum*   efc_JT;               // constraint Jacobian transposed           (nv x njmax)
       mjtNum*   efc_pos;              // constraint position (equality, contact)  (njmax x 1)
       mjtNum*   efc_margin;           // inclusion margin (contact)               (njmax x 1)
       mjtNum*   efc_frictionloss;     // frictionloss (friction)                  (njmax x 1)
       mjtNum*   efc_diagApprox;       // approximation to diagonal of A           (njmax x 1)
       mjtNum*   efc_KBIP;             // stiffness, damping, impedance, imp'      (njmax x 4)
       mjtNum*   efc_D;                // constraint mass                          (njmax x 1)
       mjtNum*   efc_R;                // inverse constraint mass                  (njmax x 1)

       // computed by mj_fwdPosition/mj_projectConstraint
       int*      efc_AR_rownnz;        // number of non-zeros in AR                (njmax x 1)
       int*      efc_AR_rowadr;        // row start address in colind array        (njmax x 1)
       int*      efc_AR_colind;        // column indices in sparse AR              (njmax x njmax)
       mjtNum*   efc_AR;               // J*inv(M)*J' + R                          (njmax x njmax)

       //-------------------------------- POSITION, VELOCITY dependent

       // computed by mj_fwdVelocity
       mjtNum*   ten_velocity;         // tendon velocities                        (ntendon x 1)
       mjtNum*   actuator_velocity;    // actuator velocities                      (nu x 1)

       // computed by mj_fwdVelocity/mj_comVel
       mjtNum*   cvel;                 // com-based velocity [3D rot; 3D tran]     (nbody x 6)
       mjtNum*   cdof_dot;             // time-derivative of cdof                  (nv x 6)

       // computed by mj_fwdVelocity/mj_rne (without acceleration)
       mjtNum*   qfrc_bias;            // C(qpos,qvel)                             (nv x 1)

       // computed by mj_fwdVelocity/mj_passive
       mjtNum*   qfrc_passive;         // passive force                            (nv x 1)

       // computed by mj_fwdVelocity/mj_referenceConstraint
       mjtNum*   efc_vel;              // velocity in constraint space: J*qvel     (njmax x 1)
       mjtNum*   efc_aref;             // reference pseudo-acceleration            (njmax x 1)

       // computed by mj_sensorVel/mj_subtreeVel if needed
       mjtNum*   subtree_linvel;       // linear velocity of subtree com           (nbody x 3)
       mjtNum*   subtree_angmom;       // angular momentum about subtree com       (nbody x 3)

       //-------------------------------- POSITION, VELOCITY, CONTROL/ACCELERATION dependent

       // computed by mj_fwdActuation
       mjtNum*   actuator_force;       // actuator force in actuation space        (nu x 1)
       mjtNum*   qfrc_actuator;        // actuator force                           (nv x 1)

       // computed by mj_fwdAcceleration
       mjtNum*   qfrc_smooth;          // net unconstrained force                  (nv x 1)
       mjtNum*   qacc_smooth;          // unconstrained acceleration               (nv x 1)

       // computed by mj_fwdConstraint/mj_inverse
       mjtNum*   efc_b;                // linear cost term: J*qacc_smooth - aref   (njmax x 1)
       mjtNum*   efc_force;            // constraint force in constraint space     (njmax x 1)
       int*      efc_state;            // constraint state (mjtConstraintState)    (njmax x 1)
       mjtNum*   qfrc_constraint;      // constraint force                         (nv x 1)

       // computed by mj_inverse
       mjtNum*   qfrc_inverse;         // net external force; should equal:        (nv x 1)
                                       //  qfrc_applied + J'*xfrc_applied + qfrc_actuator

       // computed by mj_sensorAcc/mj_rnePostConstraint if needed; rotation:translation format
       mjtNum*   cacc;                 // com-based acceleration                   (nbody x 6)
       mjtNum*   cfrc_int;             // com-based interaction force with parent  (nbody x 6)
       mjtNum*   cfrc_ext;             // com-based external force on body         (nbody x 6)
   };
   typedef struct _mjData mjData;

| Defined in `mjdata.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`_

| This is the main data structure holding the simulation state. It is the workspace where all functions read their
  modifiable inputs and write their outputs.

.. _mjvPerturb:

mjvPerturb
~~~~~~~~~~

.. code-block:: C

   struct _mjvPerturb                  // object selection and perturbation
   {
       int      select;                // selected body id; non-positive: none
       int      skinselect;            // selected skin id; non-positive: none
       int      active;                // perturbation bitmask (mjtPertBit)
       mjtNum   refpos[3];             // desired position for selected object
       mjtNum   refquat[4];            // desired orientation for selected object
       mjtNum   localpos[3];           // selection point in object coordinates
       mjtNum   scale;                 // relative mouse motion-to-space scaling (set by initPerturb)
   };
   typedef struct _mjvPerturb mjvPerturb;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| This is the data structure holding information about mouse perturbations.

.. _mjvCamera:

mjvCamera
~~~~~~~~~

.. code-block:: C

   struct _mjvCamera                   // abstract camera
   {
       // type and ids
       int      type;                  // camera type (mjtCamera)
       int      fixedcamid;            // fixed camera id
       int      trackbodyid;           // body id to track

       // abstract camera pose specification
       mjtNum   lookat[3];             // lookat point
       mjtNum   distance;              // distance to lookat point or tracked body
       mjtNum   azimuth;               // camera azimuth (deg)
       mjtNum   elevation;             // camera elevation (deg)
   };
   typedef struct _mjvCamera mjvCamera;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| This is the data structure describing one abstract camera.

.. _mjvGLCamera:

mjvGLCamera
~~~~~~~~~~~

.. code-block:: C

   struct _mjvGLCamera                 // OpenGL camera
   {
       // camera frame
       float    pos[3];                // position
       float    forward[3];            // forward direction
       float    up[3];                 // up direction

       // camera projection
       float    frustum_center;        // hor. center (left,right set to match aspect)
       float    frustum_bottom;        // bottom
       float    frustum_top;           // top
       float    frustum_near;          // near
       float    frustum_far;           // far
   };
   typedef struct _mjvGLCamera mjvGLCamera;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| This is the data structure describing one OpenGL camera.

.. _mjvGeom:

mjvGeom
~~~~~~~

.. code-block:: C

   struct _mjvGeom                     // abstract geom
   {
       // type info
       int      type;                  // geom type (mjtGeom)
       int      dataid;                // mesh, hfield or plane id; -1: none
       int      objtype;               // mujoco object type; mjOBJ_UNKNOWN for decor
       int      objid;                 // mujoco object id; -1 for decor
       int      category;              // visual category
       int      texid;                 // texture id; -1: no texture
       int      texuniform;            // uniform cube mapping
       int      texcoord;              // mesh geom has texture coordinates
       int      segid;                 // segmentation id; -1: not shown

       // OpenGL info
       float    texrepeat[2];          // texture repetition for 2D mapping
       float    size[3];               // size parameters
       float    pos[3];                // Cartesian position
       float    mat[9];                // Cartesian orientation
       float    rgba[4];               // color and transparency
       float    emission;              // emission coef
       float    specular;              // specular coef
       float    shininess;             // shininess coef
       float    reflectance;           // reflectance coef
       char     label[100];            // text label

       // transparency rendering (set internally)
       float    camdist;               // distance to camera (used by sorter)
       float    modelrbound;           // geom rbound from model, 0 if not model geom
       mjtByte  transparent;           // treat geom as transparent
   };
   typedef struct _mjvGeom mjvGeom;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| This is the data structure describing one abstract visualization geom - which could correspond to a model geom or to a
  decoration element constructed by the visualizer.

.. _mjvLight:

mjvLight
~~~~~~~~

.. code-block:: C

   struct _mjvLight                    // OpenGL light
   {
       float    pos[3];                // position rel. to body frame
       float    dir[3];                // direction rel. to body frame
       float    attenuation[3];        // OpenGL attenuation (quadratic model)
       float    cutoff;                // OpenGL cutoff
       float    exponent;              // OpenGL exponent
       float    ambient[3];            // ambient rgb (alpha=1)
       float    diffuse[3];            // diffuse rgb (alpha=1)
       float    specular[3];           // specular rgb (alpha=1)
       mjtByte  headlight;             // headlight
       mjtByte  directional;           // directional light
       mjtByte  castshadow;            // does light cast shadows
   };
   typedef struct _mjvLight mjvLight;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| This is the data structure describing one OpenGL light.

.. _mjvOption:

mjvOption
~~~~~~~~~

.. code-block:: C

   struct _mjvOption                      // abstract visualization options
   {
       int      label;                    // what objects to label (mjtLabel)
       int      frame;                    // which frame to show (mjtFrame)
       mjtByte  geomgroup[mjNGROUP];      // geom visualization by group
       mjtByte  sitegroup[mjNGROUP];      // site visualization by group
       mjtByte  jointgroup[mjNGROUP];     // joint visualization by group
       mjtByte  tendongroup[mjNGROUP];    // tendon visualization by group
       mjtByte  actuatorgroup[mjNGROUP];  // actuator visualization by group
       mjtByte  skingroup[mjNGROUP];      // skin visualization by group
       mjtByte  flags[mjNVISFLAG];        // visualization flags (indexed by mjtVisFlag)
   };
   typedef struct _mjvOption mjvOption;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| This structure contains options that enable and disable the visualization of various elements.

.. _mjvScene:

mjvScene
~~~~~~~~

.. code-block:: C

   struct _mjvScene                    // abstract scene passed to OpenGL renderer
   {
       // abstract geoms
       int      maxgeom;               // size of allocated geom buffer
       int      ngeom;                 // number of geoms currently in buffer
       mjvGeom* geoms;                 // buffer for geoms
       int*     geomorder;             // buffer for ordering geoms by distance to camera

       // skin data
       int      nskin;                 // number of skins
       int*     skinfacenum;           // number of faces in skin
       int*     skinvertadr;           // address of skin vertices
       int*     skinvertnum;           // number of vertices in skin
       float*   skinvert;              // skin vertex data
       float*   skinnormal;            // skin normal data

       // OpenGL lights
       int      nlight;                // number of lights currently in buffer
       mjvLight lights[mjMAXLIGHT];    // buffer for lights

       // OpenGL cameras
       mjvGLCamera camera[2];          // left and right camera

       // OpenGL model transformation
       mjtByte  enabletransform;       // enable model transformation
       float    translate[3];          // model translation
       float    rotate[4];             // model quaternion rotation
       float    scale;                 // model scaling

       // OpenGL rendering effects
       int      stereo;                // stereoscopic rendering (mjtStereo)
       mjtByte  flags[mjNRNDFLAG];     // rendering flags (indexed by mjtRndFlag)
   };
   typedef struct _mjvScene mjvScene;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| This structure contains everything needed to render the 3D scene in OpenGL.

.. _mjvFigure:

mjvFigure
~~~~~~~~~

.. code-block:: C

   struct _mjvFigure                   // abstract 2D figure passed to OpenGL renderer
   {
       // enable/disable flags
       int     flg_legend;             // show legend
       int     flg_ticklabel[2];       // show grid tick labels (x,y)
       int     flg_extend;             // automatically extend axis ranges to fit data
       int     flg_barplot;            // isolated line segments (i.e. GL_LINES)
       int     flg_selection;          // vertical selection line
       int     flg_symmetric;          // symmetric y-axis

       // figure options
       int     legendoff;              // number of lines to offset legend
       int     gridsize[2];            // number of grid points in (x,y)
       int     selection;              // selection line x-value
       int     highlight[2];           // if point is in legend rect, highlight line
       float   gridrgb[3];             // grid line rgb
       float   gridwidth;              // grid line width
       float   figurergba[4];          // figure color and alpha
       float   panergba[4];            // pane color and alpha
       float   legendrgba[4];          // legend color and alpha
       float   textrgb[3];             // text color
       float   range[2][2];            // axis ranges; (min>=max) automatic
       char    xlabel[100];            // x-axis label
       char    title[100];             // figure title
       char    xformat[20];            // x-tick label format for sprintf
       char    yformat[20];            // y-tick label format for sprintf
       char    minwidth[20];           // string used to determine min y-tick width

       // line data
       int     linepnt[mjMAXLINE];                   // number of points in line; (0) disable
       float   linergb[mjMAXLINE][3];                // line color
       float   linewidth[mjMAXLINE];                 // line width
       float   linedata[mjMAXLINE][2*mjMAXLINEPNT];  // line data (x,y)
       char    linename[mjMAXLINE][100];             // line name for legend

       // output from renderer
       int     xaxispixel[2];          // range of x-axis in pixels
       int     yaxispixel[2];          // range of y-axis in pixels
       float   xaxisdata[2];           // range of x-axis in data units
       float   yaxisdata[2];           // range of y-axis in data units
   };
   typedef struct _mjvFigure mjvFigure;

| Defined in `mjvisualize.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjvisualize.h>`_

| This structure contains everything needed to render a 2D plot in OpenGL. The buffers for line points etc. are
  preallocated, and the user has to populate them before calling the function :ref:`mjr_figure` with this
  data structure as an argument.

.. _mjrRect:

mjrRect
~~~~~~~

.. code-block:: C

   struct _mjrRect                     // OpenGL rectangle
   {
       int left;                       // left (usually 0)
       int bottom;                     // bottom (usually 0)
       int width;                      // width (usually buffer width)
       int height;                     // height (usually buffer height)
   };
   typedef struct _mjrRect mjrRect;

| Defined in `mjrender.h (57) <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjrender.h#L57>`_

| This structure specifies a rectangle.

.. _mjrContext:

mjrContext
~~~~~~~~~~

.. code-block:: C

   struct _mjrContext                  // custom OpenGL context
   {
       // parameters copied from mjVisual
       float lineWidth;                // line width for wireframe rendering
       float shadowClip;               // clipping radius for directional lights
       float shadowScale;              // fraction of light cutoff for spot lights
       float fogStart;                 // fog start = stat.extent * vis.map.fogstart
       float fogEnd;                   // fog end = stat.extent * vis.map.fogend
       float fogRGBA[4];               // fog rgba
       int shadowSize;                 // size of shadow map texture
       int offWidth;                   // width of offscreen buffer
       int offHeight;                  // height of offscreen buffer
       int offSamples;                 // number of offscreen buffer multisamples

       // parameters specified at creation
       int fontScale;                  // font scale
       int auxWidth[mjNAUX];           // auxiliary buffer width
       int auxHeight[mjNAUX];          // auxiliary buffer height
       int auxSamples[mjNAUX];         // auxiliary buffer multisamples

       // offscreen rendering objects
       unsigned int offFBO;            // offscreen framebuffer object
       unsigned int offFBO_r;          // offscreen framebuffer for resolving multisamples
       unsigned int offColor;          // offscreen color buffer
       unsigned int offColor_r;        // offscreen color buffer for resolving multisamples
       unsigned int offDepthStencil;   // offscreen depth and stencil buffer
       unsigned int offDepthStencil_r; // offscreen depth and stencil buffer for resolving multisamples

       // shadow rendering objects
       unsigned int shadowFBO;         // shadow map framebuffer object
       unsigned int shadowTex;         // shadow map texture

       // auxiliary buffers
       unsigned int auxFBO[mjNAUX];    // auxiliary framebuffer object
       unsigned int auxFBO_r[mjNAUX];  // auxiliary framebuffer object for resolving
       unsigned int auxColor[mjNAUX];  // auxiliary color buffer
       unsigned int auxColor_r[mjNAUX];// auxiliary color buffer for resolving

       // texture objects and info
       int ntexture;                   // number of allocated textures
       int textureType[100];           // type of texture (mjtTexture)
       unsigned int texture[100];      // texture names

       // displaylist starting positions
       unsigned int basePlane;         // all planes from model
       unsigned int baseMesh;          // all meshes from model
       unsigned int baseHField;        // all hfields from model
       unsigned int baseBuiltin;       // all buildin geoms, with quality from model
       unsigned int baseFontNormal;    // normal font
       unsigned int baseFontShadow;    // shadow font
       unsigned int baseFontBig;       // big font

       // displaylist ranges
       int     rangePlane;             // all planes from model
       int     rangeMesh;              // all meshes from model
       int     rangeHField;            // all hfields from model
       int     rangeBuiltin;           // all builtin geoms, with quality from model
       int     rangeFont;              // all characters in font

       // skin VBOs
       int      nskin;                 // number of skins
       unsigned int* skinvertVBO;      // skin vertex position VBOs
       unsigned int* skinnormalVBO;    // skin vertex normal VBOs
       unsigned int* skintexcoordVBO;  // skin vertex texture coordinate VBOs
       unsigned int* skinfaceVBO;      // skin face index VBOs

       // character info
       int     charWidth[127];         // character widths: normal and shadow
       int     charWidthBig[127];      // chacarter widths: big
       int     charHeight;             // character heights: normal and shadow
       int     charHeightBig;          // character heights: big

       // capabilities
       int     glInitialized;          // is OpenGL initialized
       int     windowAvailable;        // is default/window framebuffer available
       int     windowSamples;          // number of samples for default/window framebuffer
       int     windowStereo;           // is stereo available for default/window framebuffer
       int     windowDoublebuffer;     // is default/window framebuffer double buffered

       // framebuffer
       int     currentBuffer;          // currently active framebuffer: mjFB_WINDOW or mjFB_OFFSCREEN
   };
   typedef struct _mjrContext mjrContext;

| Defined in `mjrender.h (67) <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjrender.h#L67>`_

| This structure contains the custom OpenGL rendering context, with the ids of all OpenGL resources uploaded to the GPU.

.. _mjuiState:

mjuiState
~~~~~~~~~

.. code-block:: C

   struct _mjuiState               // mouse and keyboard state
   {
       // constants set by user
       int nrect;                  // number of rectangles used
       mjrRect rect[mjMAXUIRECT];  // rectangles (index 0: entire window)
       void* userdata;             // pointer to user data (for callbacks)

       // event type
       int type;                   // (type mjtEvent)

       // mouse buttons
       int left;                   // is left button down
       int right;                  // is right button down
       int middle;                 // is middle button down
       int doubleclick;            // is last press a double click
       int button;                 // which button was pressed (mjtButton)
       double buttontime;          // time of last button press

       // mouse position
       double x;                   // x position
       double y;                   // y position
       double dx;                  // x displacement
       double dy;                  // y displacement
       double sx;                  // x scroll
       double sy;                  // y scroll

       // keyboard
       int control;                // is control down
       int shift;                  // is shift down
       int alt;                    // is alt down
       int key;                    // which key was pressed
       double keytime;             // time of last key press

       // rectangle ownership and dragging
       int mouserect;              // which rectangle contains mouse
       int dragrect;               // which rectangle is dragged with mouse
       int dragbutton;             // which button started drag (mjtButton)
   };
   typedef struct _mjuiState mjuiState;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| This structure contains the keyboard and mouse state used by the UI framework.

.. _mjuiThemeSpacing:

mjuiThemeSpacing
~~~~~~~~~~~~~~~~

.. code-block:: C

   struct _mjuiThemeSpacing        // UI visualization theme spacing
   {
           int total;              // total width
           int scroll;             // scrollbar width
           int label;              // label width
           int section;            // section gap
           int itemside;           // item side gap
           int itemmid;            // item middle gap
           int itemver;            // item vertical gap
           int texthor;            // text horizontal gap
           int textver;            // text vertical gap
           int linescroll;         // number of pixels to scroll
           int samples;            // number of multisamples
   };
   typedef struct _mjuiThemeSpacing mjuiThemeSpacing;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| This structure defines the spacing of UI items in the theme.

.. _mjuiThemeColor:

mjuiThemeColor
~~~~~~~~~~~~~~

.. code-block:: C

   struct _mjuiThemeColor          // UI visualization theme color
   {
       float master[3];            // master background
       float thumb[3];             // scrollbar thumb
       float secttitle[3];         // section title
       float sectfont[3];          // section font
       float sectsymbol[3];        // section symbol
       float sectpane[3];          // section pane
       float shortcut[3];          // shortcut background
       float fontactive[3];        // font active
       float fontinactive[3];      // font inactive
       float decorinactive[3];     // decor inactive
       float decorinactive2[3];    // inactive slider color 2
       float button[3];            // button
       float check[3];             // check
       float radio[3];             // radio
       float select[3];            // select
       float select2[3];           // select pane
       float slider[3];            // slider
       float slider2[3];           // slider color 2
       float edit[3];              // edit
       float edit2[3];             // edit invalid
       float cursor[3];            // edit cursor
   };
   typedef struct _mjuiThemeColor mjuiThemeColor;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| This structure defines the colors of UI items in the theme.

.. _mjuiItem:

mjuiItem
~~~~~~~~

.. code-block:: C

   struct _mjuiItem                // UI item
   {
       // common properties
       int type;                   // type (mjtItem)
       char name[mjMAXUINAME];     // name
       int state;                  // 0: disable, 1: enable, 2+: use predicate
       void *pdata;                // data pointer (type-specific)
       int sectionid;              // id of section containing item
       int itemid;                 // id of item within section

       // type-specific properties
       union
       {
           // check and button-related
           struct
           {
               int modifier;       // 0: none, 1: control, 2: shift; 4: alt
               int shortcut;       // shortcut key; 0: undefined
           } single;

           // static, radio and select-related
           struct
           {
               int nelem;          // number of elements in group
               char name[mjMAXUIMULTI][mjMAXUINAME]; // element names
           } multi;

           // slider-related
           struct
           {
               double range[2];    // slider range
               double divisions;   // number of range divisions
           } slider;

           // edit-related
           struct
           {
               int nelem;          // number of elements in list
               double range[mjMAXUIEDIT][2]; // element range (min>=max: ignore)
           } edit;
       };

       // internal
       mjrRect rect;               // rectangle occupied by item
   };
   typedef struct _mjuiItem mjuiItem;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| This structure defines one UI item.

.. _mjuiSection:

mjuiSection
~~~~~~~~~~~

.. code-block:: C

   struct _mjuiSection             // UI section
   {
       // properties
       char name[mjMAXUINAME];     // name
       int state;                  // 0: closed, 1: open
       int modifier;               // 0: none, 1: control, 2: shift; 4: alt
       int shortcut;               // shortcut key; 0: undefined
       int nitem;                  // number of items in use
       mjuiItem item[mjMAXUIITEM];// preallocated array of items

       // internal
       mjrRect rtitle;             // rectangle occupied by title
       mjrRect rcontent;           // rectangle occupied by content
   };
   typedef struct _mjuiSection mjuiSection;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| This structure defines one section of the UI.

.. _mjUI:

mjUI
~~~~

.. code-block:: C

   struct _mjUI                    // entire UI
   {
       // constants set by user
       mjuiThemeSpacing spacing;   // UI theme spacing
       mjuiThemeColor color;       // UI theme color
       mjfItemEnable predicate;    // callback to set item state programmatically
       void* userdata;             // pointer to user data (passed to predicate)
       int rectid;                 // index of this ui rectangle in mjuiState
       int auxid;                  // aux buffer index of this ui
       int radiocol;               // number of radio columns (0 defaults to 2)

       // UI sizes (framebuffer units)
       int width;                  // width
       int height;                 // current heigth
       int maxheight;              // height when all sections open
       int scroll;                 // scroll from top of UI

       // mouse focus
       int mousesect;              // 0: none, -1: scroll, otherwise 1+section
       int mouseitem;              // item within section
       int mousehelp;              // help button down: print shortcuts

       // keyboard focus and edit
       int editsect;               // 0: none, otherwise 1+section
       int edititem;               // item within section
       int editcursor;             // cursor position
       int editscroll;             // horizontal scroll
       char edittext[mjMAXUITEXT]; // current text
       mjuiItem* editchanged;      // pointer to changed edit in last mjui_event

       // sections
       int nsect;                  // number of sections in use
       mjuiSection sect[mjMAXUISECT];  // preallocated array of sections
   };
   typedef struct _mjUI mjUI;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| This structure defines the entire UI.

.. _mjuiDef:

mjuiDef
~~~~~~~

.. code-block:: C

   struct _mjuiDef
   {
       int type;                   // type (mjtItem); -1: section
       char name[mjMAXUINAME];     // name
       int state;                  // state
       void* pdata;                // pointer to data
       char other[mjMAXUITEXT];    // string with type-specific properties
   };
   typedef struct _mjuiDef mjuiDef;

| Defined in `mjui.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjui.h>`_

| This structure defines one entry in the definition table used for simplified UI construction.

.. _tyXMacro:

X Macros
^^^^^^^^

The X Macros are not needed in most user projects. They are used internally to allocate the model, and are also
available for users who know how to use this programming technique. See the header file
`mjxmacro.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mjxmacro.h>`_ for the actual definitions. They are particularly useful in writing MuJoCo wrappers
for scripting languages, where dynamic structures matching the MuJoCo data structures need to be constructed
programmatically.

.. _MJOPTION_SCALARS:

MJOPTION_SCALARS
~~~~~~~~~~~~~~~~

Scalar fields of mjOption.

.. _MJOPTION_VECTORS:

MJOPTION_VECTORS
~~~~~~~~~~~~~~~~

Vector fields of mjOption.

.. _MJMODEL_INTS:

MJMODEL_INTS
~~~~~~~~~~~~

Int fields of mjModel.

.. _MJMODEL_POINTERS:

MJMODEL_POINTERS
~~~~~~~~~~~~~~~~

Pointer fields of mjModel.

.. _MJDATA_SCALAR:

MJDATA_SCALAR
~~~~~~~~~~~~~

Scalar fields of mjData.

.. _MJDATA_VECTOR:

MJDATA_VECTOR
~~~~~~~~~~~~~

Vector fields of mjData.

.. _MJDATA_POINTERS:

MJDATA_POINTERS
~~~~~~~~~~~~~~~

Pointer fields of mjData.

.. _Global-variables:

Global variables
----------------

.. _glError:

Error callbacks
^^^^^^^^^^^^^^^

All user callbacks (i.e., global function pointers whose name starts with 'mjcb') are initially set to NULL, which
disables them and allows the default processing to take place. To install a callback, simply set the corresponding
global pointer to a user function of the correct type. Keep in mind that these are global and not model-specific. So if
you are simulating multiple models in parallel, they use the same set of callbacks.

.. _mju_user_error:

mju_user_error
~~~~~~~~~~~~~~

.. code-block:: C

   extern void (*mju_user_error)(const char*);

This is called from within the main error function :ref:`mju_error`. When installed, this function overrides the default
error processing. Once it prints error messages (or whatever else the user wants to do), it must **exit** the program.
MuJoCo is written with the assumption that mju_error will not return. If it does, the behavior of the software is
undefined.

.. _mju_user_warning:

mju_user_warning
~~~~~~~~~~~~~~~~

.. code-block:: C

   extern void (*mju_user_warning)(const char*);

This is called from within the main warning function :ref:`mju_warning`. It is similar to the error handler, but instead
it must return without exiting the program.

.. _glMemory:

Memory callbacks
^^^^^^^^^^^^^^^^

The purpose of the memory callbacks is to allow the user to install custom memory allocation and deallocation
mechanisms. One example where we have found this to be useful is a MATLAB wrapper for MuJoCo, where mex files are
expected to use MATLAB's memory mechanism for permanent memory allocation.

.. _mju_user_malloc:

mju_user_malloc
~~~~~~~~~~~~~~~

.. code-block:: C

   extern void* (*mju_user_malloc)(size_t);

If this is installed, the MuJoCo runtime will use it to allocate all heap memory it needs (instead of using aligned
malloc). The user allocator must allocate memory aligned on 8-byte boundaries. Note that the parser and compiler are
written in C++ and sometimes allocate memory with the "new" operator which bypasses this mechanism.

.. _mju_user_free:

mju_user_free
~~~~~~~~~~~~~

.. code-block:: C

   extern void (*mju_user_free)(void*);

If this is installed, MuJoCo will free any heap memory it allocated by calling this function (instead of using aligned
free).

.. _glPhysics:

Physics callbacks
^^^^^^^^^^^^^^^^^

| The physics callbacks are the main mechanism for modifying the behavior of the simulator, beyond setting various
  options. The options control the operation of the default pipeline, while callbacks extend the pipeline at
  well-defined places. This enables advanced users to implement many interesting functions which we have not thought of,
  while still taking advantage of the default pipeline. As with all other callbacks, there is no automated error
  checking - instead we assume that the authors of callback functions know what they are doing.

| Custom physics callbacks will often need parameters that are not standard in MJCF. This is largely why we have
  provided custom fields as well as user data arrays in MJCF. The idea is to "instrument" the MJCF model by entering the
  necessary user parameters, and then write callbacks that look for those parameters and perform the corresponding
  computations. We strongly encourage users to write callbacks that check the model for the presence of user parameters
  before accessing them - so that when a regular model is loaded, the callback disables itself automatically instead of
  causing the software to crash.

.. _mjcb_passive:

mjcb_passive
~~~~~~~~~~~~

.. code-block:: C

   extern mjfGeneric mjcb_passive;

This is used to implement a custom passive force in joint space; if the force is more naturally defined in Cartesian
space, use the end-effector Jacobian to map it to joint space. By "passive" we do not mean a force that does no positive
work (as in physics), but simply a force that depends only on position and velocity but not on control. There are
standard passive forces in MuJoCo arising from springs, dampers, viscosity and density of the medium. They are computed
in ``mjData.qfrc_passive`` before mjcb_passive is called. The user callback should add to this vector instead of
overwriting it (otherwise the standard passive forces will be lost).

.. _mjcb_control:

mjcb_control
~~~~~~~~~~~~

.. code-block:: C

   extern mjfGeneric mjcb_control;

This is the most commonly used callback. It implements a control law, by writing in the vector of controls
``mjData.ctrl``. It can also write in ``mjData.qfrc_applied`` and ``mjData.xfrc_applied``. The values written in these
vectors can depend on position, velocity and all other quantities derived from them, but cannot depend on contact forces
and other quantities that are computed after the control is specified. If the callback accesses the latter fields, their
values do not correspond to the current time step.

The control callback is called from within :ref:`mj_forward` and :ref:`mj_step`, just before the controls and applied
forces are needed. When using the RK integrator, it will be called 4 times per step. The alternative way of specifying
controls and applied forces is to set them before ``mj_step``, or use ``mj_step1`` and ``mj_step2``. The latter approach
allows setting the controls after the position and velocity computations have been performed by ``mj_step1``, allowing
these results to be utilized in computing the control (similar to using mjcb_control). However, the only way to change
the controls between sub-steps of the RK integrator is to define the control callback.

.. _mjcb_contactfilter:

mjcb_contactfilter
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   extern mjfConFilt mjcb_contactfilter;

This callback can be used to replace MuJoCo's default collision filtering. When installed, this function is called for
each pair of geoms that have passed the broad-phase test (or are predefined geom pairs in the MJCF) and are candidates
for near-phase collision. The default processing uses the contype and conaffinity masks, the parent-child filter and
some other considerations related to welded bodies to decide if collision should be allowed. This callback replaces the
default processing, but keep in mind that the entire mechanism is being replaced. So for example if you still want to
take advantage of contype/conaffinity, you have to re-implement it in the callback.

.. _mjcb_sensor:

mjcb_sensor
~~~~~~~~~~~

.. code-block:: C

   extern mjfSensor mjcb_sensor;

This callback populates fields of ``mjData.sensordata`` corresponding to user-defined sensors. It is called if it is
installed and the model contains user-defined sensors. It is called once per compute stage (mjSTAGE_POS, mjSTAGE_VEL,
mjSTAGE_ACC) and must fill in all user sensor values for that stage. The user-defined sensors have dimensionality and
data types defined in the MJCF model which must be respected by the callback.

.. _mjcb_time:

mjcb_time
~~~~~~~~~

.. code-block:: C

   extern mjfTime mjcb_time;

Installing this callback enables the built-in profiler, and keeps timing statistics in ``mjData.timer``. The return type
is mjtNum, while the time units are up to the user. ``simulate.cc`` assumes the unit is 1 millisecond. In order to be
useful, the callback should use high-resolution timers with at least microsecond precision. This is because the
computations being timed are very fast.

.. _mjcb_act_dyn:

mjcb_act_dyn
~~~~~~~~~~~~

.. code-block:: C

   extern mjfAct mjcb_act_dyn;

This callback implements custom activation dynamics: it must return the value of ``mjData.act_dot`` for the specified
actuator. This is the time-derivative of the activation state vector ``mjData.act``. It is called for model actuators
with user dynamics (mjDYN_USER). If such actuators exist in the model but the callback is not installed, their
time-derivative is set to 0.

.. _mjcb_act_gain:

mjcb_act_gain
~~~~~~~~~~~~~

.. code-block:: C

   extern mjfAct mjcb_act_gain;

This callback implements custom actuator gains: it must return the gain for the specified actuator with
``mjModel.actuator_gaintype`` set to mjGAIN_USER. If such actuators exist in the model and this callback is not
installed, their gains are set to 1.

.. _mjcb_act_bias:

mjcb_act_bias
~~~~~~~~~~~~~

.. code-block:: C

   extern mjfAct mjcb_act_bias;

This callback implements custom actuator biases: it must return the bias for the specified actuator with
``mjModel.actuator_biastype`` set to mjBIAS_USER. If such actuators exist in the model and this callback is not
installed, their biases are set to 0.

.. _glCollision:

Collision table
^^^^^^^^^^^^^^^

.. _mjCOLLISIONFUNC:

mjCOLLISIONFUNC
~~~~~~~~~~~~~~~

.. code-block:: C

   extern mjfCollision mjCOLLISIONFUNC[mjNGEOMTYPES][mjNGEOMTYPES];

Table of pairwise collision functions indexed by geom types. Only the upper-right triangle is used. The user can replace
these function pointers with custom routines, replacing MuJoCo's collision mechanism. If a given entry is NULL, the
corresponding pair of geom types cannot be collided. Note that these functions apply only to near-phase collisions. The
broadphase mechanism is built-in and cannot be modified.

.. _glString:

String constants
^^^^^^^^^^^^^^^^

The string constants described here are provided for user convenience. They correspond to the English names of lists of
options, and can be displayed in menus or dialogs in a GUI. The code sample :ref:`saSimulate` illustrates how they can
be used.

.. _mjDISABLESTRING:

mjDISABLESTRING
~~~~~~~~~~~~~~~

.. code-block:: C

   extern const char* mjDISABLESTRING[mjNDISABLE];

Names of the disable bits defined by :ref:`mjtDisableBit`.

.. _mjENABLESTRING:

mjENABLESTRING
~~~~~~~~~~~~~~

.. code-block:: C

   extern const char* mjENABLESTRING[mjNENABLE];

Names of the enable bits defined by :ref:`mjtEnableBit`.

.. _mjTIMERSTRING:

mjTIMERSTRING
~~~~~~~~~~~~~

.. code-block:: C

   extern const char* mjTIMERSTRING[mjNTIMER];

Names of the mjData timers defined by :ref:`mjtTimer`.

.. _mjLABELSTRING:

mjLABELSTRING
~~~~~~~~~~~~~

.. code-block:: C

   extern const char* mjLABELSTRING[mjNLABEL];

Names of the visual labeling modes defined by :ref:`mjtLabel`.

.. _mjFRAMESTRING:

mjFRAMESTRING
~~~~~~~~~~~~~

.. code-block:: C

   extern const char* mjFRAMESTRING[mjNFRAME];

Names of the frame visualization modes defined by :ref:`mjtFrame`.

.. _mjVISSTRING:

mjVISSTRING
~~~~~~~~~~~

.. code-block:: C

   extern const char* mjVISSTRING[mjNVISFLAG][3];

| Descriptions of the abstract visualization flags defined by :ref:`mjtVisFlag`. For each flag there are three strings,
  with the following meaning:

| [0]: flag name;

| [1]: the string "0" or "1" indicating if the flag is on or off by default, as set by
  :ref:`mjv_defaultOption`;

| [2]: one-character string with a suggested keyboard shortcut, used in ``simulate.cc``.

.. _mjRNDSTRING:

mjRNDSTRING
~~~~~~~~~~~

.. code-block:: C

   extern const char* mjRNDSTRING[mjNRNDFLAG][3];

Descriptions of the OpenGL rendering flags defined by :ref:`mjtRndFlag`. The three strings for each flag have the same
format as above, except the defaults here are set by :ref:`mjv_makeScene`.

.. _glNumeric:

Numeric constants
^^^^^^^^^^^^^^^^^

| Many integer constants were already documented in the primitive types above. In addition, the header files define
  several other constants documented here. Unless indicated otherwise, each entry in the table below is defined in
  mjmodel.h. Note that some extended key codes are defined in mjui.h which are not shown in the table below. Their names
  are in the format mjKEY_XXX. They correspond to GLFW key codes.

+------------------+--------+----------------------------------------------------------------------------------------+
| symbol           | value  | description                                                                            |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMINVAL         | 1E-15  | The minimal value allowed in any denominator, and in general any mathematical          |
|                  |        | operation where 0 is not allowed. In almost all cases, MuJoCo silently clamps smaller  |
|                  |        | values to mjMINVAL.                                                                    |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjPI             | pi     | The value of pi. This is used in various trigonometric functions, and also for         |
|                  |        | conversion from degrees to radians in the compiler.                                    |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXVAL         | 1E+10  | The maximal absolute value allowed in mjData.qpos, mjData.qvel, mjData.qacc. The API   |
|                  |        | functions :ref:`mj_checkPos`, :ref:`mj_checkVel`, :ref:`mj_checkAcc` use this constant |
|                  |        | to detect instability.                                                                 |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMINMU          | 1E-5   | The minimal value allowed in any friction coefficient. Recall that MuJoCo's contact    |
|                  |        | model allows different number of friction dimensions to be included, as specified by   |
|                  |        | the :at:`condim`    attribute. If however a given friction dimension is included, its  |
|                  |        | friction is not allowed to be smaller than this constant. Smaller values are           |
|                  |        | automatically clamped to this constant.                                                |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMINIMP         | 0.0001 | The minimal value allowed in any constraint impedance. Smaller values are              |
|                  |        | automatically clamped to this constant.                                                |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXIMP         | 0.9999 | The maximal value allowed in any constraint impedance. Larger values are automatically |
|                  |        | clamped to this constant.                                                              |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXCONPAIR     | 50     | The maximal number of contacts points that can be generated per geom pair. MuJoCo's    |
|                  |        | built-in collision functions respect this limit, and user-defined functions should     |
|                  |        | also respect it. Such functions are called with a return buffer of size mjMAXCONPAIR;  |
|                  |        | attempting to write more contacts in the buffer can cause unpredictable behavior.      |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXVFS         | 200    | The maximal number of files in the virtual file system.                                |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXVFSNAME     | 100    | The maximal number of characters in the name of each file in the virtual file system.  |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNEQDATA        | 11     | The maximal number of real-valued parameters used to define each equality constraint.  |
|                  |        | Determines the size of mjModel.eq_data. This and the next five constants correspond to |
|                  |        | array sizes which we have not fully settled. There may be reasons to increase them in  |
|                  |        | the future, so as to accommodate extra parameters needed for more elaborate            |
|                  |        | computations. This is why we maintain them as symbolic constants that can be easily    |
|                  |        | changed, as opposed to the array size for representing quaternions for example - which |
|                  |        | has no reason to change.                                                               |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNDYN           | 10     | The maximal number of real-valued parameters used to define the activation dynamics of |
|                  |        | each actuator. Determines the size of mjModel.actuator_dynprm.                         |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNGAIN          | 10     | The maximal number of real-valued parameters used to define the gain of each actuator. |
|                  |        | Determines the size of mjModel.actuator_gainprm.                                       |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNBIAS          | 10     | The maximal number of real-valued parameters used to define the bias of each actuator. |
|                  |        | Determines the size of mjModel.actuator_biasprm.                                       |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNFLUID         | 12     | The number of per-geom fluid interaction parameters required by the ellipsoidal model. |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNREF           | 2      | The maximal number of real-valued parameters used to define the reference acceleration |
|                  |        | of each scalar constraint. Determines the size of all mjModel.XXX_solref fields.       |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNIMP           | 5      | The maximal number of real-valued parameters used to define the impedance of each      |
|                  |        | scalar constraint. Determines the size of all mjModel.XXX_solimp fields.               |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNSOLVER        | 1000   | The size of the preallocated array ``mjData.solver``. This is used to store diagnostic |
|                  |        | information about each iteration of the constraint solver. The actual number of        |
|                  |        | iterations is given by ``mjData.solver_iter``.                                         |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNGROUP         | 6      | The number of geom, site, joint, tendon and actuator groups whose rendering can be     |
|                  |        | enabled and disabled via mjvOption. Defined in mjvisualize.h.                          |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXOVERLAY     | 500    | The maximal number of characters in overlay text for rendering. Defined in             |
|                  |        | mjvisualize.h.                                                                         |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXLINE        | 100    | The maximal number of lines per 2D figure (mjvFigure). Defined in mjvisualize.h.       |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXLINEPNT     | 1000   | The maximal number of points in each line in a 2D figure. Note that the buffer         |
|                  |        | mjvFigure.linepnt has length 2*mjMAXLINEPNT because each point has X and Y             |
|                  |        | coordinates. Defined in mjvisualize.h.                                                 |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXPLANEGRID   | 200    | The maximal number of grid lines in each dimension for rendering planes. Defined in    |
|                  |        | mjvisualize.h.                                                                         |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjNAUX           | 10     | Number of auxiliary buffers that can be allocated in mjrContext. Defined in            |
|                  |        | mjrender.h.                                                                            |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXTEXTURE     | 1000   | Maximum number of textures allowed. Defined in mjrender.h.                             |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXUISECT      | 10     | Maximum number of UI sections. Defined in mjui.h.                                      |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXUIITEM      | 80     | Maximum number of items per UI section. Defined in mjui.h.                             |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXUITEXT      | 500    | Maximum number of characters in UI fields 'edittext' and 'other'. Defined in mjui.h.   |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXUINAME      | 40     | Maximum number of characters in any UI name. Defined in mjui.h.                        |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXUIMULTI     | 20     | Maximum number of radio and select items in UI group. Defined in mjui.h.               |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXUIEDIT      | 5      | Maximum number of elements in UI edit list. Defined in mjui.h.                         |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjMAXUIRECT      | 15     | Maximum number of UI rectangles. Defined in mjui.h.                                    |
+------------------+--------+----------------------------------------------------------------------------------------+
| mjVERSION_HEADER | 211    | The version of the MuJoCo headers; changes with every release. This is an integer      |
|                  |        | equal to 100x the software version, so 210 corresponds to version 2.1. Defined in      |
|                  |        | mujoco.h. The API function :ref:`mj_version` returns a number with the same meaning    |
|                  |        | but for the compiled library.                                                          |
+------------------+--------+----------------------------------------------------------------------------------------+

.. _API:

API functions
-------------

The main header `mujoco.h <https://github.com/deepmind/mujoco/blob/main/include/mujoco/mujoco.h>`_ exposes a very large number
of functions. However the functions that most users are likely to need are a small fraction. For example,
``simulate.cc`` which is as elaborate as a MuJoCo application is likely to get, calls around 40 of these functions,
while ``basic.cc`` calls around 20. The rest are explosed just in case someone has a use for them. This includes us as
users of MuJoCo -- we do our own work with the public library instead of relying on internal builds.

.. _Activation:

Activation
^^^^^^^^^^

The functions in this section are maintained for backward compatibility with the now-removed activation mechanism.

.. _mj_activate:

mj_activate
~~~~~~~~~~~

.. code-block:: C

   int mj_activate(const char* filename);

Does nothing, returns 1.

.. _mj_deactivate:

mj_deactivate
~~~~~~~~~~~~~

.. code-block:: C

   void mj_deactivate(void);

Does nothing.

.. _Virtualfilesystem:

Virtual file system
^^^^^^^^^^^^^^^^^^^

Virtual file system (VFS) functionality was introduced in MuJoCo 1.50. It enables the user to load all necessary files
in memory, including MJB binary model files, XML files (MJCF, URDF and included files), STL meshes, PNGs for textures
and height fields, and HF files in our custom height field format. Model and resource files in the VFS can also be
constructed programmatically (say using a Python library that writes to memory). Once all desired files are in the VFS,
the user can call :ref:`mj_loadModel` or :ref:`mj_loadXML` with a pointer to the VFS. When this pointer is not NULL, the
loaders will first check the VFS for any file they are about to load, and only access the disk if the file is not found
in the VFS. The file names stored in the VFS have their name and extension but the path information is stripped; this
can be bypassed however by using a custom path symbol in the file names, say "mydir_myfile.xml".

The entire VFS is contained in the data structure :ref:`mjVFS`. All utility functions for maintaining the VFS operate on
this data structure. The common usage pattern is to first clear it with mj_defaultVFS, then add disk files to it with
mj_addFileVFS (which allocates memory buffers and loads the file content in memory), then call mj_loadXML or
mj_loadModel, and then clear everything with mj_deleteVFS.

.. _mj_defaultVFS:

mj_defaultVFS
~~~~~~~~~~~~~

.. code-block:: C

   void mj_defaultVFS(mjVFS* vfs);

Initialize VFS to empty (no deallocation).

.. _mj_addFileVFS:

mj_addFileVFS
~~~~~~~~~~~~~

.. code-block:: C

   int mj_addFileVFS(mjVFS* vfs, const char* directory, const char* filename);

Add file to VFS, return 0: success, 1: full, 2: repeated name, -1: not found on disk.

.. _mj_makeEmptyFileVFS:

mj_makeEmptyFileVFS
~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   int mj_makeEmptyFileVFS(mjVFS* vfs, const char* filename, int filesize);

Make empty file in VFS, return 0: success, 1: full, 2: repeated name.

.. _mj_findFileVFS:

mj_findFileVFS
~~~~~~~~~~~~~~

.. code-block:: C

   int mj_findFileVFS(const mjVFS* vfs, const char* filename);

Return file index in VFS, or -1 if not found in VFS.

.. _mj_deleteFileVFS:

mj_deleteFileVFS
~~~~~~~~~~~~~~~~

.. code-block:: C

   int mj_deleteFileVFS(mjVFS* vfs, const char* filename);

Delete file from VFS, return 0: success, -1: not found in VFS.

.. _mj_deleteVFS:

mj_deleteVFS
~~~~~~~~~~~~

.. code-block:: C

   void mj_deleteVFS(mjVFS* vfs);

Delete all files from VFS.

.. _Parseandcompile:

Parse and compile
^^^^^^^^^^^^^^^^^

The key function here is mj_loadXML. It invokes the built-in parser and compiler, and either returns a pointer to a
valid mjModel, or NULL - in which case the user should check the error information in the user-provided string. The
model and all files referenced in it can be loaded from disk or from a VFS when provided.

.. _mj_loadXML:

mj_loadXML
~~~~~~~~~~

.. code-block:: C

   mjModel* mj_loadXML(const char* filename, const mjVFS* vfs,
                       char* error, int error_sz);

Parse XML file in MJCF or URDF format, compile it, return low-level model. If vfs is not NULL, look up files in vfs
before reading from disk. If error is not NULL, it must have size error_sz.

.. _mj_saveLastXML:

mj_saveLastXML
~~~~~~~~~~~~~~

.. code-block:: C

   int mj_saveLastXML(const char* filename, const mjModel* m,
                      char* error, int error_sz);

Update XML data structures with info from low-level model, save as MJCF. If error is not NULL, it must have size
error_sz.

.. _mj_freeLastXML:

mj_freeLastXML
~~~~~~~~~~~~~~

.. code-block:: C

   void mj_freeLastXML(void);

Free last XML model if loaded. Called internally at each load.

.. _mj_printSchema:

mj_printSchema
~~~~~~~~~~~~~~

.. code-block:: C

   int mj_printSchema(const char* filename, char* buffer, int buffer_sz,
                      int flg_html, int flg_pad);

Print internal XML schema as plain text or HTML, with style-padding or ``&nbsp;``.

.. _Mainsimulation:

Main simulation
^^^^^^^^^^^^^^^

These are the main entry points to the simulator. Most users will only need to call ``mj_step``, which computes
everything and advanced the simulation state by one time step. Controls and applied forces must either be set in advance
(in mjData.ctrl, qfrc_applied and xfrc_applied), or a control callback mjcb_control must be installed which will be
called just before the controls and applied forces are needed. Alternatively, one can use ``mj_step1`` and ``mj_step2``
which break down the simulation pipeline into computations that are executed before and after the controls are needed;
in this way one can set controls that depend on the results from ``mj_step1``. Keep in mind though that the RK4 solver
does not work with mj_step1/2.

mj_forward performs the same computations as ``mj_step`` but without the integration. It is useful after loading or
resetting a model (to put the entire mjData in a valid state), and also for out-of-order computations that involve
sampling or finite-difference approximations.

mj_inverse runs the inverse dynamics, and writes its output in mjData.qfrc_inverse. Note that mjData.qacc must be set
before calling this function. Given the state (qpos, qvel, act), mj_forward maps from force to acceleration, while
mj_inverse maps from acceleration to force. Mathematically these functions are inverse of each other, but numerically
this may not always be the case because the forward dynamics rely on a constraint optimization algorithm which is
usually terminated early. The difference between the results of forward and inverse dynamics can be computed with the
function :ref:`mj_compareFwdInv`, which can be though of as another solver accuracy check (as well as a general sanity
check).

The skip version of mj_forward and mj_inverse are useful for example when qpos was unchanged but qvel was changed
(usually in the context of finite differencing). Then there is no point repeating the computations that only depend on
qpos. Calling the dynamics with skipstage = mjSTAGE_POS will achieve these savings.

.. _mj_step:

mj_step
~~~~~~~

.. code-block:: C

   void mj_step(const mjModel* m, mjData* d);

Advance simulation, use control callback to obtain external force and control.

.. _mj_step1:

mj_step1
~~~~~~~~

.. code-block:: C

   void mj_step1(const mjModel* m, mjData* d);

Advance simulation in two steps: before external force and control is set by user.

.. _mj_step2:

mj_step2
~~~~~~~~

.. code-block:: C

   void mj_step2(const mjModel* m, mjData* d);

Advance simulation in two steps: after external force and control is set by user.

.. _mj_forward:

mj_forward
~~~~~~~~~~

.. code-block:: C

   void mj_forward(const mjModel* m, mjData* d);

Forward dynamics: same as mj_step but do not integrate in time.

.. _mj_inverse:

mj_inverse
~~~~~~~~~~

.. code-block:: C

   void mj_inverse(const mjModel* m, mjData* d);

Inverse dynamics: qacc must be set before calling.

.. _mj_forwardSkip:

mj_forwardSkip
~~~~~~~~~~~~~~

.. code-block:: C

   void mj_forwardSkip(const mjModel* m, mjData* d,
                       int skipstage, int skipsensor);

Forward dynamics with skip; skipstage is mjtStage.

.. _mj_inverseSkip:

mj_inverseSkip
~~~~~~~~~~~~~~

.. code-block:: C

   void mj_inverseSkip(const mjModel* m, mjData* d,
                       int skipstage, int skipsensor);

Inverse dynamics with skip; skipstage is mjtStage.

.. _Initialization:

Initialization
^^^^^^^^^^^^^^

This section contains functions that load/initialize the model or other data structures. Their use is well illustrated
in the code samples.

.. _mj_defaultLROpt:

mj_defaultLROpt
~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_defaultLROpt(mjLROpt* opt);

Set default options for length range computation.

.. _mj_defaultSolRefImp:

mj_defaultSolRefImp
~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_defaultSolRefImp(mjtNum* solref, mjtNum* solimp);

Set solver parameters to default values.

.. _mj_defaultOption:

mj_defaultOption
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_defaultOption(mjOption* opt);

Set physics options to default values.

.. _mj_defaultVisual:

mj_defaultVisual
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_defaultVisual(mjVisual* vis);

Set visual options to default values.

.. _mj_copyModel:

mj_copyModel
~~~~~~~~~~~~

.. code-block:: C

   mjModel* mj_copyModel(mjModel* dest, const mjModel* src);

Copy mjModel, allocate new if dest is NULL.

.. _mj_saveModel:

mj_saveModel
~~~~~~~~~~~~

.. code-block:: C

   void mj_saveModel(const mjModel* m, const char* filename, void* buffer, int buffer_sz);

Save model to binary MJB file or memory buffer; buffer has precedence when given.

.. _mj_loadModel:

mj_loadModel
~~~~~~~~~~~~

.. code-block:: C

   mjModel* mj_loadModel(const char* filename, const mjVFS* vfs);

Load model from binary MJB file. If vfs is not NULL, look up file in vfs before reading from disk.

.. _mj_deleteModel:

mj_deleteModel
~~~~~~~~~~~~~~

.. code-block:: C

   void mj_deleteModel(mjModel* m);

Free memory allocation in model.

.. _mj_sizeModel:

mj_sizeModel
~~~~~~~~~~~~

.. code-block:: C

   int mj_sizeModel(const mjModel* m);

Return size of buffer needed to hold model.

.. _mj_makeData:

mj_makeData
~~~~~~~~~~~

.. code-block:: C

   mjData* mj_makeData(const mjModel* m);

Allocate mjData corresponding to given model.

.. _mj_copyData:

mj_copyData
~~~~~~~~~~~

.. code-block:: C

   mjData* mj_copyData(mjData* dest, const mjModel* m, const mjData* src);

Copy mjData.

.. _mj_resetData:

mj_resetData
~~~~~~~~~~~~

.. code-block:: C

   void mj_resetData(const mjModel* m, mjData* d);

Reset data to defaults.

.. _mj_resetDataDebug:

mj_resetDataDebug
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_resetDataDebug(const mjModel* m, mjData* d, unsigned char debug_value);

Reset data to defaults, fill everything else with debug_value.

.. _mj_resetDataKeyframe:

mj_resetDataKeyframe
~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_resetDataKeyframe(const mjModel* m, mjData* d, int key);

Reset data, set fields from specified keyframe.

.. _mj_stackAlloc:

mj_stackAlloc
~~~~~~~~~~~~~

.. code-block:: C

   mjtNum* mj_stackAlloc(mjData* d, int size);

Allocate array of specified size on mjData stack. Call mju_error on stack overflow.

.. _mj_deleteData:

mj_deleteData
~~~~~~~~~~~~~

.. code-block:: C

   void mj_deleteData(mjData* d);

Free memory allocation in mjData.

.. _mj_resetCallbacks:

mj_resetCallbacks
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_resetCallbacks(void);

Reset all callbacks to NULL pointers (NULL is the default).

.. _mj_setConst:

mj_setConst
~~~~~~~~~~~

.. code-block:: C

   void mj_setConst(mjModel* m, mjData* d);

Set constant fields of mjModel, corresponding to qpos0 configuration.

.. _mj_setLengthRange:

mj_setLengthRange
~~~~~~~~~~~~~~~~~

.. code-block:: C

   int mj_setLengthRange(mjModel* m, mjData* d, int index,
                         const mjLROpt* opt, char* error, int error_sz);

Set actuator_lengthrange for specified actuator; return 1 if ok, 0 if error.

.. _Printing:

Printing
^^^^^^^^

These functions can be used to print various quantities to the screen for debugging purposes.


.. _mj_printFormattedModel:

mj_printFormattedModel
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_printFormattedModel(const mjModel* m, const char* filename, const char* float_format);

Print ``mjModel`` to text file, specifying format. ``float_format`` must be a valid printf-style format string for a
single float value.

.. _mj_printModel:

mj_printModel
~~~~~~~~~~~~~

.. code-block:: C

   void mj_printModel(const mjModel* m, const char* filename);

Print model to text file.

.. _mj_printFormattedData:

mj_printFormattedData
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_printFormattedData(const mjModel* m, mjData* d, const char* filename, const char* float_format);

Print ``mjData`` to text file, specifying format. ``float_format`` must be a valid printf-style format string for a
single float value.

.. _mj_printData:

mj_printData
~~~~~~~~~~~~

.. code-block:: C

   void mj_printData(const mjModel* m, mjData* d, const char* filename);

Print data to text file.

.. _mju_printMat:

mju_printMat
~~~~~~~~~~~~

.. code-block:: C

   void mju_printMat(const mjtNum* mat, int nr, int nc);

Print matrix to screen.

.. _mju_printMatSparse:

mju_printMatSparse
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_printMatSparse(const mjtNum* mat, int nr,
                           const int* rownnz, const int* rowadr,
                           const int* colind);

Print sparse matrix to screen.

.. _Components:

Components
^^^^^^^^^^

These are components of the simulation pipeline, called internally from mj_step, mj_forward and mj_inverse. It is
unlikely that the user will need to call them.

.. _mj_fwdPosition:

mj_fwdPosition
~~~~~~~~~~~~~~

.. code-block:: C

   void mj_fwdPosition(const mjModel* m, mjData* d);

Run position-dependent computations.

.. _mj_fwdVelocity:

mj_fwdVelocity
~~~~~~~~~~~~~~

.. code-block:: C

   void mj_fwdVelocity(const mjModel* m, mjData* d);

Run velocity-dependent computations.

.. _mj_fwdActuation:

mj_fwdActuation
~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_fwdActuation(const mjModel* m, mjData* d);

Compute actuator force qfrc_actuator.

.. _mj_fwdAcceleration:

mj_fwdAcceleration
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_fwdAcceleration(const mjModel* m, mjData* d);

Add up all non-constraint forces, compute qacc_smooth.

.. _mj_fwdConstraint:

mj_fwdConstraint
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_fwdConstraint(const mjModel* m, mjData* d);

Run selected constraint solver.

.. _mj_Euler:

mj_Euler
~~~~~~~~

.. code-block:: C

   void mj_Euler(const mjModel* m, mjData* d);

Euler integrator, semi-implicit in velocity.

.. _mj_RungeKutta:

mj_RungeKutta
~~~~~~~~~~~~~

.. code-block:: C

   void mj_RungeKutta(const mjModel* m, mjData* d, int N);

Runge-Kutta explicit order-N integrator.

.. _mj_invPosition:

mj_invPosition
~~~~~~~~~~~~~~

.. code-block:: C

   void mj_invPosition(const mjModel* m, mjData* d);

Run position-dependent computations in inverse dynamics.

.. _mj_invVelocity:

mj_invVelocity
~~~~~~~~~~~~~~

.. code-block:: C

   void mj_invVelocity(const mjModel* m, mjData* d);

Run velocity-dependent computations in inverse dynamics.

.. _mj_invConstraint:

mj_invConstraint
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_invConstraint(const mjModel* m, mjData* d);

Apply the analytical formula for inverse constraint dynamics.

.. _mj_compareFwdInv:

mj_compareFwdInv
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_compareFwdInv(const mjModel* m, mjData* d);

Compare forward and inverse dynamics, save results in fwdinv.

.. _Subcomponents:

Sub components
^^^^^^^^^^^^^^

These are sub-components of the simulation pipeline, called internally from the components above. It is very unlikely
that the user will need to call them.

.. _mj_sensorPos:

mj_sensorPos
~~~~~~~~~~~~

.. code-block:: C

   void mj_sensorPos(const mjModel* m, mjData* d);

Evaluate position-dependent sensors.

.. _mj_sensorVel:

mj_sensorVel
~~~~~~~~~~~~

.. code-block:: C

   void mj_sensorVel(const mjModel* m, mjData* d);

Evaluate velocity-dependent sensors.

.. _mj_sensorAcc:

mj_sensorAcc
~~~~~~~~~~~~

.. code-block:: C

   void mj_sensorAcc(const mjModel* m, mjData* d);

Evaluate acceleration and force-dependent sensors.

.. _mj_energyPos:

mj_energyPos
~~~~~~~~~~~~

.. code-block:: C

   void mj_energyPos(const mjModel* m, mjData* d);

Evaluate position-dependent energy (potential).

.. _mj_energyVel:

mj_energyVel
~~~~~~~~~~~~

.. code-block:: C

   void mj_energyVel(const mjModel* m, mjData* d);

Evaluate velocity-dependent energy (kinetic).

.. _mj_checkPos:

mj_checkPos
~~~~~~~~~~~

.. code-block:: C

   void mj_checkPos(const mjModel* m, mjData* d);

Check qpos, reset if any element is too big or nan.

.. _mj_checkVel:

mj_checkVel
~~~~~~~~~~~

.. code-block:: C

   void mj_checkVel(const mjModel* m, mjData* d);

Check qvel, reset if any element is too big or nan.

.. _mj_checkAcc:

mj_checkAcc
~~~~~~~~~~~

.. code-block:: C

   void mj_checkAcc(const mjModel* m, mjData* d);

Check qacc, reset if any element is too big or nan.

.. _mj_kinematics:

mj_kinematics
~~~~~~~~~~~~~

.. code-block:: C

   void mj_kinematics(const mjModel* m, mjData* d);

Run forward kinematics.

.. _mj_comPos:

mj_comPos
~~~~~~~~~

.. code-block:: C

   void mj_comPos(const mjModel* m, mjData* d);

Map inertias and motion dofs to global frame centered at CoM.

mj_camlight
~~~~~~~~~~~

.. code-block:: C

   void mj_camlight(const mjModel* m, mjData* d);

Compute camera and light positions and orientations.

mj_tendon
~~~~~~~~~

.. code-block:: C

   void mj_tendon(const mjModel* m, mjData* d);

Compute tendon lengths, velocities and moment arms.

mj_transmission
~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_transmission(const mjModel* m, mjData* d);

Compute actuator transmission lengths and moments.

mj_crb
~~~~~~

.. code-block:: C

   void mj_crb(const mjModel* m, mjData* d);

Run composite rigid body inertia algorithm (CRB).

.. _mj_factorM:

mj_factorM
~~~~~~~~~~

.. code-block:: C

   void mj_factorM(const mjModel* m, mjData* d);

Compute sparse :math:`L^T D L` factorizaton of inertia matrix.

.. _mj_solveM:

mj_solveM
~~~~~~~~~

.. code-block:: C

   void mj_solveM(const mjModel* m, mjData* d, mjtNum* x, const mjtNum* y, int n);

Solve linear system :math:`M x = y` using factorization: :math:`x = (L^T D L)^{-1} y`

.. _mj_solveM2:

mj_solveM2
~~~~~~~~~~

.. code-block:: C

   void mj_solveM2(const mjModel* m, mjData* d, mjtNum* x, const mjtNum* y, int n);

Half of linear solve: :math:`x = \sqrt{D^{-1}} (L^T)^{-1} y`

.. _mj_comVel:

mj_comVel
~~~~~~~~~

.. code-block:: C

   void mj_comVel(const mjModel* m, mjData* d);

Compute cvel, cdof_dot.

mj_passive
~~~~~~~~~~

.. code-block:: C

   void mj_passive(const mjModel* m, mjData* d);

Compute qfrc_passive from spring-dampers, viscosity and density.

.. _mj_subtreeVel:

mj_subtreeVel
~~~~~~~~~~~~~

.. code-block:: C

   void mj_subtreeVel(const mjModel* m, mjData* d);

subtree linear velocity and angular momentum

mj_rne
~~~~~~

.. code-block:: C

   void mj_rne(const mjModel* m, mjData* d, int flg_acc, mjtNum* result);

RNE: compute M(qpos)*qacc + C(qpos,qvel); flg_acc=0 removes inertial term.

.. _mj_rnePostConstraint:

mj_rnePostConstraint
~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_rnePostConstraint(const mjModel* m, mjData* d);

RNE with complete data: compute cacc, cfrc_ext, cfrc_int.

mj_collision
~~~~~~~~~~~~

.. code-block:: C

   void mj_collision(const mjModel* m, mjData* d);

Run collision detection.

.. _mj_makeConstraint:

mj_makeConstraint
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_makeConstraint(const mjModel* m, mjData* d);

Construct constraints.

.. _mj_projectConstraint:

mj_projectConstraint
~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_projectConstraint(const mjModel* m, mjData* d);

Compute inverse constraint inertia efc_AR.

.. _mj_referenceConstraint:

mj_referenceConstraint
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_referenceConstraint(const mjModel* m, mjData* d);

Compute efc_vel, efc_aref.

.. _mj_constraintUpdate:

mj_constraintUpdate
~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_constraintUpdate(const mjModel* m, mjData* d, const mjtNum* jar,
                            mjtNum cost[1], int flg_coneHessian);

Compute efc_state, efc_force, qfrc_constraint, and (optionally) cone Hessians. If cost is not NULL, set \*cost = s(jar)
where jar = Jac*qacc-aref.

.. _Support:

Support
^^^^^^^

These are support functions that need access to mjModel and mjData, unlike the utility functions which do not need such
access. Support functions are called within the simulator but some of them can also be useful for custom computations,
and are documented in more detail below.

.. _mj_addContact:

mj_addContact
~~~~~~~~~~~~~

.. code-block:: C

   int mj_addContact(const mjModel* m, mjData* d, const mjContact* con);

Add contact to d->contact list; return 0 if success; 1 if buffer full.

.. _mj_isPyramidal:

mj_isPyramidal
~~~~~~~~~~~~~~

.. code-block:: C

   int mj_isPyramidal(const mjModel* m);

Determine type of friction cone.

.. _mj_isSparse:

mj_isSparse
~~~~~~~~~~~

.. code-block:: C

   int mj_isSparse(const mjModel* m);

Determine type of constraint Jacobian.

.. _mj_isDual:

mj_isDual
~~~~~~~~~

.. code-block:: C

   int mj_isDual(const mjModel* m);

Determine type of solver (PGS is dual, CG and Newton are primal).

.. _mj_mulJacVec:

mj_mulJacVec
~~~~~~~~~~~~

.. code-block:: C

   void mj_mulJacVec(const mjModel* m, mjData* d,
                     mjtNum* res, const mjtNum* vec);

This function multiplies the constraint Jacobian mjData.efc_J by a vector. Note that the Jacobian can be either dense or
sparse; the function is aware of this setting. Multiplication by J maps velocities from joint space to constraint space.

.. _mj_mulJacTVec:

mj_mulJacTVec
~~~~~~~~~~~~~

.. code-block:: C

   void mj_mulJacTVec(const mjModel* m, mjData* d, mjtNum* res, const mjtNum* vec);

Same as mj_mulJacVec but multiplies by the transpose of the Jacobian. This maps forces from constraint space to joint
space.

.. _mj_jac:

mj_jac
~~~~~~

.. code-block:: C

   void mj_jac(const mjModel* m, const mjData* d,
               mjtNum* jacp, mjtNum* jacr, const mjtNum point[3], int body);

This function computes an "end-effector" Jacobian, which is unrelated to the constraint Jacobian above. Any MuJoCo body
can be treated as end-effector, and the point for which the Jacobian is computed can be anywhere in space (it is treated
as attached to the body). The Jacobian has translational (jacp) and rotational (jacr) components. Passing NULL for
either pointer will skip part of the computation. Each component is a 3-by-nv matrix. Each row of this matrix is the
gradient of the corresponding 3D coordinate of the specified point with respect to the degrees of freedom. The ability
to compute end-effector Jacobians analytically is one of the advantages of working in minimal coordinates - so use it!

.. _mj_jacBody:

mj_jacBody
~~~~~~~~~~

.. code-block:: C

   void mj_jacBody(const mjModel* m, const mjData* d,
                   mjtNum* jacp, mjtNum* jacr, int body);

This and the remaining variants of the Jacobian function call mj_jac internally, with the center of the body, geom or
site. They are just shortcuts; the same can be achieved by calling mj_jac directly.

.. _mj_jacBodyCom:

mj_jacBodyCom
~~~~~~~~~~~~~

.. code-block:: C

   void mj_jacBodyCom(const mjModel* m, const mjData* d,
                      mjtNum* jacp, mjtNum* jacr, int body);

Compute body center-of-mass end-effector Jacobian.

.. _mj_jacSubtreeCom:

mj_jacSubtreeCom
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_jacSubtreeCom(const mjModel* m, mjData* d, mjtNum* jacp, int body);

Compute subtree center-of-mass end-effector Jacobian. ``jacp`` is 3 x nv.

.. _mj_jacGeom:

mj_jacGeom
~~~~~~~~~~

.. code-block:: C

   void mj_jacGeom(const mjModel* m, const mjData* d,
                   mjtNum* jacp, mjtNum* jacr, int geom);

Compute geom end-effector Jacobian.

.. _mj_jacSite:

mj_jacSite
~~~~~~~~~~

.. code-block:: C

   void mj_jacSite(const mjModel* m, const mjData* d,
                   mjtNum* jacp, mjtNum* jacr, int site);

Compute site end-effector Jacobian.

.. _mj_jacPointAxis:

mj_jacPointAxis
~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_jacPointAxis(const mjModel* m, mjData* d,
                        mjtNum* jacPoint, mjtNum* jacAxis,
                        const mjtNum point[3], const mjtNum axis[3], int body);

Compute translation end-effector Jacobian of point, and rotation Jacobian of axis.

.. _mj_name2id:

mj_name2id
~~~~~~~~~~

.. code-block:: C

   int mj_name2id(const mjModel* m, int type, const char* name);

Get id of object with specified name, return -1 if not found; type is mjtObj.

.. _mj_id2name:

mj_id2name
~~~~~~~~~~

.. code-block:: C

   const char* mj_id2name(const mjModel* m, int type, int id);

Get name of object with specified id, return 0 if invalid type or id; type is mjtObj.

.. _mj_fullM:

mj_fullM
~~~~~~~~

.. code-block:: C

   void mj_fullM(const mjModel* m, mjtNum* dst, const mjtNum* M);

Convert sparse inertia matrix M into full (i.e. dense) matrix.

.. _mj_mulM:

mj_mulM
~~~~~~~

.. code-block:: C

   void mj_mulM(const mjModel* m, const mjData* d, mjtNum* res, const mjtNum* vec);

This function multiplies the joint-space inertia matrix stored in mjData.qM by a vector. qM has a custom sparse format
that the user should not attempt to manipulate directly. Alternatively one can convert qM to a dense matrix with
mj_fullM and then user regular matrix-vector multiplication, but this is slower because it no longer benefits from
sparsity.

.. _mj_mulM2:

mj_mulM2
~~~~~~~~

.. code-block:: C

   void mj_mulM2(const mjModel* m, const mjData* d, mjtNum* res, const mjtNum* vec);

Multiply vector by (inertia matrix)^(1/2).

.. _mj_addM:

mj_addM
~~~~~~~

.. code-block:: C

   void mj_addM(const mjModel* m, mjData* d, mjtNum* dst,
                int* rownnz, int* rowadr, int* colind);

Add inertia matrix to destination matrix. Destination can be sparse uncompressed, or dense when all int\* are NULL

.. _mj_applyFT:

mj_applyFT
~~~~~~~~~~

.. code-block:: C

   void mj_applyFT(const mjModel* m, mjData* d,
                   const mjtNum[3] force, const mjtNum[3] torque,
                   const mjtNum[3] point, int body, mjtNum* qfrc_target);

This function can be used to apply a Cartesian force and torque to a point on a body, and add the result to the vector
mjData.qfrc_applied of all applied forces. Note that the function requires a pointer to this vector, because sometimes
we want to add the result to a different vector.

.. _mj_objectVelocity:

mj_objectVelocity
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_objectVelocity(const mjModel* m, const mjData* d,
                          int objtype, int objid, mjtNum[6] res, int flg_local);

Compute object 6D velocity in object-centered frame, world/local orientation.

.. _mj_objectAcceleration:

mj_objectAcceleration
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_objectAcceleration(const mjModel* m, const mjData* d,
                              int objtype, int objid, mjtNum[6] res, int flg_local);

Compute object 6D acceleration in object-centered frame, world/local orientation.

.. _mj_contactForce:

mj_contactForce
~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_contactForce(const mjModel* m, const mjData* d, int id, mjtNum[6] result);

Extract 6D force:torque given contact id, in the contact frame.

.. _mj_differentiatePos:

mj_differentiatePos
~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_differentiatePos(const mjModel* m, mjtNum* qvel, mjtNum dt,
                            const mjtNum* qpos1, const mjtNum* qpos2);

This function subtracts two vectors in the format of qpos (and divides the result by dt), while respecting the
properties of quaternions. Recall that unit quaternions represent spatial orientations. They are points on the unit
sphere in 4D. The tangent to that sphere is a 3D plane of rotational velocities. Thus when we subtract two quaternions
in the right way, the result is a 3D vector and not a 4D vector. This the output qvel has dimensionality nv while the
inputs have dimensionality nq.

.. _mj_integratePos:

mj_integratePos
~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_integratePos(const mjModel* m, mjtNum* qpos, const mjtNum* qvel, mjtNum dt);

This is the opposite of mj_differentiatePos. It adds a vector in the format of qvel (scaled by dt) to a vector in the
format of qpos.

.. _mj_normalizeQuat:

mj_normalizeQuat
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_normalizeQuat(const mjModel* m, mjtNum* qpos);

Normalize all quaternions in qpos-type vector.

.. _mj_local2Global:

mj_local2Global
~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_local2Global(mjData* d, mjtNum[3] xpos, mjtNum[9] xmat,
                        const mjtNum[3] pos, const mjtNum[4] quat,
                        int body, mjtByte sameframe);

Map from body local to global Cartesian coordinates.

.. _mj_getTotalmass:

mj_getTotalmass
~~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mj_getTotalmass(const mjModel* m);

Sum all body masses.

.. _mj_setTotalmass:

mj_setTotalmass
~~~~~~~~~~~~~~~

.. code-block:: C

   void mj_setTotalmass(mjModel* m, mjtNum newmass);

Scale body masses and inertias to achieve specified total mass.

.. _mj_version:

mj_version
~~~~~~~~~~

.. code-block:: C

   int mj_version(void);

Return version number: 1.0.2 is encoded as 102.

.. mj_versionString:

mj_versionString
~~~~~~~~~~~~~~~~

.. code-block:: C

   const char* mj_versionString();

Return the current version of MuJoCo as a null-terminated string.

.. _Raycollisions:

Ray collisions
^^^^^^^^^^^^^^

Ray collision functionality was added in MuJoCo 1.50. This is a new collision detection module that uses analytical
formulas to intersect a ray (p + x*v, x>=0) with a geom, where p is the origin of the ray and v is the vector specifying
the direction. All functions in this family return the distance to the nearest geom surface, or -1 if there is no
intersection. Note that if p is inside a geom, the ray will intersect the surface from the inside which still counts as
an intersection.

All ray collision functions rely on quantities computed by :ref:`mj_kinematics` (see :ref:`mjData`), so must be called
after  :ref:`mj_kinematics`, or functions that call it (e.g. :ref:`mj_fwdPosition`).

.. _mj_ray:

mj_ray
~~~~~~

.. code-block:: C

   mjtNum mj_ray(const mjModel* m, const mjData* d, const mjtNum[3] pnt, const mjtNum[3] vec,
                 const mjtByte* geomgroup, mjtByte flg_static, int bodyexclude,
                 int geomid[1]);

Intersect ray (pnt+x*vec, x>=0) with visible geoms, except geoms in bodyexclude. Return geomid and distance (x) to
nearest surface, or -1 if no intersection.

geomgroup is an array of length mjNGROUP, where 1 means the group should be included. Pass geomgroup=NULL to skip
group exclusion.
If flg_static is 0, static geoms will be excluded.
bodyexclude=-1 can be used to indicate that all bodies are included.

.. _mj_rayHfield:

mj_rayHfield
~~~~~~~~~~~~

.. code-block:: C

   mjtNum mj_rayHfield(const mjModel* m, const mjData* d, int geomid,
                       const mjtNum[3] pnt, const mjtNum[3] vec);

Interect ray with hfield, return nearest distance or -1 if no intersection.

.. _mj_rayMesh:

mj_rayMesh
~~~~~~~~~~

.. code-block:: C

   mjtNum mj_rayMesh(const mjModel* m, const mjData* d, int geomid,
                     const mjtNum[3] pnt, const mjtNum[3] vec);

Interect ray with mesh, return nearest distance or -1 if no intersection.

.. _mju_rayGeom:

mju_rayGeom
~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_rayGeom(const mjtNum[3] pos, const mjtNum[9] mat, const mjtNum[3] size,
                      const mjtNum[3] pnt, const mjtNum[3] vec, int geomtype);

Interect ray with pure geom, return nearest distance or -1 if no intersection.

.. _mju_raySkin:

mju_raySkin
~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_raySkin(int nface, int nvert, const int* face, const float* vert,
                      const mjtNum[3] pnt, const mjtNum[3] vec, int vertid[1]);

Interect ray with skin, return nearest vertex id.

.. _Interaction:

Interaction
^^^^^^^^^^^

These function implement abstract mouse interactions, allowing control over cameras and perturbations. Their use is well
illustrated in ``simulate.cc``.

.. _mjv_defaultCamera:

mjv_defaultCamera
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_defaultCamera(mjvCamera* cam);

Set default camera.

.. _mjv_defaultFreeCamera:

mjv_defaultFreeCamera
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_defaultFreeCamera(const mjModel* m, mjvCamera* cam);

Set default free camera.

.. _mjv_defaultPerturb:

mjv_defaultPerturb
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_defaultPerturb(mjvPerturb* pert);

Set default perturbation.

.. _mjv_room2model:

mjv_room2model
~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_room2model(mjtNum[3] modelpos, mjtNum[4] modelquat, const mjtNum[3] roompos,
                       const mjtNum[4] roomquat, const mjvScene* scn);

Transform pose from room to model space.

.. _mjv_model2room:

mjv_model2room
~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_model2room(mjtNum[3] roompos, mjtNum[4] roomquat, const mjtNum[3] modelpos,
                       const mjtNum[4] modelquat, const mjvScene* scn);

Transform pose from model to room space.

.. _mjv_cameraInModel:

mjv_cameraInModel
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_cameraInModel(mjtNum[3] headpos, mjtNum[3] forward, mjtNum[3] up,
                          const mjvScene* scn);

Get camera info in model space; average left and right OpenGL cameras.

.. _mjv_cameraInRoom:

mjv_cameraInRoom
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_cameraInRoom(mjtNum[3] headpos, mjtNum[3] forward, mjtNum[3] up,
                         const mjvScene* scn);

Get camera info in room space; average left and right OpenGL cameras.

.. _mjv_frustumHeight:

mjv_frustumHeight
~~~~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mjv_frustumHeight(const mjvScene* scn);

Get frustum height at unit distance from camera; average left and right OpenGL cameras.

.. _mjv_alignToCamera:

mjv_alignToCamera
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_alignToCamera(mjtNum[3] res, const mjtNum[3] vec, const mjtNum[3] forward);

Rotate 3D vec in horizontal plane by angle between (0,1) and (forward_x,forward_y).

.. _mjv_moveCamera:

mjv_moveCamera
~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_moveCamera(const mjModel* m, int action, mjtNum reldx, mjtNum reldy,
                       const mjvScene* scn, mjvCamera* cam);

Move camera with mouse; action is mjtMouse.

.. _mjv_movePerturb:

mjv_movePerturb
~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_movePerturb(const mjModel* m, const mjData* d, int action, mjtNum reldx,
                        mjtNum reldy, const mjvScene* scn, mjvPerturb* pert);

Move perturb object with mouse; action is mjtMouse.

.. _mjv_moveModel:

mjv_moveModel
~~~~~~~~~~~~~

.. code-block:: C

   void mjv_moveModel(const mjModel* m, int action, mjtNum reldx, mjtNum reldy,
                      const mjtNum roomup[3], mjvScene* scn);

Move model with mouse; action is mjtMouse.

.. _mjv_initPerturb:

mjv_initPerturb
~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_initPerturb(const mjModel* m, const mjData* d,
                        const mjvScene* scn, mjvPerturb* pert);

Copy perturb pos,quat from selected body; set scale for perturbation.

.. _mjv_applyPerturbPose:

mjv_applyPerturbPose
~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_applyPerturbPose(const mjModel* m, mjData* d, const mjvPerturb* pert,
                             int flg_paused);

Set perturb pos,quat in d->mocap when selected body is mocap, and in d->qpos otherwise. Write d->qpos only if flg_paused
and subtree root for selected body has free joint.

.. _mjv_applyPerturbForce:

mjv_applyPerturbForce
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_applyPerturbForce(const mjModel* m, mjData* d, const mjvPerturb* pert);

Set perturb force,torque in d->xfrc_applied, if selected body is dynamic.

.. _mjv_averageCamera:

mjv_averageCamera
~~~~~~~~~~~~~~~~~

.. code-block:: C

   mjvGLCamera mjv_averageCamera(const mjvGLCamera* cam1, const mjvGLCamera* cam2);

Return the average of two OpenGL cameras.

.. _mjv_select:

mjv_select
~~~~~~~~~~

.. code-block:: C

   int mjv_select(const mjModel* m, const mjData* d, const mjvOption* vopt,
                  mjtNum aspectratio, mjtNum relx, mjtNum rely,
                  const mjvScene* scn, mjtNum[3] selpnt, int geomid[1], int skinid[1]);

This function is used for mouse selection. Previously selection was done via OpenGL, but as of MuJoCo 1.50 it relies on
ray intersections which are much more efficient. aspectratio is the viewport width/height. relx and rely are the
relative coordinates of the 2D point of interest in the viewport (usually mouse cursor). The function returns the id of
the geom under the specified 2D point, or -1 if there is no geom (note that they skybox if present is not a model geom).
The 3D coordinates of the clicked point are returned in selpnt. See ``simulate.cc`` for an illustration.

.. _Visualization-api:

Visualization
^^^^^^^^^^^^^

The functions in this section implement abstract visualization. The results are used by the OpenGL rendered, and can
also be used by users wishing to implement their own rendered, or hook up MuJoCo to advanced rendering tools such as
Unity or Unreal Engine. See ``simulate.cc`` for illustration of how to use these functions.

.. _mjv_defaultOption:

mjv_defaultOption
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_defaultOption(mjvOption* opt);

Set default visualization options.

.. _mjv_defaultFigure:

mjv_defaultFigure
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_defaultFigure(mjvFigure* fig);

Set default figure.

.. _mjv_initGeom:

mjv_initGeom
~~~~~~~~~~~~

.. code-block:: C

   void mjv_initGeom(mjvGeom* geom, int type, const mjtNum[3] size,
                     const mjtNum[3] pos, const mjtNum[9] mat, const float[4] rgba);

Initialize given geom fields when not NULL, set the rest to their default values.

.. _mjv_makeConnector:

mjv_makeConnector
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_makeConnector(mjvGeom* geom, int type, mjtNum width,
                          mjtNum a0, mjtNum a1, mjtNum a2,
                          mjtNum b0, mjtNum b1, mjtNum b2);

Set (type, size, pos, mat) for connector-type geom between given points. Assume that mjv_initGeom was already called to
set all other properties.

.. _mjv_defaultScene:

mjv_defaultScene
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_defaultScene(mjvScene* scn);

Set default abstract scene.

.. _mjv_makeScene:

mjv_makeScene
~~~~~~~~~~~~~

.. code-block:: C

   void mjv_makeScene(const mjModel* m, mjvScene* scn, int maxgeom);

Allocate resources in abstract scene.

.. _mjv_freeScene:

mjv_freeScene
~~~~~~~~~~~~~

.. code-block:: C

   void mjv_freeScene(mjvScene* scn);

Free abstract scene.

.. _mjv_updateScene:

mjv_updateScene
~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_updateScene(const mjModel* m, mjData* d, const mjvOption* opt,
                        const mjvPerturb* pert, mjvCamera* cam, int catmask, mjvScene* scn);

Update entire scene given model state.

.. _mjv_addGeoms:

mjv_addGeoms
~~~~~~~~~~~~

.. code-block:: C

   void mjv_addGeoms(const mjModel* m, mjData* d, const mjvOption* opt,
                     const mjvPerturb* pert, int catmask, mjvScene* scn);

Add geoms from selected categories.

.. _mjv_makeLights:

mjv_makeLights
~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_makeLights(const mjModel* m, mjData* d, mjvScene* scn);

Make list of lights.

.. _mjv_updateCamera:

mjv_updateCamera
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_updateCamera(const mjModel* m, mjData* d, mjvCamera* cam, mjvScene* scn);

Update camera.

.. _mjv_updateSkin:

mjv_updateSkin
~~~~~~~~~~~~~~

.. code-block:: C

   void mjv_updateSkin(const mjModel* m, mjData* d, mjvScene* scn);

Update skins.

.. _OpenGLrendering:

OpenGL rendering
^^^^^^^^^^^^^^^^

These functions expose the OpenGL renderer. See ``simulate.cc`` for illustration of how to use these functions.

.. _mjr_defaultContext:

mjr_defaultContext
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_defaultContext(mjrContext* con);

Set default mjrContext.

.. _mjr_makeContext:

mjr_makeContext
~~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_makeContext(const mjModel* m, mjrContext* con, int fontscale);

Allocate resources in custom OpenGL context; fontscale is mjtFontScale.

.. _mjr_changeFont:

mjr_changeFont
~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_changeFont(int fontscale, mjrContext* con);

Change font of existing context.

.. _mjr_addAux:

mjr_addAux
~~~~~~~~~~

.. code-block:: C

   void mjr_addAux(int index, int width, int height, int samples, mjrContext* con);

Add Aux buffer with given index to context; free previous Aux buffer.

.. _mjr_freeContext:

mjr_freeContext
~~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_freeContext(mjrContext* con);

Free resources in custom OpenGL context, set to default.

.. _mjr_uploadTexture:

mjr_uploadTexture
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_uploadTexture(const mjModel* m, const mjrContext* con, int texid);

Upload texture to GPU, overwriting previous upload if any.

.. _mjr_uploadMesh:

mjr_uploadMesh
~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_uploadMesh(const mjModel* m, const mjrContext* con, int meshid);

Upload mesh to GPU, overwriting previous upload if any.

.. _mjr_uploadHField:

mjr_uploadHField
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_uploadHField(const mjModel* m, const mjrContext* con, int hfieldid);

Upload height field to GPU, overwriting previous upload if any.

.. _mjr_restoreBuffer:

mjr_restoreBuffer
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_restoreBuffer(const mjrContext* con);

Make con->currentBuffer current again.

.. _mjr_setBuffer:

mjr_setBuffer
~~~~~~~~~~~~~

.. code-block:: C

   void mjr_setBuffer(int framebuffer, mjrContext* con);

Set OpenGL framebuffer for rendering: mjFB_WINDOW or mjFB_OFFSCREEN. If only one buffer is available, set that buffer
and ignore framebuffer argument.

.. _mjr_readPixels:

mjr_readPixels
~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_readPixels(unsigned char* rgb, float* depth,
                       mjrRect viewport, const mjrContext* con);

Read pixels from current OpenGL framebuffer to client buffer. Viewport is in OpenGL framebuffer; client buffer starts at
(0,0).

.. _mjr_drawPixels:

mjr_drawPixels
~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_drawPixels(const unsigned char* rgb, const float* depth,
                       mjrRect viewport, const mjrContext* con);

Draw pixels from client buffer to current OpenGL framebuffer. Viewport is in OpenGL framebuffer; client buffer starts at
(0,0).

.. _mjr_blitBuffer:

mjr_blitBuffer
~~~~~~~~~~~~~~

.. code-block:: C

   void mjr_blitBuffer(mjrRect src, mjrRect dst,
                       int flg_color, int flg_depth, const mjrContext* con);

Blit from src viewpoint in current framebuffer to dst viewport in other framebuffer. If src, dst have different size and
flg_depth==0, color is interpolated with GL_LINEAR.

.. _mjr_setAux:

mjr_setAux
~~~~~~~~~~

.. code-block:: C

   void mjr_setAux(int index, const mjrContext* con);

Set Aux buffer for custom OpenGL rendering (call restoreBuffer when done).

.. _mjr_blitAux:

mjr_blitAux
~~~~~~~~~~~

.. code-block:: C

   void mjr_blitAux(int index, mjrRect src, int left, int bottom,
                    const mjrContext* con);

Blit from Aux buffer to con->currentBuffer.

.. _mjr_text:

mjr_text
~~~~~~~~

.. code-block:: C

   void mjr_text(int font, const char* txt, const mjrContext* con,
                 float x, float y, float r, float g, float b);

Draw text at (x,y) in relative coordinates; font is mjtFont.

.. _mjr_overlay:

mjr_overlay
~~~~~~~~~~~

.. code-block:: C

   void mjr_overlay(int font, int gridpos, mjrRect viewport,
                    const char* overlay, const char* overlay2, const mjrContext* con);

Draw text overlay; font is mjtFont; gridpos is mjtGridPos.

.. _mjr_maxViewport:

mjr_maxViewport
~~~~~~~~~~~~~~~

.. code-block:: C

   mjrRect mjr_maxViewport(const mjrContext* con);

Get maximum viewport for active buffer.

.. _mjr_rectangle:

mjr_rectangle
~~~~~~~~~~~~~

.. code-block:: C

   void mjr_rectangle(mjrRect viewport, float r, float g, float b, float a);

Draw rectangle.

.. _mjr_label:

mjr_label
~~~~~~~~~~~~~

.. code-block:: C

   void mjr_label(mjrRect viewport, int font, const char* txt,
                  float r, float g, float b, float a, float rt, float gt, float bt,
                  const mjrContext* con);

Draw rectangle with centered text.

.. _mjr_figure:

mjr_figure
~~~~~~~~~~

.. code-block:: C

   void mjr_figure(mjrRect viewport, mjvFigure* fig, const mjrContext* con);

Draw 2D figure.

.. _mjr_render:

mjr_render
~~~~~~~~~~

.. code-block:: C

   void mjr_render(mjrRect viewport, mjvScene* scn, const mjrContext* con);

Render 3D scene.

.. _mjr_finish:

mjr_finish
~~~~~~~~~~

.. code-block:: C

   void mjr_finish(void);

Call glFinish.

.. _mjr_getError:

mjr_getError
~~~~~~~~~~~~

.. code-block:: C

   int mjr_getError(void);

Call glGetError and return result.

.. _mjr_findRect:

mjr_findRect
~~~~~~~~~~~~

.. code-block:: C

   int mjr_findRect(int x, int y, int nrect, const mjrRect* rect);

Find first rectangle containing mouse, -1: not found.

.. _UIframework:

UI framework
^^^^^^^^^^^^

.. _mjui_themeSpacing:

mjui_themeSpacing
~~~~~~~~~~~~~~~~~

.. code-block:: C

   mjuiThemeSpacing mjui_themeSpacing(int ind);

Get builtin UI theme spacing (ind: 0-1).

.. _mjui_themeColor:

mjui_themeColor
~~~~~~~~~~~~~~~

.. code-block:: C

   mjuiThemeColor mjui_themeColor(int ind);

Get builtin UI theme color (ind: 0-3).

mjui_add
~~~~~~~~

.. code-block:: C

   void mjui_add(mjUI* ui, const mjuiDef* def);

Add definitions to UI.

mjui_addToSection
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjui_addToSection(mjUI* ui, int sect, const mjuiDef* def);

Add definitions to UI section.

mjui_resize
~~~~~~~~~~~

.. code-block:: C

   void mjui_resize(mjUI* ui, const mjrContext* con);

Compute UI sizes.

.. _mjui_update:

mjui_update
~~~~~~~~~~~

.. code-block:: C

   void mjui_update(int section, int item, const mjUI* ui,
                    const mjuiState* state, const mjrContext* con);

Update specific section/item; -1: update all.

mjui_event
~~~~~~~~~~

.. code-block:: C

   mjuiItem* mjui_event(mjUI* ui, mjuiState* state, const mjrContext* con);

Handle UI event, return pointer to changed item, NULL if no change.

mjui_render
~~~~~~~~~~~

.. code-block:: C

   void mjui_render(mjUI* ui, const mjuiState* state, const mjrContext* con);

Copy UI image to current buffer.

.. _Errorandmemory:

Error and memory
^^^^^^^^^^^^^^^^

.. _mju_error:

mju_error
~~~~~~~~~

.. code-block:: C

   void mju_error(const char* msg);

Main error function; does not return to caller.

.. _mju_error_i:

mju_error_i
~~~~~~~~~~~

.. code-block:: C

   void mju_error_i(const char* msg, int i);

Error function with int argument; msg is a printf format string.

.. _mju_error_s:

mju_error_s
~~~~~~~~~~~

.. code-block:: C

   void mju_error_s(const char* msg, const char* text);

Error function with string argument.

.. _mju_warning:

mju_warning
~~~~~~~~~~~

.. code-block:: C

   void mju_warning(const char* msg);

Main warning function; returns to caller.

mju_warning_i
~~~~~~~~~~~~~

.. code-block:: C

   void mju_warning_i(const char* msg, int i);

Warning function with int argument.

mju_warning_s
~~~~~~~~~~~~~

.. code-block:: C

   void mju_warning_s(const char* msg, const char* text);

Warning function with string argument.

.. _mju_clearHandlers:

mju_clearHandlers
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_clearHandlers(void);

Clear user error and memory handlers.

.. _mju_malloc:

mju_malloc
~~~~~~~~~~

.. code-block:: C

   void* mju_malloc(size_t size);

Allocate memory; byte-align on 64; pad size to multiple of 64.

.. _mju_free:

mju_free
~~~~~~~~

.. code-block:: C

   void mju_free(void* ptr);

Free memory, using free() by default.

.. _mj_warning:

mj_warning
~~~~~~~~~~

.. code-block:: C

   void mj_warning(mjData* d, int warning, int info);

High-level warning function: count warnings in mjData, print only the first.

.. _mju_writeLog:

mju_writeLog
~~~~~~~~~~~~

.. code-block:: C

   void mju_writeLog(const char* type, const char* msg);

Write [datetime, type: message] to MUJOCO_LOG.TXT.

.. _Standardmath:

Standard math
^^^^^^^^^^^^^

The "functions" in this section are preprocessor macros replaced with the corresponding C standard library math
functions. When MuJoCo is compiled with single precision (which is not currently available to the public, but we
sometimes use it internally) these macros are replaced with the corresponding single-precision functions (not shown
here). So one can think of them as having inputs and outputs of type mjtNum, where mjtNum is defined as double or float
depending on how MuJoCo is compiled. We will not document these functions here; see the C standard library
specification.

mju_sqrt
~~~~~~~~

.. code-block:: C

   #define mju_sqrt    sqrt

mju_exp
~~~~~~~

.. code-block:: C

   #define mju_exp     exp

mju_sin
~~~~~~~

.. code-block:: C

   #define mju_sin     sin

mju_cos
~~~~~~~

.. code-block:: C

   #define mju_cos     cos

mju_tan
~~~~~~~

.. code-block:: C

   #define mju_tan     tan

mju_asin
~~~~~~~~

.. code-block:: C

   #define mju_asin    asin

mju_acos
~~~~~~~~

.. code-block:: C

   #define mju_acos    acos

mju_atan2
~~~~~~~~~

.. code-block:: C

   #define mju_atan2   atan2

mju_tanh
~~~~~~~~

.. code-block:: C

   #define mju_tanh    tanh

mju_pow
~~~~~~~

.. code-block:: C

   #define mju_pow     pow

mju_abs
~~~~~~~

.. code-block:: C

   #define mju_abs     fabs

mju_log
~~~~~~~

.. code-block:: C

   #define mju_log     log

mju_log10
~~~~~~~~~

.. code-block:: C

   #define mju_log10   log10

mju_floor
~~~~~~~~~

.. code-block:: C

   #define mju_floor   floor

mju_ceil
~~~~~~~~

.. code-block:: C

   #define mju_ceil    ceil

.. _Vectormath:

Vector math
^^^^^^^^^^^

mju_zero3
~~~~~~~~~

.. code-block:: C

   void mju_zero3(mjtNum res[3]);

Set res = 0.

mju_copy3
~~~~~~~~~

.. code-block:: C

   void mju_copy3(mjtNum res[3], const mjtNum data[3]);

Set res = vec.

mju_scl3
~~~~~~~~

.. code-block:: C

   void mju_scl3(mjtNum res[3], const mjtNum vec[3], mjtNum scl);

Set res = vec*scl.

mju_add3
~~~~~~~~

.. code-block:: C

   void mju_add3(mjtNum res[3], const mjtNum vec1[3], const mjtNum vec2[3]);

Set res = vec1 + vec2.

mju_sub3
~~~~~~~~

.. code-block:: C

   void mju_sub3(mjtNum res[3], const mjtNum vec1[3], const mjtNum vec2[3]);

Set res = vec1 - vec2.

.. _mju_addTo3:

mju_addTo3
~~~~~~~~~~

.. code-block:: C

   void mju_addTo3(mjtNum res[3], const mjtNum vec[3]);

Set res = res + vec.

.. _mju_subFrom3:

mju_subFrom3
~~~~~~~~~~~~

.. code-block:: C

   void mju_subFrom3(mjtNum res[3], const mjtNum vec[3]);

Set res = res - vec.

.. _mju_addToScl3:

mju_addToScl3
~~~~~~~~~~~~~

.. code-block:: C

   void mju_addToScl3(mjtNum res[3], const mjtNum vec[3], mjtNum scl);

Set res = res + vec*scl.

.. _mju_addScl3:

mju_addScl3
~~~~~~~~~~~

.. code-block:: C

   void mju_addScl3(mjtNum res[3], const mjtNum vec1[3], const mjtNum vec2[3], mjtNum scl);

Set res = vec1 + vec2*scl.

mju_normalize3
~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_normalize3(mjtNum res[3]);

Normalize vector, return length before normalization.

mju_norm3
~~~~~~~~~

.. code-block:: C

   mjtNum mju_norm3(const mjtNum vec[3]);

Return vector length (without normalizing the vector).

mju_dot3
~~~~~~~~

.. code-block:: C

   mjtNum mju_dot3(const mjtNum vec1[3], const mjtNum vec2[3]);

Return dot-product of vec1 and vec2.

mju_dist3
~~~~~~~~~

.. code-block:: C

   mjtNum mju_dist3(const mjtNum pos1[3], const mjtNum pos2[3]);

Return Cartesian distance between 3D vectors pos1 and pos2.

.. _mju_rotVecMat:

mju_rotVecMat
~~~~~~~~~~~~~

.. code-block:: C

   void mju_rotVecMat(mjtNum res[3], const mjtNum vec[3], const mjtNum mat[9]);

Multiply vector by 3D rotation matrix: res = mat \* vec.

.. _mju_rotVecMatT:

mju_rotVecMatT
~~~~~~~~~~~~~~

.. code-block:: C

   void mju_rotVecMatT(mjtNum res[3], const mjtNum vec[3], const mjtNum mat[9]);

Multiply vector by transposed 3D rotation matrix: res = mat' \* vec.

mju_cross
~~~~~~~~~

.. code-block:: C

   void mju_cross(mjtNum res[3], const mjtNum a[3], const mjtNum b[3]);

Compute cross-product: res = cross(a, b).

mju_zero4
~~~~~~~~~

.. code-block:: C

   void mju_zero4(mjtNum res[4]);

Set res = 0.

mju_unit4
~~~~~~~~~

.. code-block:: C

   void mju_unit4(mjtNum res[4]);

Set res = (1,0,0,0).

mju_copy4
~~~~~~~~~

.. code-block:: C

   void mju_copy4(mjtNum res[4], const mjtNum data[4]);

Set res = vec.

mju_normalize4
~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_normalize4(mjtNum res[4]);

Normalize vector, return length before normalization.

mju_zero
~~~~~~~~

.. code-block:: C

   void mju_zero(mjtNum* res, int n);

Set res = 0.

mju_copy
~~~~~~~~

.. code-block:: C

   void mju_copy(mjtNum* res, const mjtNum* data, int n);

Set res = vec.

mju_sum
~~~~~~~

.. code-block:: C

   mjtNum mju_sum(const mjtNum* vec, int n);

Return sum(vec).

.. _mju_L1:

mju_L1
~~~~~~

.. code-block:: C

   mjtNum mju_L1(const mjtNum* vec, int n);

Return L1 norm: sum(abs(vec)).

.. _mju_scl:

mju_scl
~~~~~~~

.. code-block:: C

   void mju_scl(mjtNum* res, const mjtNum* vec, mjtNum scl, int n);

Set res = vec*scl.

mju_add
~~~~~~~

.. code-block:: C

   void mju_add(mjtNum* res, const mjtNum* vec1, const mjtNum* vec2, int n);

Set res = vec1 + vec2.

mju_sub
~~~~~~~

.. code-block:: C

   void mju_sub(mjtNum* res, const mjtNum* vec1, const mjtNum* vec2, int n);

Set res = vec1 - vec2.

.. _mju_addTo:

mju_addTo
~~~~~~~~~

.. code-block:: C

   void mju_addTo(mjtNum* res, const mjtNum* vec, int n);

Set res = res + vec.

.. _mju_subFrom:

mju_subFrom
~~~~~~~~~~~

.. code-block:: C

   void mju_subFrom(mjtNum* res, const mjtNum* vec, int n);

Set res = res - vec.

.. _mju_addToScl:

mju_addToScl
~~~~~~~~~~~~

.. code-block:: C

   void mju_addToScl(mjtNum* res, const mjtNum* vec, mjtNum scl, int n);

Set res = res + vec*scl.

.. _mju_addScl:

mju_addScl
~~~~~~~~~~

.. code-block:: C

   void mju_addScl(mjtNum* res, const mjtNum* vec1, const mjtNum* vec2, mjtNum scl, int n);

Set res = vec1 + vec2*scl.

mju_normalize
~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_normalize(mjtNum* res, int n);

Normalize vector, return length before normalization.

mju_norm
~~~~~~~~

.. code-block:: C

   mjtNum mju_norm(const mjtNum* res, int n);

Return vector length (without normalizing vector).

mju_dot
~~~~~~~

.. code-block:: C

   mjtNum mju_dot(const mjtNum* vec1, const mjtNum* vec2, const int n);

Return dot-product of vec1 and vec2.

.. _mju_mulMatVec:

mju_mulMatVec
~~~~~~~~~~~~~

.. code-block:: C

   void mju_mulMatVec(mjtNum* res, const mjtNum* mat, const mjtNum* vec,
                      int nr, int nc);

Multiply matrix and vector: res = mat \* vec.

.. _mju_mulMatTVec:

mju_mulMatTVec
~~~~~~~~~~~~~~

.. code-block:: C

   void mju_mulMatTVec(mjtNum* res, const mjtNum* mat, const mjtNum* vec,
                       int nr, int nc);

Multiply transposed matrix and vector: res = mat' \* vec.

mju_transpose
~~~~~~~~~~~~~

.. code-block:: C

   void mju_transpose(mjtNum* res, const mjtNum* mat, int nr, int nc);

Transpose matrix: res = mat'.

.. _mju_mulMatMat:

mju_mulMatMat
~~~~~~~~~~~~~

.. code-block:: C

   void mju_mulMatMat(mjtNum* res, const mjtNum* mat1, const mjtNum* mat2,
                      int r1, int c1, int c2);

Multiply matrices: res = mat1 \* mat2.

.. _mju_mulMatMatT:

mju_mulMatMatT
~~~~~~~~~~~~~~

.. code-block:: C

   void mju_mulMatMatT(mjtNum* res, const mjtNum* mat1, const mjtNum* mat2,
                       int r1, int c1, int r2);

Multiply matrices, second argument transposed: res = mat1 \* mat2'.

.. _mju_mulMatTMat:

mju_mulMatTMat
~~~~~~~~~~~~~~

.. code-block:: C

   void mju_mulMatTMat(mjtNum* res, const mjtNum* mat1, const mjtNum* mat2,
                       int r1, int c1, int c2);

Multiply matrices, first argument transposed: res = mat1' \* mat2.

.. _mju_sqrMatTD:

mju_sqrMatTD
~~~~~~~~~~~~

.. code-block:: C

   void mju_sqrMatTD(mjtNum* res, const mjtNum* mat, const mjtNum* diag, int nr, int nc);

Set res = mat' \* diag \* mat if diag is not NULL, and res = mat' \* mat otherwise.

.. _mju_transformSpatial:

mju_transformSpatial
~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_transformSpatial(mjtNum res[6], const mjtNum vec[6], int flg_force,
                             const mjtNum newpos[3], const mjtNum oldpos[3],
                             const mjtNum rotnew2old[9]);

Coordinate transform of 6D motion or force vector in rotation:translation format. rotnew2old is 3-by-3, NULL means no
rotation; flg_force specifies force or motion type.

.. _Quaternions:

Quaternions
^^^^^^^^^^^

.. _mju_rotVecQuat:

mju_rotVecQuat
~~~~~~~~~~~~~~

.. code-block:: C

   void mju_rotVecQuat(mjtNum res[3], const mjtNum vec[3], const mjtNum quat[4]);

Rotate vector by quaternion.

.. _mju_negQuat:

mju_negQuat
~~~~~~~~~~~

.. code-block:: C

   void mju_negQuat(mjtNum res[4], const mjtNum quat[4]);

Negate quaternion.

.. _mju_mulQuat:

mju_mulQuat
~~~~~~~~~~~

.. code-block:: C

   void mju_mulQuat(mjtNum res[4], const mjtNum quat1[4], const mjtNum quat2[4]);

Multiply quaternions.

.. _mju_mulQuatAxis:

mju_mulQuatAxis
~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_mulQuatAxis(mjtNum res[4], const mjtNum quat[4], const mjtNum axis[3]);

Multiply quaternion and axis.

.. _mju_axisAngle2Quat:

mju_axisAngle2Quat
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_axisAngle2Quat(mjtNum res[4], const mjtNum axis[3], mjtNum angle);

Convert axisAngle to quaternion.

.. _mju_quat2Vel:

mju_quat2Vel
~~~~~~~~~~~~

.. code-block:: C

   void mju_quat2Vel(mjtNum res[3], const mjtNum quat[4], mjtNum dt);

Convert quaternion (corresponding to orientation difference) to 3D velocity.

.. _mju_subQuat:

mju_subQuat
~~~~~~~~~~~

.. code-block:: C

   void mju_subQuat(mjtNum res[3], const mjtNum qa[4], const mjtNum qb[4]);

Subtract quaternions, express as 3D velocity: qb*quat(res) = qa.

.. _mju_quat2Mat:

mju_quat2Mat
~~~~~~~~~~~~

.. code-block:: C

   void mju_quat2Mat(mjtNum res[9], const mjtNum quat[4]);

Convert quaternion to 3D rotation matrix.

.. _mju_mat2Quat:

mju_mat2Quat
~~~~~~~~~~~~

.. code-block:: C

   void mju_mat2Quat(mjtNum quat[4], const mjtNum mat[9]);

Convert 3D rotation matrix to quaternion.

.. _mju_derivQuat:

mju_derivQuat
~~~~~~~~~~~~~

.. code-block:: C

   void mju_derivQuat(mjtNum res[4], const mjtNum quat[4], const mjtNum vel[3]);

Compute time-derivative of quaternion, given 3D rotational velocity.

.. _mju_quatIntegrate:

mju_quatIntegrate
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_quatIntegrate(mjtNum quat[4], const mjtNum vel[3], mjtNum scale);

Integrate quaternion given 3D angular velocity.

.. _mju_quatZ2Vec:

mju_quatZ2Vec
~~~~~~~~~~~~~

.. code-block:: C

   void mju_quatZ2Vec(mjtNum quat[4], const mjtNum vec[3]);

Construct quaternion performing rotation from z-axis to given vector.

.. _Poses:

Poses
^^^^^

.. _mju_mulPose:

mju_mulPose
~~~~~~~~~~~

.. code-block:: C

   void mju_mulPose(mjtNum posres[3], mjtNum quatres[4],
                    const mjtNum pos1[3], const mjtNum quat1[4],
                    const mjtNum pos2[3], const mjtNum quat2[4]);

Multiply two poses.

.. _mju_negPose:

mju_negPose
~~~~~~~~~~~

.. code-block:: C

   void mju_negPose(mjtNum posres[3], mjtNum quatres[4],
                    const mjtNum pos[3], const mjtNum quat[4]);

Negate pose.

.. _mju_trnVecPose:

mju_trnVecPose
~~~~~~~~~~~~~~

.. code-block:: C

   void mju_trnVecPose(mjtNum res[3], const mjtNum pos[3], const mjtNum quat[4],
                       const mjtNum vec[3]);

Transform vector by pose.

.. _Decompositions:

Decompositions
^^^^^^^^^^^^^^

.. _mju_cholFactor:

mju_cholFactor
~~~~~~~~~~~~~~

.. code-block:: C

   int mju_cholFactor(mjtNum* mat, int n, mjtNum mindiag);

Cholesky decomposition: mat = L*L'; return rank, decomposition performed in-place into mat.

.. _mju_cholSolve:

mju_cholSolve
~~~~~~~~~~~~~

.. code-block:: C

   void mju_cholSolve(mjtNum* res, const mjtNum* mat, const mjtNum* vec, int n);

Solve mat \* res = vec, where mat is Cholesky-factorized

.. _mju_cholUpdate:

mju_cholUpdate
~~~~~~~~~~~~~~

.. code-block:: C

   int mju_cholUpdate(mjtNum* mat, mjtNum* x, int n, int flg_plus);

Cholesky rank-one update: L*L' +/- x*x'; return rank.

mju_eig3
~~~~~~~~

.. code-block:: C

   int mju_eig3(mjtNum[3] eigval, mjtNum[9] eigvec, mjtNum[4] quat, const mjtNum[9] mat);

Eigenvalue decomposition of symmetric 3x3 matrix.

.. _Miscellaneous:

Miscellaneous
^^^^^^^^^^^^^

.. _mju_muscleGain:

mju_muscleGain
~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_muscleGain(mjtNum len, mjtNum vel, const mjtNum lengthrange[2],
                         mjtNum acc0, const mjtNum prm[9]);

Muscle active force, prm = (range[2], force, scale, lmin, lmax, vmax, fpmax, fvmax).

.. _mju_muscleBias:

mju_muscleBias
~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_muscleBias(mjtNum len, const mjtNum lengthrange[2],
                         mjtNum acc0, const mjtNum prm[9]);

Muscle passive force, prm = (range[2], force, scale, lmin, lmax, vmax, fpmax, fvmax).

.. _mju_muscleDynamics:

mju_muscleDynamics
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_muscleDynamics(mjtNum ctrl, mjtNum act, const mjtNum prm[2]);

Muscle activation dynamics, prm = (tau_act, tau_deact).

.. _mju_encodePyramid:

mju_encodePyramid
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_encodePyramid(mjtNum* pyramid, const mjtNum* force,
                          const mjtNum* mu, int dim);

Convert contact force to pyramid representation.

.. _mju_decodePyramid:

mju_decodePyramid
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_decodePyramid(mjtNum* force, const mjtNum* pyramid,
                          const mjtNum* mu, int dim);

Convert pyramid representation to contact force.

.. _mju_springDamper:

mju_springDamper
~~~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_springDamper(mjtNum pos0, mjtNum vel0, mjtNum Kp, mjtNum Kv, mjtNum dt);

Integrate spring-damper analytically, return pos(dt).

.. _mju_min:

mju_min
~~~~~~~

.. code-block:: C

   mjtNum mju_min(mjtNum a, mjtNum b);

Return min(a,b) with single evaluation of a and b.

.. _mju_max:

mju_max
~~~~~~~

.. code-block:: C

   mjtNum mju_max(mjtNum a, mjtNum b);

Return max(a,b) with single evaluation of a and b.

mju_sign
~~~~~~~~

.. code-block:: C

   mjtNum mju_sign(mjtNum x);

Return sign of x: +1, -1 or 0.

mju_round
~~~~~~~~~

.. code-block:: C

   int mju_round(mjtNum x);

Round x to nearest integer.

.. _mju_type2Str:

mju_type2Str
~~~~~~~~~~~~

.. code-block:: C

   const char* mju_type2Str(int type);

Convert type id (mjtObj) to type name.

.. _mju_str2Type:

mju_str2Type
~~~~~~~~~~~~

.. code-block:: C

   int mju_str2Type(const char* str);

Convert type name to type id (mjtObj).

.. _mju_warningText:

mju_warningText
~~~~~~~~~~~~~~~

.. code-block:: C

   const char* mju_warningText(int warning, int info);

Construct a warning message given the warning type and info.

.. _mju_isBad:

mju_isBad
~~~~~~~~~

.. code-block:: C

   int mju_isBad(mjtNum x);

Return 1 if nan or abs(x)>mjMAXVAL, 0 otherwise. Used by check functions.

.. _mju_isZero:

mju_isZero
~~~~~~~~~~

.. code-block:: C

   int mju_isZero(mjtNum* vec, int n);

Return 1 if all elements are 0.

.. _mju_standardNormal:

mju_standardNormal
~~~~~~~~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_standardNormal(mjtNum* num2);

Standard normal random number generator (optional second number).

mju_f2n
~~~~~~~

.. code-block:: C

   void mju_f2n(mjtNum* res, const float* vec, int n);

Convert from float to mjtNum.

mju_n2f
~~~~~~~

.. code-block:: C

   void mju_n2f(float* res, const mjtNum* vec, int n);

Convert from mjtNum to float.

mju_d2n
~~~~~~~

.. code-block:: C

   void mju_d2n(mjtNum* res, const double* vec, int n);

Convert from double to mjtNum.

mju_n2d
~~~~~~~

.. code-block:: C

   void mju_n2d(double* res, const mjtNum* vec, int n);

Convert from mjtNum to double.

.. _mju_insertionSort:

mju_insertionSort
~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_insertionSort(mjtNum* list, int n);

Insertion sort, resulting list is in increasing order.

.. _mju_insertionSortInt:

mju_insertionSortInt
~~~~~~~~~~~~~~~~~~~~

.. code-block:: C

   void mju_insertionSortInt(int* list, int n);

Integer insertion sort, resulting list is in increasing order.

.. _mju_Halton:

mju_Halton
~~~~~~~~~~

.. code-block:: C

   mjtNum mju_Halton(int index, int base);

Generate Halton sequence.

mju_strncpy
~~~~~~~~~~~

.. code-block:: C

   char* mju_strncpy(char *dst, const char *src, int n);

Call strncpy, then set dst[n-1] = 0.

mju_sigmoid
~~~~~~~~~~~

.. code-block:: C

   mjtNum mju_sigmoid(mjtNum x);

Sigmoid function over 0<=x<=1 constructed from half-quadratics.

.. _mjd_transitionFD:

mjd_transitionFD
~~~~~~~~~~~~~~~~

.. code-block:: C

   void mjd_transitionFD(const mjModel* m, mjData* d, mjtNum eps, mjtByte centered, mjtNum* A, mjtNum* B);

Finite differenced state-transition and control-transition matrices dx(t+h) = A*dx(t) + B*du(t). Required output matrix
dimensions: A: (2*nv+na x 2*nv+na), B: (2*nv+na x nu).

.. _Macros:

Macros
^^^^^^

.. _mjMARKSTACK:

mjMARKSTACK
~~~~~~~~~~~

.. code-block:: C

   #define mjMARKSTACK int _mark = d->pstack;

This macro is helpful when using the MuJoCo stack in custom computations. It works together with the next macro and the
:ref:`mj_stackAlloc` function, and assumes that mjData\* d is defined. The use pattern is this:

::

       mjMARKSTACK
       mjtNum* temp = mj_stackAlloc(d, 100);
       // ... use temp as needed
       mjFREESTACK

.. _mjFREESTACK:

mjFREESTACK
~~~~~~~~~~~

.. code-block:: C

   #define mjFREESTACK d->pstack = _mark;

Reset the MuJoCo stack pointer to the variable \_mark, normally saved by mjMARKSTACK.

.. _mjDISABLED:

mjDISABLED
~~~~~~~~~~

.. code-block:: C

   #define mjDISABLED(x) (m->opt.disableflags & (x))

Check if a given standard feature has been disabled via the physics options, assuming mjModel\* m is defined. x is of
type :ref:`mjtDisableBit`.

.. _mjENABLED:

mjENABLED
~~~~~~~~~

.. code-block:: C

   #define mjENABLED(x) (m->opt.enableflags & (x))

Check if a given optional feature has been enabled via the physics options, assuming mjModel\* m is defined. x is of
type :ref:`mjtEnableBit`.

.. _mjMAX:

mjMAX
~~~~~

.. code-block:: C

   #define mjMAX(a,b) (((a) > (b)) ? (a) : (b))

Return maximum value. To avoid repeated evaluation with mjtNum types, use the function :ref:`mju_max`.

.. _mjMIN:

mjMIN
~~~~~

.. code-block:: C

   #define mjMIN(a,b) (((a) < (b)) ? (a) : (b))

Return minimum value. To avoid repeated evaluation with mjtNum types, use the function :ref:`mju_min`.
