Datasets:

introvoyz041
/

mujoco

	..
	AUTOGENERATED: DO NOT EDIT MANUALLY


	.. _Parseandcompile:

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

	The key function here is :ref:`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 <#mj_loadXML>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_loadXML

	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_parseXML:

	`mj_parseXML <#mj_parseXML>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_parseXML

	Parse spec from XML file.

	.. _mj_parseXMLString:

	`mj_parseXMLString <#mj_parseXMLString>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_parseXMLString

	Parse spec from XML string.

	.. _mj_compile:

	`mj_compile <#mj_compile>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_compile

	Compile :ref:`mjSpec` to :ref:`mjModel`. A spec can be edited and compiled multiple times, returning a new
	:ref:`mjModel` instance that takes the edits into account.
	If compilation fails, :ref:`mj_compile` returns ``NULL``; the error can be read with :ref:`mjs_getError`.

	.. _mj_copyBack:

	`mj_copyBack <#mj_copyBack>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_copyBack

	Copy real-valued arrays from model to spec, returns 1 on success.

	.. _mj_recompile:

	`mj_recompile <#mj_recompile>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_recompile

	Recompile spec to model, preserving the state. Like :ref:`mj_compile`, this function compiles an :ref:`mjSpec` to an
	:ref:`mjModel`, with two differences. First, rather than returning an entirely new model, it will
	reallocate existing :ref:`mjModel` and :ref:`mjData` instances in-place. Second, it will preserve the
	:ref:`integration state<geIntegrationState>`, as given in the provided :ref:`mjData` instance, while accounting for
	newly added or removed degrees of freedom. This allows the user to continue simulation with the same model and data
	struct pointers while editing the model programmatically.

	:ref:`mj_recompile` returns 0 if compilation succeed. In the case of failure, the given :ref:`mjModel` and :ref:`mjData`
	instances will be deleted; as in :ref:`mj_compile`, the compilation error can be read with :ref:`mjs_getError`.

	.. _mj_saveLastXML:

	`mj_saveLastXML <#mj_saveLastXML>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_saveLastXML

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

	Note that this function only saves models that have been loaded with :ref:`mj_loadXML`, the legacy loading mechanism.
	See the :ref:`model editing<meOverview>` chapter to understand the difference between the old and new model loading and
	saving mechanisms.

	.. _mj_freeLastXML:

	`mj_freeLastXML <#mj_freeLastXML>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_freeLastXML

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

	.. _mj_saveXMLString:

	`mj_saveXMLString <#mj_saveXMLString>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_saveXMLString

	Save spec to XML string, return 0 on success, -1 on failure. If the length of the output buffer is too small, returns
	the required size. XML saving automatically compiles the spec before saving.

	.. _mj_saveXML:

	`mj_saveXML <#mj_saveXML>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_saveXML

	Save spec to XML file, return 0 on success, -1 otherwise. XML saving requires that the spec first be compiled.

	.. _Mainsimulation:

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

	These are the main entry points to the simulator. Most users will only need to call :ref:`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, xfrc_applied}``), or a control callback :ref:`mjcb_control` must be installed which
	will be called just before the controls and applied forces are needed. Alternatively, one can use :ref:`mj_step1` and
	:ref:`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 :ref:`mj_step1`. Keep in mind
	though that the RK4 solver does not work with mj_step1/2. See :ref:`Pipeline` for a more detailed description.

	mj_forward performs the same computations as :ref:`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.

	:ref:`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 thought of as another solver accuracy check (as well as a
	general sanity check).

	The skip version of :ref:`mj_forward` and :ref:`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 = :ref:`mjSTAGE_POS<mjtStage>` will achieve these savings.

	.. _mj_step:

	`mj_step <#mj_step>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_step

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

	.. _mj_step1:

	`mj_step1 <#mj_step1>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_step1

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

	.. _mj_step2:

	`mj_step2 <#mj_step2>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_step2

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

	.. _mj_forward:

	`mj_forward <#mj_forward>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_forward

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

	.. _mj_inverse:

	`mj_inverse <#mj_inverse>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_inverse

	Inverse dynamics: qacc must be set before calling.

	.. _mj_forwardSkip:

	`mj_forwardSkip <#mj_forwardSkip>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_forwardSkip

	Forward dynamics with skip; skipstage is mjtStage.

	.. _mj_inverseSkip:

	`mj_inverseSkip <#mj_inverseSkip>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_inverseSkip

	Inverse dynamics with skip; skipstage is mjtStage.

	.. _Support:

	Support
	^^^^^^^

	These are support functions that need access to :ref:`mjModel` and :ref:`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_stateSize:

	`mj_stateSize <#mj_stateSize>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_stateSize

	Returns the number of :ref:`mjtNum` \|-\| s required for a given state specification. The bits of the integer ``spec``
	correspond to element fields of :ref:`mjtState`.

	.. _mj_getState:

	`mj_getState <#mj_getState>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_getState

	Copy concatenated state components specified by ``spec`` from ``d`` into ``state``. The bits of the integer
	``spec`` correspond to element fields of :ref:`mjtState`. Fails with :ref:`mju_error` if ``spec`` is invalid.

	.. _mj_setState:

	`mj_setState <#mj_setState>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_setState

	Copy concatenated state components specified by ``spec`` from ``state`` into ``d``. The bits of the integer
	``spec`` correspond to element fields of :ref:`mjtState`. Fails with :ref:`mju_error` if ``spec`` is invalid.

	.. _mj_setKeyframe:

	`mj_setKeyframe <#mj_setKeyframe>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_setKeyframe

	Copy current state to the k-th model keyframe.

	.. _mj_addContact:

	`mj_addContact <#mj_addContact>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_addContact

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

	.. _mj_isPyramidal:

	`mj_isPyramidal <#mj_isPyramidal>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_isPyramidal

	Determine type of friction cone.

	.. _mj_isSparse:

	`mj_isSparse <#mj_isSparse>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_isSparse

	Determine type of constraint Jacobian.

	.. _mj_isDual:

	`mj_isDual <#mj_isDual>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_isDual

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

	.. _mj_mulJacVec:

	`mj_mulJacVec <#mj_mulJacVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_mulJacVec

	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 <#mj_mulJacTVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_mulJacTVec

	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 <#mj_jac>`__
	~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_jac

	This function computes an end-effector kinematic Jacobian, describing the local linear relationship between the
	degrees-of-freedom and a given point. Given a body specified by its integer id (``body``) and a 3D point in the world
	frame (``point``) treated as attached to the body, the Jacobian has both translational (``jacp``) and rotational
	(``jacr``) components. Passing ``NULL`` for either pointer will skip that part of the computation. Each component is a
	3-by-nv matrix. Each row of this matrix is the gradient of the corresponding coordinate of the specified point with
	respect to the degrees-of-freedom. The frame with respect to which the Jacobian is computed is centered at the body
	center-of-mass but aligned with the world frame. The minimal :ref:`pipeline stages<piForward>` required for Jacobian
	computations to be consistent with the current generalized positions ``mjData.qpos`` are :ref:`mj_kinematics` followed
	by :ref:`mj_comPos`.

	.. _mj_jacBody:

	`mj_jacBody <#mj_jacBody>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_jacBody

	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 <#mj_jacBodyCom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_jacBodyCom

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

	.. _mj_jacSubtreeCom:

	`mj_jacSubtreeCom <#mj_jacSubtreeCom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_jacSubtreeCom

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

	.. _mj_jacGeom:

	`mj_jacGeom <#mj_jacGeom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_jacGeom

	Compute geom end-effector Jacobian.

	.. _mj_jacSite:

	`mj_jacSite <#mj_jacSite>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_jacSite

	Compute site end-effector Jacobian.

	.. _mj_jacPointAxis:

	`mj_jacPointAxis <#mj_jacPointAxis>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_jacPointAxis

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

	.. _mj_jacDot:

	`mj_jacDot <#mj_jacDot>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_jacDot

	This function computes the time-derivative of an end-effector kinematic Jacobian computed by :ref:`mj_jac`.
	The minimal :ref:`pipeline stages<piStages>` required for computation to be
	consistent with the current generalized positions and velocities ``mjData.{qpos, qvel}`` are
	:ref:`mj_kinematics`, :ref:`mj_comPos`, :ref:`mj_comVel` (in that order).

	.. _mj_angmomMat:

	`mj_angmomMat <#mj_angmomMat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_angmomMat

	This function computes the ``3 x nv`` angular momentum matrix :math:`H(q)`, providing the linear mapping from
	generalized velocities to subtree angular momentum. More precisely if :math:`h` is the subtree angular momentum of
	body index ``body`` in ``mjData.subtree_angmom`` (reported by the :ref:`subtreeangmom<sensor-subtreeangmom>` sensor)
	and :math:`\dot q` is the generalized velocity ``mjData.qvel``, then :math:`h = H \dot q`.

	.. _mj_name2id:

	`mj_name2id <#mj_name2id>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_name2id

	Get id of object with the specified :ref:`mjtObj` type and name, returns -1 if id not found.

	.. _mj_id2name:

	`mj_id2name <#mj_id2name>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_id2name

	Get name of object with the specified :ref:`mjtObj` type and id, returns ``NULL`` if name not found.

	.. _mj_fullM:

	`mj_fullM <#mj_fullM>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_fullM

	Convert sparse inertia matrix ``M`` into full (i.e. dense) matrix.
	\|br\| ``dst`` must be of size ``nv x nv``, ``M`` must be of the same size as ``mjData.qM``.

	.. _mj_mulM:

	`mj_mulM <#mj_mulM>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_mulM

	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 <#mj_mulM2>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_mulM2

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

	.. _mj_addM:

	`mj_addM <#mj_addM>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_addM

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

	.. _mj_applyFT:

	`mj_applyFT <#mj_applyFT>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_applyFT

	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 <#mj_objectVelocity>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_objectVelocity

	Compute object 6D velocity (rot:lin) in object-centered frame, world/local orientation.

	.. _mj_objectAcceleration:

	`mj_objectAcceleration <#mj_objectAcceleration>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_objectAcceleration

	Compute object 6D acceleration (rot:lin) in object-centered frame, world/local orientation. If acceleration or force
	sensors are not present in the model, :ref:`mj_rnePostConstraint` must be manually called in order to calculate
	mjData.cacc -- the total body acceleration, including contributions from the constraint solver.

	.. _mj_geomDistance:

	`mj_geomDistance <#mj_geomDistance>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_geomDistance

	Returns the smallest signed distance between two geoms and optionally the segment from ``geom1`` to ``geom2``.
	Returned distances are bounded from above by ``distmax``. \|br\| If no collision of distance smaller than ``distmax`` is
	found, the function will return ``distmax`` and ``fromto``, if given, will be set to (0, 0, 0, 0, 0, 0).

	.. admonition:: different (correct) behavior under `nativeccd`
	:class: note

	As explained in :ref:`Collision Detection<coDistance>`, distances are inaccurate when using the
	:ref:`legacy CCD pipeline<coCCD>`, and its use is discouraged.

	.. _mj_contactForce:

	`mj_contactForce <#mj_contactForce>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_contactForce

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

	.. _mj_differentiatePos:

	`mj_differentiatePos <#mj_differentiatePos>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_differentiatePos

	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. Thus the output qvel has dimensionality nv while the
	inputs have dimensionality nq.

	.. _mj_integratePos:

	`mj_integratePos <#mj_integratePos>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_integratePos

	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 <#mj_normalizeQuat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_normalizeQuat

	Normalize all quaternions in qpos-type vector.

	.. _mj_local2Global:

	`mj_local2Global <#mj_local2Global>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_local2Global

	Map from body local to global Cartesian coordinates, sameframe takes values from mjtSameFrame.

	.. _mj_getTotalmass:

	`mj_getTotalmass <#mj_getTotalmass>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_getTotalmass

	Sum all body masses.

	.. _mj_setTotalmass:

	`mj_setTotalmass <#mj_setTotalmass>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_setTotalmass

	Scale body masses and inertias to achieve specified total mass.

	.. _mj_getPluginConfig:

	`mj_getPluginConfig <#mj_getPluginConfig>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_getPluginConfig

	Return a config attribute value of a plugin instance;
	NULL: invalid plugin instance ID or attribute name

	.. _mj_loadPluginLibrary:

	`mj_loadPluginLibrary <#mj_loadPluginLibrary>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_loadPluginLibrary

	Load a dynamic library. The dynamic library is assumed to register one or more plugins.

	.. _mj_loadAllPluginLibraries:

	`mj_loadAllPluginLibraries <#mj_loadAllPluginLibraries>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_loadAllPluginLibraries

	Scan a directory and load all dynamic libraries. Dynamic libraries in the specified directory
	are assumed to register one or more plugins. Optionally, if a callback is specified, it is called
	for each dynamic library encountered that registers plugins.

	.. _mj_version:

	`mj_version <#mj_version>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_version

	Return version number: 1.0.2 is encoded as 102.

	.. _mj_versionString:

	`mj_versionString <#mj_versionString>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_versionString

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

	.. _Components:

	Components
	^^^^^^^^^^

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

	.. _mj_fwdPosition:

	`mj_fwdPosition <#mj_fwdPosition>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_fwdPosition

	Run position-dependent computations.

	.. _mj_fwdVelocity:

	`mj_fwdVelocity <#mj_fwdVelocity>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_fwdVelocity

	Run velocity-dependent computations.

	.. _mj_fwdActuation:

	`mj_fwdActuation <#mj_fwdActuation>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_fwdActuation

	Compute actuator force qfrc_actuator.

	.. _mj_fwdAcceleration:

	`mj_fwdAcceleration <#mj_fwdAcceleration>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_fwdAcceleration

	Add up all non-constraint forces, compute qacc_smooth.

	.. _mj_fwdConstraint:

	`mj_fwdConstraint <#mj_fwdConstraint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_fwdConstraint

	Run selected constraint solver.

	.. _mj_Euler:

	`mj_Euler <#mj_Euler>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_Euler

	Euler integrator, semi-implicit in velocity.

	.. _mj_RungeKutta:

	`mj_RungeKutta <#mj_RungeKutta>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_RungeKutta

	Runge-Kutta explicit order-N integrator.

	.. _mj_implicit:

	`mj_implicit <#mj_implicit>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_implicit

	Integrates the simulation state using an implicit-in-velocity integrator (either "implicit" or "implicitfast", see
	:ref:`Numerical Integration<geIntegration>`), and advances simulation time. See `mjdata.h
	<https://github.com/google-deepmind/mujoco/blob/main/include/mujoco/mjdata.h>`__ for fields computed by this function.

	.. _mj_invPosition:

	`mj_invPosition <#mj_invPosition>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_invPosition

	Run position-dependent computations in inverse dynamics.

	.. _mj_invVelocity:

	`mj_invVelocity <#mj_invVelocity>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_invVelocity

	Run velocity-dependent computations in inverse dynamics.

	.. _mj_invConstraint:

	`mj_invConstraint <#mj_invConstraint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_invConstraint

	Apply the analytical formula for inverse constraint dynamics.

	.. _mj_compareFwdInv:

	`mj_compareFwdInv <#mj_compareFwdInv>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_compareFwdInv

	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.

	.. _mj_sensorPos:

	`mj_sensorPos <#mj_sensorPos>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_sensorPos

	Evaluate position-dependent sensors.

	.. _mj_sensorVel:

	`mj_sensorVel <#mj_sensorVel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_sensorVel

	Evaluate velocity-dependent sensors.

	.. _mj_sensorAcc:

	`mj_sensorAcc <#mj_sensorAcc>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_sensorAcc

	Evaluate acceleration and force-dependent sensors.

	.. _mj_energyPos:

	`mj_energyPos <#mj_energyPos>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_energyPos

	Evaluate position-dependent energy (potential).

	.. _mj_energyVel:

	`mj_energyVel <#mj_energyVel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_energyVel

	Evaluate velocity-dependent energy (kinetic).

	.. _mj_checkPos:

	`mj_checkPos <#mj_checkPos>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_checkPos

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

	.. _mj_checkVel:

	`mj_checkVel <#mj_checkVel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_checkVel

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

	.. _mj_checkAcc:

	`mj_checkAcc <#mj_checkAcc>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_checkAcc

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

	.. _mj_kinematics:

	`mj_kinematics <#mj_kinematics>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_kinematics

	Run forward kinematics.

	.. _mj_comPos:

	`mj_comPos <#mj_comPos>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_comPos

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

	.. _mj_camlight:

	`mj_camlight <#mj_camlight>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_camlight

	Compute camera and light positions and orientations.

	.. _mj_flex:

	`mj_flex <#mj_flex>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_flex

	Compute flex-related quantities.

	.. _mj_tendon:

	`mj_tendon <#mj_tendon>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_tendon

	Compute tendon lengths, velocities and moment arms.

	.. _mj_transmission:

	`mj_transmission <#mj_transmission>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_transmission

	Compute actuator transmission lengths and moments.

	.. _mj_crb:

	`mj_crb <#mj_crb>`__
	~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_crb

	Run composite rigid body inertia algorithm (CRB).

	.. _mj_makeM:

	`mj_makeM <#mj_makeM>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_makeM

	Compute the composite rigid body inertia with :ref:`mj_crb`, add terms due
	to :ref:`tendon armature<tendon-spatial-armature>`. The joint-space inertia matrix is stored in both ``mjData.qM`` and
	``mjData.M``. These arrays represent the same quantity using different layouts (parent-based and compressed sparse row,
	respectively).

	.. _mj_factorM:

	`mj_factorM <#mj_factorM>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_factorM

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

	.. _mj_solveM:

	`mj_solveM <#mj_solveM>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_solveM

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

	.. _mj_solveM2:

	`mj_solveM2 <#mj_solveM2>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_solveM2

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

	.. _mj_comVel:

	`mj_comVel <#mj_comVel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_comVel

	Compute cvel, cdof_dot.

	.. _mj_passive:

	`mj_passive <#mj_passive>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_passive

	Compute qfrc_passive from spring-dampers, gravity compensation and fluid forces.

	.. _mj_subtreeVel:

	`mj_subtreeVel <#mj_subtreeVel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_subtreeVel

	Sub-tree linear velocity and angular momentum: compute ``subtree_linvel``, ``subtree_angmom``.
	This function is triggered automatically if the subtree :ref:`velocity<sensor-subtreelinvel>` or
	:ref:`momentum<sensor-subtreeangmom>` sensors are present in the model.
	It is also triggered for :ref:`user sensors<sensor-user>` of :ref:`stage<sensor-user-needstage>` "vel".

	.. _mj_rne:

	`mj_rne <#mj_rne>`__
	~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_rne

	Recursive Newton Euler: compute :math:`M(q) \ddot q + C(q,\dot q)`. ``flg_acc=0`` removes the inertial term (i.e.
	assumes :math:`\ddot q = 0`).

	.. _mj_rnePostConstraint:

	`mj_rnePostConstraint <#mj_rnePostConstraint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_rnePostConstraint

	Recursive Newton Euler with final computed forces and accelerations.
	Computes three body-level ``nv x 6`` arrays, all defined in the subtreecom-based
	:ref:`c-frame<tyNotesCom>` and arranged in ``[rotation(3), translation(3)]`` order.

	- ``cacc``: Body acceleration, required for :ref:`mj_objectAcceleration`.
	- ``cfrc_int``: Interaction force with the parent body.
	- ``cfrc_ext``: External force acting on the body.

	This function is triggered automatically if the following sensors are present in the model:
	:ref:`accelerometer<sensor-accelerometer>`, :ref:`force<sensor-force>`, :ref:`torque<sensor-torque>`,
	:ref:`framelinacc<sensor-framelinacc>`, :ref:`frameangacc<sensor-frameangacc>`.
	It is also triggered for :ref:`user sensors<sensor-user>` of :ref:`stage<sensor-user-needstage>` "acc".

	The computed force arrays ``cfrc_int`` and ``cfrc_ext`` currently suffer from a know bug, they do not take into account
	the effect of spatial tendons, see :github:issue:`832`.

	.. _mj_collision:

	`mj_collision <#mj_collision>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_collision

	Run collision detection.

	.. _mj_makeConstraint:

	`mj_makeConstraint <#mj_makeConstraint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_makeConstraint

	Construct constraints.

	.. _mj_island:

	`mj_island <#mj_island>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_island

	Find constraint islands.

	.. _mj_projectConstraint:

	`mj_projectConstraint <#mj_projectConstraint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_projectConstraint

	Compute inverse constraint inertia efc_AR.

	.. _mj_referenceConstraint:

	`mj_referenceConstraint <#mj_referenceConstraint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_referenceConstraint

	Compute efc_vel, efc_aref.

	.. _mj_constraintUpdate:

	`mj_constraintUpdate <#mj_constraintUpdate>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_constraintUpdate

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

	.. _Raycollisions:

	Ray casting
	^^^^^^^^^^^

	Ray collisions, also known as ray casting, find the distance ``x`` of a ray's intersection with a geom, where a ray is
	a line emanating from the 3D point ``p`` in the direction ``v`` i.e., ``(p + x*v, x >= 0)``. 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`). The top level functions, which
	intersect with all geoms types, are :ref:`mj_ray` which casts a single ray, and :ref:`mj_multiRay` which casts multiple
	rays from a single point.

	.. _mj_multiRay:

	`mj_multiRay <#mj_multiRay>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_multiRay

	Intersect multiple rays emanating from a single point.
	Similar semantics to mj_ray, but vec is an array of (nray x 3) directions.

	.. _mj_ray:

	`mj_ray <#mj_ray>`__
	~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_ray

	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 <#mj_rayHfield>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_rayHfield

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

	.. _mj_rayMesh:

	`mj_rayMesh <#mj_rayMesh>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_rayMesh

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

	.. _mju_rayGeom:

	`mju_rayGeom <#mju_rayGeom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_rayGeom

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

	.. _mju_rayFlex:

	`mju_rayFlex <#mju_rayFlex>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_rayFlex

	Intersect ray with flex, return nearest distance or -1 if no intersection,
	and also output nearest vertex id.

	.. _mju_raySkin:

	`mju_raySkin <#mju_raySkin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_raySkin

	Intersect ray with skin, return nearest distance or -1 if no intersection,
	and also output nearest vertex id.

	.. _Printing:

	Printing
	^^^^^^^^

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

	.. _mj_printFormattedModel:

	`mj_printFormattedModel <#mj_printFormattedModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_printFormattedModel

	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 <#mj_printModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_printModel

	Print model to text file.

	.. _mj_printFormattedData:

	`mj_printFormattedData <#mj_printFormattedData>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_printFormattedData

	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 <#mj_printData>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_printData

	Print data to text file.

	.. _mju_printMat:

	`mju_printMat <#mju_printMat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_printMat

	Print matrix to screen.

	.. _mju_printMatSparse:

	`mju_printMatSparse <#mju_printMatSparse>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_printMatSparse

	Print sparse matrix to screen.

	.. _mj_printSchema:

	`mj_printSchema <#mj_printSchema>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_printSchema

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

	.. _Virtualfilesystem:

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

	Virtual file system (VFS) 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
	files they are about to load, and only access the disk if the file is not found in the VFS.

	The VFS must first be allocated using :ref:`mj_defaultVFS` and must be freed with :ref:`mj_deleteVFS`.


	.. _mj_defaultVFS:

	`mj_defaultVFS <#mj_defaultVFS>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_defaultVFS

	Initialize an empty VFS, :ref:`mj_deleteVFS` must be called to deallocate the VFS.

	.. _mj_addFileVFS:

	`mj_addFileVFS <#mj_addFileVFS>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_addFileVFS

	Add file to VFS. The directory argument is optional and can be NULL or empty. Returns 0 on success,
	2 on name collision, or -1 when an internal error occurs.

	.. _mj_addBufferVFS:

	`mj_addBufferVFS <#mj_addBufferVFS>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_addBufferVFS

	Add file to VFS from buffer, return 0: success, 2: repeated name, -1: failed to load.

	.. _mj_deleteFileVFS:

	`mj_deleteFileVFS <#mj_deleteFileVFS>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_deleteFileVFS

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

	.. _mj_deleteVFS:

	`mj_deleteVFS <#mj_deleteVFS>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_deleteVFS

	Delete all files from VFS and deallocates VFS internal memory.

	.. _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 <#mj_defaultLROpt>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_defaultLROpt

	Set default options for length range computation.

	.. _mj_defaultSolRefImp:

	`mj_defaultSolRefImp <#mj_defaultSolRefImp>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_defaultSolRefImp

	Set solver parameters to default values.

	.. _mj_defaultOption:

	`mj_defaultOption <#mj_defaultOption>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_defaultOption

	Set physics options to default values.

	.. _mj_defaultVisual:

	`mj_defaultVisual <#mj_defaultVisual>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_defaultVisual

	Set visual options to default values.

	.. _mj_copyModel:

	`mj_copyModel <#mj_copyModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_copyModel

	Copy mjModel, allocate new if dest is NULL.

	.. _mj_saveModel:

	`mj_saveModel <#mj_saveModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_saveModel

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

	.. _mj_loadModel:

	`mj_loadModel <#mj_loadModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_loadModel

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

	.. _mj_deleteModel:

	`mj_deleteModel <#mj_deleteModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_deleteModel

	Free memory allocation in model.

	.. _mj_sizeModel:

	`mj_sizeModel <#mj_sizeModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_sizeModel

	Return size of buffer needed to hold model.

	.. _mj_makeData:

	`mj_makeData <#mj_makeData>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_makeData

	Allocate mjData corresponding to given model.
	If the model buffer is unallocated the initial configuration will not be set.

	.. _mj_copyData:

	`mj_copyData <#mj_copyData>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_copyData

	Copy mjData.
	m is only required to contain the size fields from MJMODEL_INTS.

	.. _mjv_copyData:

	`mjv_copyData <#mjv_copyData>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_copyData

	Copy mjData, skip large arrays not required for visualization.

	.. _mj_resetData:

	`mj_resetData <#mj_resetData>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_resetData

	Reset data to defaults.

	.. _mj_resetDataDebug:

	`mj_resetDataDebug <#mj_resetDataDebug>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_resetDataDebug

	Reset data to defaults, fill everything else with debug_value.

	.. _mj_resetDataKeyframe:

	`mj_resetDataKeyframe <#mj_resetDataKeyframe>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_resetDataKeyframe

	Reset data. If 0 <= key < nkey, set fields from specified keyframe.

	.. _mj_markStack:

	`mj_markStack <#mj_markStack>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_markStack

	Mark a new frame on the mjData stack.

	.. _mj_freeStack:

	`mj_freeStack <#mj_freeStack>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_freeStack

	Free the current mjData stack frame. All pointers returned by mj_stackAlloc since the last call
	to mj_markStack must no longer be used afterwards.

	.. _mj_stackAllocByte:

	`mj_stackAllocByte <#mj_stackAllocByte>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_stackAllocByte

	Allocate a number of bytes on mjData stack at a specific alignment.
	Call mju_error on stack overflow.

	.. _mj_stackAllocNum:

	`mj_stackAllocNum <#mj_stackAllocNum>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_stackAllocNum

	Allocate array of mjtNums on mjData stack. Call mju_error on stack overflow.

	.. _mj_stackAllocInt:

	`mj_stackAllocInt <#mj_stackAllocInt>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_stackAllocInt

	Allocate array of ints on mjData stack. Call mju_error on stack overflow.

	.. _mj_deleteData:

	`mj_deleteData <#mj_deleteData>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_deleteData

	Free memory allocation in mjData.

	.. _mj_resetCallbacks:

	`mj_resetCallbacks <#mj_resetCallbacks>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_resetCallbacks

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

	.. _mj_setConst:

	`mj_setConst <#mj_setConst>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_setConst

	Set constant fields of mjModel, corresponding to qpos0 configuration.

	.. _mj_setLengthRange:

	`mj_setLengthRange <#mj_setLengthRange>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_setLengthRange

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

	.. _mj_makeSpec:

	`mj_makeSpec <#mj_makeSpec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_makeSpec

	Create empty spec.

	.. _mj_copySpec:

	`mj_copySpec <#mj_copySpec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_copySpec

	Copy spec.

	.. _mj_deleteSpec:

	`mj_deleteSpec <#mj_deleteSpec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_deleteSpec

	Free memory allocation in mjSpec.

	.. _mjs_activatePlugin:

	`mjs_activatePlugin <#mjs_activatePlugin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_activatePlugin

	Activate plugin. Returns 0 on success.

	.. _mjs_setDeepCopy:

	`mjs_setDeepCopy <#mjs_setDeepCopy>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setDeepCopy

	Turn deep copy on or off attach. Returns 0 on success.

	.. _Errorandmemory:

	Error and memory
	^^^^^^^^^^^^^^^^

	.. _mju_error:

	`mju_error <#mju_error>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_error

	Main error function; does not return to caller.

	.. _mju_error_i:

	`mju_error_i <#mju_error_i>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_error_i

	Deprecated: use mju_error.

	.. _mju_error_s:

	`mju_error_s <#mju_error_s>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_error_s

	Deprecated: use mju_error.

	.. _mju_warning:

	`mju_warning <#mju_warning>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_warning

	Main warning function; returns to caller.

	.. _mju_warning_i:

	`mju_warning_i <#mju_warning_i>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_warning_i

	Deprecated: use mju_warning.

	.. _mju_warning_s:

	`mju_warning_s <#mju_warning_s>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_warning_s

	Deprecated: use mju_warning.

	.. _mju_clearHandlers:

	`mju_clearHandlers <#mju_clearHandlers>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_clearHandlers

	Clear user error and memory handlers.

	.. _mju_malloc:

	`mju_malloc <#mju_malloc>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_malloc

	Allocate memory; byte-align on 64; pad size to multiple of 64.

	.. _mju_free:

	`mju_free <#mju_free>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_free

	Free memory, using free() by default.

	.. _mj_warning:

	`mj_warning <#mj_warning>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mj_warning

	High-level warning function: count warnings in mjData, print only the first.

	.. _mju_writeLog:

	`mju_writeLog <#mju_writeLog>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_writeLog

	Write [datetime, type: message] to MUJOCO_LOG.TXT.

	.. _mjs_getError:

	`mjs_getError <#mjs_getError>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getError

	Get compiler error message from spec.

	.. _mjs_isWarning:

	`mjs_isWarning <#mjs_isWarning>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_isWarning

	Return 1 if compiler error is a warning.

	.. _Miscellaneous:

	Miscellaneous
	^^^^^^^^^^^^^

	.. _mju_muscleGain:

	`mju_muscleGain <#mju_muscleGain>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_muscleGain

	Muscle active force, prm = (range[2], force, scale, lmin, lmax, vmax, fpmax, fvmax).

	.. _mju_muscleBias:

	`mju_muscleBias <#mju_muscleBias>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_muscleBias

	Muscle passive force, prm = (range[2], force, scale, lmin, lmax, vmax, fpmax, fvmax).

	.. _mju_muscleDynamics:

	`mju_muscleDynamics <#mju_muscleDynamics>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_muscleDynamics

	Muscle activation dynamics, prm = (tau_act, tau_deact, smoothing_width).

	.. _mju_encodePyramid:

	`mju_encodePyramid <#mju_encodePyramid>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_encodePyramid

	Convert contact force to pyramid representation.

	.. _mju_decodePyramid:

	`mju_decodePyramid <#mju_decodePyramid>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_decodePyramid

	Convert pyramid representation to contact force.

	.. _mju_springDamper:

	`mju_springDamper <#mju_springDamper>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_springDamper

	Integrate spring-damper analytically, return pos(dt).

	.. _mju_min:

	`mju_min <#mju_min>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_min

	Return min(a,b) with single evaluation of a and b.

	.. _mju_max:

	`mju_max <#mju_max>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_max

	Return max(a,b) with single evaluation of a and b.

	.. _mju_clip:

	`mju_clip <#mju_clip>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_clip

	Clip x to the range [min, max].

	.. _mju_sign:

	`mju_sign <#mju_sign>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_sign

	Return sign of x: +1, -1 or 0.

	.. _mju_round:

	`mju_round <#mju_round>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_round

	Round x to nearest integer.

	.. _mju_type2Str:

	`mju_type2Str <#mju_type2Str>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_type2Str

	Convert type id (mjtObj) to type name.

	.. _mju_str2Type:

	`mju_str2Type <#mju_str2Type>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_str2Type

	Convert type name to type id (mjtObj).

	.. _mju_writeNumBytes:

	`mju_writeNumBytes <#mju_writeNumBytes>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_writeNumBytes

	Return human readable number of bytes using standard letter suffix.

	.. _mju_warningText:

	`mju_warningText <#mju_warningText>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_warningText

	Construct a warning message given the warning type and info.

	.. _mju_isBad:

	`mju_isBad <#mju_isBad>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_isBad

	Return 1 if nan or abs(x)>mjMAXVAL, 0 otherwise. Used by check functions.

	.. _mju_isZero:

	`mju_isZero <#mju_isZero>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_isZero

	Return 1 if all elements are 0.

	.. _mju_standardNormal:

	`mju_standardNormal <#mju_standardNormal>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_standardNormal

	Standard normal random number generator (optional second number).

	.. _mju_f2n:

	`mju_f2n <#mju_f2n>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_f2n

	Convert from float to mjtNum.

	.. _mju_n2f:

	`mju_n2f <#mju_n2f>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_n2f

	Convert from mjtNum to float.

	.. _mju_d2n:

	`mju_d2n <#mju_d2n>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_d2n

	Convert from double to mjtNum.

	.. _mju_n2d:

	`mju_n2d <#mju_n2d>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_n2d

	Convert from mjtNum to double.

	.. _mju_insertionSort:

	`mju_insertionSort <#mju_insertionSort>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_insertionSort

	Insertion sort, resulting list is in increasing order.

	.. _mju_insertionSortInt:

	`mju_insertionSortInt <#mju_insertionSortInt>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_insertionSortInt

	Integer insertion sort, resulting list is in increasing order.

	.. _mju_Halton:

	`mju_Halton <#mju_Halton>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_Halton

	Generate Halton sequence.

	.. _mju_strncpy:

	`mju_strncpy <#mju_strncpy>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_strncpy

	Call strncpy, then set dst[n-1] = 0.

	.. _mju_sigmoid:

	`mju_sigmoid <#mju_sigmoid>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_sigmoid

	Twice continuously differentiable sigmoid function using a quintic polynomial:

	.. math::
	s(x) =
	\begin{cases}
	0, & & x \le 0 \\
	6x^5 - 15x^4 + 10x^3, & 0 \lt & x \lt 1 \\
	1, & 1 \le & x \qquad
	\end{cases}

	.. _Interaction:

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

	These functions implement abstract mouse interactions, allowing control over cameras and perturbations. Their use is well
	illustrated in :ref:`simulate<saSimulate>`.

	.. _mjv_defaultCamera:

	`mjv_defaultCamera <#mjv_defaultCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_defaultCamera

	Set default camera.

	.. _mjv_defaultFreeCamera:

	`mjv_defaultFreeCamera <#mjv_defaultFreeCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_defaultFreeCamera

	Set default free camera.

	.. _mjv_defaultPerturb:

	`mjv_defaultPerturb <#mjv_defaultPerturb>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_defaultPerturb

	Set default perturbation.

	.. _mjv_room2model:

	`mjv_room2model <#mjv_room2model>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_room2model

	Transform pose from room to model space.

	.. _mjv_model2room:

	`mjv_model2room <#mjv_model2room>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_model2room

	Transform pose from model to room space.

	.. _mjv_cameraInModel:

	`mjv_cameraInModel <#mjv_cameraInModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_cameraInModel

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

	.. _mjv_cameraInRoom:

	`mjv_cameraInRoom <#mjv_cameraInRoom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_cameraInRoom

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

	.. _mjv_frustumHeight:

	`mjv_frustumHeight <#mjv_frustumHeight>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_frustumHeight

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

	.. _mjv_alignToCamera:

	`mjv_alignToCamera <#mjv_alignToCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_alignToCamera

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

	.. _mjv_moveCamera:

	`mjv_moveCamera <#mjv_moveCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_moveCamera

	Move camera with mouse; action is mjtMouse.

	.. _mjv_movePerturb:

	`mjv_movePerturb <#mjv_movePerturb>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_movePerturb

	Move perturb object with mouse; action is mjtMouse.

	.. _mjv_moveModel:

	`mjv_moveModel <#mjv_moveModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_moveModel

	Move model with mouse; action is mjtMouse.

	.. _mjv_initPerturb:

	`mjv_initPerturb <#mjv_initPerturb>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_initPerturb

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

	.. _mjv_applyPerturbPose:

	`mjv_applyPerturbPose <#mjv_applyPerturbPose>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_applyPerturbPose

	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 <#mjv_applyPerturbForce>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_applyPerturbForce

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

	.. _mjv_averageCamera:

	`mjv_averageCamera <#mjv_averageCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_averageCamera

	Return the average of two OpenGL cameras.

	.. _mjv_select:

	`mjv_select <#mjv_select>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_select

	This function is used for mouse selection, relying on ray intersections. 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 :ref:`simulate<saSimulate>` for
	an illustration.

	.. _Visualization-api:

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

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

	.. _mjv_defaultOption:

	`mjv_defaultOption <#mjv_defaultOption>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_defaultOption

	Set default visualization options.

	.. _mjv_defaultFigure:

	`mjv_defaultFigure <#mjv_defaultFigure>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_defaultFigure

	Set default figure.

	.. _mjv_initGeom:

	`mjv_initGeom <#mjv_initGeom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_initGeom

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

	.. _mjv_connector:

	`mjv_connector <#mjv_connector>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_connector

	Set (type, size, pos, mat) for connector-type geom between given points.
	Assume that mjv_initGeom was already called to set all other properties.
	Width of mjGEOM_LINE is denominated in pixels.

	.. _mjv_defaultScene:

	`mjv_defaultScene <#mjv_defaultScene>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_defaultScene

	Set default abstract scene.

	.. _mjv_makeScene:

	`mjv_makeScene <#mjv_makeScene>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_makeScene

	Allocate resources in abstract scene.

	.. _mjv_freeScene:

	`mjv_freeScene <#mjv_freeScene>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_freeScene

	Free abstract scene.

	.. _mjv_updateScene:

	`mjv_updateScene <#mjv_updateScene>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_updateScene

	Update entire scene given model state.

	.. _mjv_copyModel:

	`mjv_copyModel <#mjv_copyModel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_copyModel

	Copy mjModel, skip large arrays not required for abstract visualization.

	.. _mjv_addGeoms:

	`mjv_addGeoms <#mjv_addGeoms>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_addGeoms

	Add geoms from selected categories.

	.. _mjv_makeLights:

	`mjv_makeLights <#mjv_makeLights>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_makeLights

	Make list of lights.

	.. _mjv_updateCamera:

	`mjv_updateCamera <#mjv_updateCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_updateCamera

	Update camera.

	.. _mjv_updateSkin:

	`mjv_updateSkin <#mjv_updateSkin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjv_updateSkin

	Update skins.

	.. _OpenGLrendering:

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

	These functions expose the OpenGL renderer. See :ref:`simulate<saSimulate>` for an illustration
	of how to use these functions.

	.. _mjr_defaultContext:

	`mjr_defaultContext <#mjr_defaultContext>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_defaultContext

	Set default mjrContext.

	.. _mjr_makeContext:

	`mjr_makeContext <#mjr_makeContext>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_makeContext

	Allocate resources in custom OpenGL context; fontscale is mjtFontScale.

	.. _mjr_changeFont:

	`mjr_changeFont <#mjr_changeFont>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_changeFont

	Change font of existing context.

	.. _mjr_addAux:

	`mjr_addAux <#mjr_addAux>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_addAux

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

	.. _mjr_freeContext:

	`mjr_freeContext <#mjr_freeContext>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_freeContext

	Free resources in custom OpenGL context, set to default.

	.. _mjr_resizeOffscreen:

	`mjr_resizeOffscreen <#mjr_resizeOffscreen>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_resizeOffscreen

	Resize offscreen buffers.

	.. _mjr_uploadTexture:

	`mjr_uploadTexture <#mjr_uploadTexture>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_uploadTexture

	Upload texture to GPU, overwriting previous upload if any.

	.. _mjr_uploadMesh:

	`mjr_uploadMesh <#mjr_uploadMesh>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_uploadMesh

	Upload mesh to GPU, overwriting previous upload if any.

	.. _mjr_uploadHField:

	`mjr_uploadHField <#mjr_uploadHField>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_uploadHField

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

	.. _mjr_restoreBuffer:

	`mjr_restoreBuffer <#mjr_restoreBuffer>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_restoreBuffer

	Make con->currentBuffer current again.

	.. _mjr_setBuffer:

	`mjr_setBuffer <#mjr_setBuffer>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_setBuffer

	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 <#mjr_readPixels>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_readPixels

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

	.. _mjr_drawPixels:

	`mjr_drawPixels <#mjr_drawPixels>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_drawPixels

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

	.. _mjr_blitBuffer:

	`mjr_blitBuffer <#mjr_blitBuffer>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_blitBuffer

	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 <#mjr_setAux>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_setAux

	Set Aux buffer for custom OpenGL rendering (call restoreBuffer when done).

	.. _mjr_blitAux:

	`mjr_blitAux <#mjr_blitAux>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_blitAux

	Blit from Aux buffer to con->currentBuffer.

	.. _mjr_text:

	`mjr_text <#mjr_text>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_text

	Draw text at (x,y) in relative coordinates; font is mjtFont.

	.. _mjr_overlay:

	`mjr_overlay <#mjr_overlay>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_overlay

	Draw text overlay; font is mjtFont; gridpos is mjtGridPos.

	.. _mjr_maxViewport:

	`mjr_maxViewport <#mjr_maxViewport>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_maxViewport

	Get maximum viewport for active buffer.

	.. _mjr_rectangle:

	`mjr_rectangle <#mjr_rectangle>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_rectangle

	Draw rectangle.

	.. _mjr_label:

	`mjr_label <#mjr_label>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_label

	Draw rectangle with centered text.

	.. _mjr_figure:

	`mjr_figure <#mjr_figure>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_figure

	Draw 2D figure.

	.. _mjr_render:

	`mjr_render <#mjr_render>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_render

	Render 3D scene.

	.. _mjr_finish:

	`mjr_finish <#mjr_finish>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_finish

	Call glFinish.

	.. _mjr_getError:

	`mjr_getError <#mjr_getError>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_getError

	Call glGetError and return result.

	.. _mjr_findRect:

	`mjr_findRect <#mjr_findRect>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjr_findRect

	Find first rectangle containing mouse, -1: not found.

	.. _UIframework:

	UI framework
	^^^^^^^^^^^^

	For a high-level description of the UI framework, see :ref:`UI`.

	.. _mjui_themeSpacing:

	`mjui_themeSpacing <#mjui_themeSpacing>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjui_themeSpacing

	Get builtin UI theme spacing (ind: 0-1).

	.. _mjui_themeColor:

	`mjui_themeColor <#mjui_themeColor>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjui_themeColor

	Get builtin UI theme color (ind: 0-3).

	.. _mjui_add:

	`mjui_add <#mjui_add>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjui_add

	This is the helper function used to construct a UI. The second argument points to an array of :ref:`mjuiDef` structs,
	each corresponding to one item. The last (unused) item has its type set to -1, to mark termination. The items are added
	after the end of the last used section. There is also another version of this function
	(:ref:`mjui_addToSection<mjui_addToSection>`) which adds items to a specified section instead of adding them at the end
	of the UI. Keep in mind that there is a maximum preallocated number of sections and items per section, given by
	:ref:`mjMAXUISECT<glNumeric>` and :ref:`mjMAXUIITEM<glNumeric>`. Exceeding these maxima results in low-level errors.

	.. _mjui_addToSection:

	`mjui_addToSection <#mjui_addToSection>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjui_addToSection

	Add definitions to UI section.

	.. _mjui_resize:

	`mjui_resize <#mjui_resize>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjui_resize

	Compute UI sizes.

	.. _mjui_update:

	`mjui_update <#mjui_update>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjui_update

	This is the main UI update function. It needs to be called whenever the user data (pointed to by the item data pointers)
	changes, or when the UI state itself changes. It is normally called by a higher-level function implemented by the user
	(``UiModify`` in :ref:`simulate.cc <saSimulate>`) which also recomputes the layout of all rectangles and associated
	auxiliary buffers. The function updates the pixels in the offscreen OpenGL buffer. To perform minimal updates, the user
	specifies the section and the item that was modified. A value of -1 means all items and/or sections need to be updated
	(which is needed following major changes.)

	.. _mjui_event:

	`mjui_event <#mjui_event>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjui_event

	This function is the low-level event handler. It makes the necessary changes in the UI and returns a pointer to the item
	that received the event (or ``NULL`` if no valid event was recorded). This is normally called within the event handler
	implemented by the user (``UiEvent`` in :ref:`simulate.cc <saSimulate>`), and then some action is taken by user code
	depending on which UI item was modified and what the state of that item is after the event is handled.

	.. _mjui_render:

	`mjui_render <#mjui_render>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjui_render

	This function is called in the screen refresh loop. It copies the offscreen OpenGL buffer to the window framebuffer. If
	there are multiple UIs in the application, it should be called once for each UI. Thus ``mjui_render`` is called all the
	time, while :ref:`mjui_update` is called only when changes in the UI take place. dsffsdg

	.. _Derivatives-api:

	Derivatives
	^^^^^^^^^^^

	The functions below provide useful derivatives of various functions, both analytic and
	finite-differenced. The latter have names with the suffix ``FD``. Note that unlike much of the API,
	outputs of derivative functions are the trailing rather than leading arguments.

	.. _mjd_transitionFD:

	`mjd_transitionFD <#mjd_transitionFD>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjd_transitionFD

	Compute finite-differenced discrete-time transition matrices.

	Letting :math:`x, u` denote the current :ref:`state<gePhysicsState>` and :ref:`control<geInput>`
	vector in an mjData instance, and letting :math:`y, s` denote the next state and sensor
	values, the top-level :ref:`mj_step` function computes :math:`(x,u) \rightarrow (y,s)`
	:ref:`mjd_transitionFD` computes the four associated Jacobians using finite-differencing.
	These matrices and their dimensions are:

	.. csv-table::
	:header: "matrix", "Jacobian", "dimension"
	:widths: auto
	:align: left

	``A``, :math:`\partial y / \partial x`, ``2nv+na x 2nv+na``
	``B``, :math:`\partial y / \partial u`, ``2*nv+na x nu``
	``C``, :math:`\partial s / \partial x`, ``nsensordata x 2*nv+na``
	``D``, :math:`\partial s / \partial u`, ``nsensordata x nu``

	- All outputs are optional (can be NULL).
	- ``eps`` is the finite-differencing epsilon.
	- ``flg_centered`` denotes whether to use forward (0) or centered (1) differences.
	- The Runge-Kutta integrator (:ref:`mjINT_RK4<mjtIntegrator>`) is not supported.

	.. admonition:: Improving speed and accuracy
	:class: tip

	warmstart
	If warm-starts are not :ref:`disabled<option-flag-warmstart>`, the warm-start accelerations
	``mjData.qacc_warmstart`` which are present at call-time are loaded at the start of every relevant pipeline call,
	to preserve determinism. If solver computations are an expensive part of the simulation, the following trick can
	lead to significant speed-ups: First call :ref:`mj_forward` to let the solver converge, then reduce :ref:`solver
	iterations<option-iterations>` significantly, then call :ref:`mjd_transitionFD`, finally, restore the original
	value of :ref:`iterations<option-iterations>`. Because we are already near the solution, few iteration are required
	to find the new minimum. This is especially true for the :ref:`Newton<option-solver>` solver, where the required
	number of iteration for convergence near the minimum can be as low as 1.

	tolerance
	Accuracy can be improved if solver :ref:`tolerance<option-tolerance>` is set to 0. This means that all calls to
	the solver will perform exactly the same number of iterations, preventing numerical errors due to early
	termination. Of course, this means that :ref:`solver iterations<option-iterations>` should be small, to not tread
	water at the minimum. This method and the one described above can and should be combined.

	.. _mjd_inverseFD:

	`mjd_inverseFD <#mjd_inverseFD>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjd_inverseFD

	Finite differenced continuous-time inverse-dynamics Jacobians.

	Letting :math:`x, a` denote the current :ref:`state<gePhysicsState>` and acceleration vectors in an mjData instance, and
	letting :math:`f, s` denote the forces computed by the inverse dynamics (``qfrc_inverse``), the function
	:ref:`mj_inverse` computes :math:`(x,a) \rightarrow (f,s)`. :ref:`mjd_inverseFD` computes seven associated Jacobians
	using finite-differencing. These matrices and their dimensions are:

	.. csv-table::
	:header: "matrix", "Jacobian", "dimension"
	:widths: auto
	:align: left

	``DfDq``, :math:`\partial f / \partial q`, ``nv x nv``
	``DfDv``, :math:`\partial f / \partial v`, ``nv x nv``
	``DfDa``, :math:`\partial f / \partial a`, ``nv x nv``
	``DsDq``, :math:`\partial s / \partial q`, ``nv x nsensordata``
	``DsDv``, :math:`\partial s / \partial v`, ``nv x nsensordata``
	``DsDa``, :math:`\partial s / \partial a`, ``nv x nsensordata``
	``DmDq``, :math:`\partial M / \partial q`, ``nv x nM``

	- All outputs are optional (can be NULL).
	- All outputs are transposed relative to Control Theory convention (i.e., column major).
	- ``DmDq``, which contains a sparse representation of the ``nv x nv x nv`` tensor :math:`\partial M / \partial q`, is
	not strictly an inverse dynamics Jacobian but is useful in related applications. It is provided as a convenience to
	the user, since the required values are already computed if either of the other two :math:`\partial / \partial q`
	Jacobians are requested.
	- ``eps`` is the (forward) finite-differencing epsilon.
	- ``flg_actuation`` denotes whether to subtract actuation forces (``qfrc_actuator``) from the output of the inverse
	dynamics. If this flag is positive, actuator forces are not considered as external.
	- The model option flag ``invdiscrete`` should correspond to the representation of ``mjData.qacc`` in order to compute
	the correct derivative information.

	.. attention::
	- The Runge-Kutta 4th-order integrator (``mjINT_RK4``) is not supported.
	- The noslip solver is not supported.

	.. _mjd_subQuat:

	`mjd_subQuat <#mjd_subQuat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjd_subQuat

	Derivatives of :ref:`mju_subQuat` (quaternion difference).

	.. _mjd_quatIntegrate:

	`mjd_quatIntegrate <#mjd_quatIntegrate>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjd_quatIntegrate

	Derivatives of :ref:`mju_quatIntegrate`.

	:math:`{\tt \small mju\_quatIntegrate}(q, v, h)` performs the in-place rotation :math:`q \leftarrow q + v h`,
	where :math:`q \in \mathbf{S}^3` is a unit quaternion, :math:`v \in \mathbf{R}^3` is a 3D angular velocity and
	:math:`h \in \mathbf{R^+}` is a timestep. This is equivalent to :math:`{\tt \small mju\_quatIntegrate}(q, s, 1.0)`,
	where :math:`s` is the scaled velocity :math:`s = h v`.

	:math:`{\tt \small mjd\_quatIntegrate}(v, h, D_q, D_v, D_h)` computes the Jacobians of the output :math:`q` with respect
	to the inputs. Below, :math:`\bar q` denotes the pre-modified quaternion:

	.. math::
	\begin{aligned}
	D_q &= \partial q / \partial \bar q \\
	D_v &= \partial q / \partial v \\
	D_h &= \partial q / \partial h
	\end{aligned}

	Note that derivatives depend only on :math:`h` and :math:`v` (in fact, on :math:`s = h v`).
	All outputs are optional.

	.. _Plugins-api:

	Plugins
	^^^^^^^
	.. _mjp_defaultPlugin:

	`mjp_defaultPlugin <#mjp_defaultPlugin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_defaultPlugin

	Set default plugin definition.

	.. _mjp_registerPlugin:

	`mjp_registerPlugin <#mjp_registerPlugin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_registerPlugin

	Globally register a plugin. This function is thread-safe.
	If an identical mjpPlugin is already registered, this function does nothing.
	If a non-identical mjpPlugin with the same name is already registered, an mju_error is raised.
	Two mjpPlugins are considered identical if all member function pointers and numbers are equal,
	and the name and attribute strings are all identical, however the char pointers to the strings
	need not be the same.

	.. _mjp_pluginCount:

	`mjp_pluginCount <#mjp_pluginCount>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_pluginCount

	Return the number of globally registered plugins.

	.. _mjp_getPlugin:

	`mjp_getPlugin <#mjp_getPlugin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_getPlugin

	Look up a plugin by name. If slot is not NULL, also write its registered slot number into it.

	.. _mjp_getPluginAtSlot:

	`mjp_getPluginAtSlot <#mjp_getPluginAtSlot>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_getPluginAtSlot

	Look up a plugin by the registered slot number that was returned by mjp_registerPlugin.

	.. _mjp_defaultResourceProvider:

	`mjp_defaultResourceProvider <#mjp_defaultResourceProvider>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_defaultResourceProvider

	Set default resource provider definition.

	.. _mjp_registerResourceProvider:

	`mjp_registerResourceProvider <#mjp_registerResourceProvider>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_registerResourceProvider

	Globally register a resource provider in a thread-safe manner. The provider must have a prefix
	that is not a sub-prefix or super-prefix of any current registered providers. This function
	returns a slot number > 0 on success.

	.. _mjp_resourceProviderCount:

	`mjp_resourceProviderCount <#mjp_resourceProviderCount>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_resourceProviderCount

	Return the number of globally registered resource providers.

	.. _mjp_getResourceProvider:

	`mjp_getResourceProvider <#mjp_getResourceProvider>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_getResourceProvider

	Return the resource provider with the prefix that matches against the resource name.
	If no match, return NULL.

	.. _mjp_getResourceProviderAtSlot:

	`mjp_getResourceProviderAtSlot <#mjp_getResourceProviderAtSlot>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjp_getResourceProviderAtSlot

	Look up a resource provider by slot number returned by mjp_registerResourceProvider.
	If invalid slot number, return NULL.

	.. _Thread:

	Threads
	^^^^^^^
	.. _mju_threadPoolCreate:

	`mju_threadPoolCreate <#mju_threadPoolCreate>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_threadPoolCreate

	Create a thread pool with the specified number of threads running.

	.. _mju_bindThreadPool:

	`mju_bindThreadPool <#mju_bindThreadPool>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_bindThreadPool

	Adds a thread pool to mjData and configures it for multi-threaded use.

	.. _mju_threadPoolEnqueue:

	`mju_threadPoolEnqueue <#mju_threadPoolEnqueue>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_threadPoolEnqueue

	Enqueue a task in a thread pool.

	.. _mju_threadPoolDestroy:

	`mju_threadPoolDestroy <#mju_threadPoolDestroy>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_threadPoolDestroy

	Destroy a thread pool.

	.. _mju_defaultTask:

	`mju_defaultTask <#mju_defaultTask>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_defaultTask

	Initialize an mjTask.

	.. _mju_taskJoin:

	`mju_taskJoin <#mju_taskJoin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_taskJoin

	Wait for a task to complete.

	.. _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:

	`mju_zero3 <#mju_zero3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_zero3

	Set res = 0.

	.. _mju_copy3:

	`mju_copy3 <#mju_copy3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_copy3

	Set res = vec.

	.. _mju_scl3:

	`mju_scl3 <#mju_scl3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_scl3

	Set res = vec*scl.

	.. _mju_add3:

	`mju_add3 <#mju_add3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_add3

	Set res = vec1 + vec2.

	.. _mju_sub3:

	`mju_sub3 <#mju_sub3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_sub3

	Set res = vec1 - vec2.

	.. _mju_addTo3:

	`mju_addTo3 <#mju_addTo3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_addTo3

	Set res = res + vec.

	.. _mju_subFrom3:

	`mju_subFrom3 <#mju_subFrom3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_subFrom3

	Set res = res - vec.

	.. _mju_addToScl3:

	`mju_addToScl3 <#mju_addToScl3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_addToScl3

	Set res = res + vec*scl.

	.. _mju_addScl3:

	`mju_addScl3 <#mju_addScl3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_addScl3

	Set res = vec1 + vec2*scl.

	.. _mju_normalize3:

	`mju_normalize3 <#mju_normalize3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_normalize3

	Normalize vector, return length before normalization.

	.. _mju_norm3:

	`mju_norm3 <#mju_norm3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_norm3

	Return vector length (without normalizing the vector).

	.. _mju_dot3:

	`mju_dot3 <#mju_dot3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_dot3

	Return dot-product of vec1 and vec2.

	.. _mju_dist3:

	`mju_dist3 <#mju_dist3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_dist3

	Return Cartesian distance between 3D vectors pos1 and pos2.

	.. _mju_mulMatVec3:

	`mju_mulMatVec3 <#mju_mulMatVec3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulMatVec3

	Multiply 3-by-3 matrix by vector: res = mat * vec.

	.. _mju_mulMatTVec3:

	`mju_mulMatTVec3 <#mju_mulMatTVec3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulMatTVec3

	Multiply transposed 3-by-3 matrix by vector: res = mat' * vec.

	.. _mju_cross:

	`mju_cross <#mju_cross>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_cross

	Compute cross-product: res = cross(a, b).

	.. _mju_zero4:

	`mju_zero4 <#mju_zero4>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_zero4

	Set res = 0.

	.. _mju_unit4:

	`mju_unit4 <#mju_unit4>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_unit4

	Set res = (1,0,0,0).

	.. _mju_copy4:

	`mju_copy4 <#mju_copy4>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_copy4

	Set res = vec.

	.. _mju_normalize4:

	`mju_normalize4 <#mju_normalize4>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_normalize4

	Normalize vector, return length before normalization.

	.. _mju_zero:

	`mju_zero <#mju_zero>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_zero

	Set res = 0.

	.. _mju_fill:

	`mju_fill <#mju_fill>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_fill

	Set res = val.

	.. _mju_copy:

	`mju_copy <#mju_copy>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_copy

	Set res = vec.

	.. _mju_sum:

	`mju_sum <#mju_sum>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_sum

	Return sum(vec).

	.. _mju_L1:

	`mju_L1 <#mju_L1>`__
	~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_L1

	Return L1 norm: sum(abs(vec)).

	.. _mju_scl:

	`mju_scl <#mju_scl>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_scl

	Set res = vec*scl.

	.. _mju_add:

	`mju_add <#mju_add>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_add

	Set res = vec1 + vec2.

	.. _mju_sub:

	`mju_sub <#mju_sub>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_sub

	Set res = vec1 - vec2.

	.. _mju_addTo:

	`mju_addTo <#mju_addTo>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_addTo

	Set res = res + vec.

	.. _mju_subFrom:

	`mju_subFrom <#mju_subFrom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_subFrom

	Set res = res - vec.

	.. _mju_addToScl:

	`mju_addToScl <#mju_addToScl>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_addToScl

	Set res = res + vec*scl.

	.. _mju_addScl:

	`mju_addScl <#mju_addScl>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_addScl

	Set res = vec1 + vec2*scl.

	.. _mju_normalize:

	`mju_normalize <#mju_normalize>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_normalize

	Normalize vector, return length before normalization.

	.. _mju_norm:

	`mju_norm <#mju_norm>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_norm

	Return vector length (without normalizing vector).

	.. _mju_dot:

	`mju_dot <#mju_dot>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_dot

	Return dot-product of vec1 and vec2.

	.. _mju_mulMatVec:

	`mju_mulMatVec <#mju_mulMatVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulMatVec

	Multiply matrix and vector: res = mat * vec.

	.. _mju_mulMatTVec:

	`mju_mulMatTVec <#mju_mulMatTVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulMatTVec

	Multiply transposed matrix and vector: res = mat' * vec.

	.. _mju_mulVecMatVec:

	`mju_mulVecMatVec <#mju_mulVecMatVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulVecMatVec

	Multiply square matrix with vectors on both sides: returns vec1' * mat * vec2.

	.. _mju_transpose:

	`mju_transpose <#mju_transpose>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_transpose

	Transpose matrix: res = mat'.

	.. _mju_symmetrize:

	`mju_symmetrize <#mju_symmetrize>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_symmetrize

	Symmetrize square matrix :math:`R = \frac{1}{2}(M + M^T)`.

	.. _mju_eye:

	`mju_eye <#mju_eye>`__
	~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_eye

	Set mat to the identity matrix.

	.. _mju_mulMatMat:

	`mju_mulMatMat <#mju_mulMatMat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulMatMat

	Multiply matrices: res = mat1 * mat2.

	.. _mju_mulMatMatT:

	`mju_mulMatMatT <#mju_mulMatMatT>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulMatMatT

	Multiply matrices, second argument transposed: res = mat1 * mat2'.

	.. _mju_mulMatTMat:

	`mju_mulMatTMat <#mju_mulMatTMat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulMatTMat

	Multiply matrices, first argument transposed: res = mat1' * mat2.

	.. _mju_sqrMatTD:

	`mju_sqrMatTD <#mju_sqrMatTD>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_sqrMatTD

	Set res = mat' * diag * mat if diag is not NULL, and res = mat' * mat otherwise.

	.. _mju_transformSpatial:

	`mju_transformSpatial <#mju_transformSpatial>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_transformSpatial

	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.

	.. _Sparsemath:

	Sparse math
	^^^^^^^^^^^
	.. _mju_dense2sparse:

	`mju_dense2sparse <#mju_dense2sparse>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_dense2sparse

	Convert matrix from dense to sparse.
	nnz is size of res and colind, return 1 if too small, 0 otherwise.

	.. _mju_sparse2dense:

	`mju_sparse2dense <#mju_sparse2dense>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_sparse2dense

	Convert matrix from sparse to dense.

	.. _Quaternions:

	Quaternions
	^^^^^^^^^^^

	.. _mju_rotVecQuat:

	`mju_rotVecQuat <#mju_rotVecQuat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_rotVecQuat

	Rotate vector by quaternion.

	.. _mju_negQuat:

	`mju_negQuat <#mju_negQuat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_negQuat

	Conjugate quaternion, corresponding to opposite rotation.

	.. _mju_mulQuat:

	`mju_mulQuat <#mju_mulQuat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulQuat

	Multiply quaternions.

	.. _mju_mulQuatAxis:

	`mju_mulQuatAxis <#mju_mulQuatAxis>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulQuatAxis

	Multiply quaternion and axis.

	.. _mju_axisAngle2Quat:

	`mju_axisAngle2Quat <#mju_axisAngle2Quat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_axisAngle2Quat

	Convert axisAngle to quaternion.

	.. _mju_quat2Vel:

	`mju_quat2Vel <#mju_quat2Vel>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_quat2Vel

	Convert quaternion (corresponding to orientation difference) to 3D velocity.

	.. _mju_subQuat:

	`mju_subQuat <#mju_subQuat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_subQuat

	Subtract quaternions, express as 3D velocity: qb*quat(res) = qa.

	.. _mju_quat2Mat:

	`mju_quat2Mat <#mju_quat2Mat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_quat2Mat

	Convert quaternion to 3D rotation matrix.

	.. _mju_mat2Quat:

	`mju_mat2Quat <#mju_mat2Quat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mat2Quat

	Convert 3D rotation matrix to quaternion.

	.. _mju_derivQuat:

	`mju_derivQuat <#mju_derivQuat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_derivQuat

	Compute time-derivative of quaternion, given 3D rotational velocity.

	.. _mju_quatIntegrate:

	`mju_quatIntegrate <#mju_quatIntegrate>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_quatIntegrate

	Integrate quaternion given 3D angular velocity.

	.. _mju_quatZ2Vec:

	`mju_quatZ2Vec <#mju_quatZ2Vec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_quatZ2Vec

	Construct quaternion performing rotation from z-axis to given vector.

	.. _mju_mat2Rot:

	`mju_mat2Rot <#mju_mat2Rot>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mat2Rot

	Extract 3D rotation from an arbitrary 3x3 matrix by refining the input quaternion.
	Returns the number of iterations required to converge

	.. _mju_euler2Quat:

	`mju_euler2Quat <#mju_euler2Quat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_euler2Quat

	Convert sequence of Euler angles (radians) to quaternion.
	seq[0,1,2] must be in 'xyzXYZ', lower/upper-case mean intrinsic/extrinsic rotations.

	.. _Poses:

	Poses
	^^^^^

	.. _mju_mulPose:

	`mju_mulPose <#mju_mulPose>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_mulPose

	Multiply two poses.

	.. _mju_negPose:

	`mju_negPose <#mju_negPose>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_negPose

	Conjugate pose, corresponding to the opposite spatial transformation.

	.. _mju_trnVecPose:

	`mju_trnVecPose <#mju_trnVecPose>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_trnVecPose

	Transform vector by pose.

	.. _Decompositions:

	Decompositions / Solvers
	^^^^^^^^^^^^^^^^^^^^^^^^

	.. _mju_cholFactor:

	`mju_cholFactor <#mju_cholFactor>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_cholFactor

	Cholesky decomposition: mat = L*L'; return rank, decomposition performed in-place into mat.

	.. _mju_cholSolve:

	`mju_cholSolve <#mju_cholSolve>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_cholSolve

	Solve (matmat') res = vec, where mat is a Cholesky factor.

	.. _mju_cholUpdate:

	`mju_cholUpdate <#mju_cholUpdate>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_cholUpdate

	Cholesky rank-one update: LL' +/- xx'; return rank.

	.. _mju_cholFactorBand:

	`mju_cholFactorBand <#mju_cholFactorBand>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_cholFactorBand

	Band-dense Cholesky decomposition.
	\|br\| Add ``diagadd + diagmul*mat_ii`` to diagonal before decomposition.
	\|br\| Returns the minimum value of the factorized diagonal or 0 if rank-deficient.

	Symmetric band-dense matrices

	:ref:`mju_cholFactorBand` and subsequent functions containing the substring "band" operate on matrices which are a
	generalization of symmetric `band matrices <https://en.wikipedia.org/wiki/Band_matrix>`_. Symmetric band-dense or
	"arrowhead" matrices have non-zeros along proximal diagonal bands and dense blocks on the bottom rows and right
	columns. These matrices have the property that Cholesky factorization creates no fill-in and can therefore be
	performed efficiently in-place. Matrix structure is defined by three integers:

	- ``ntotal``: the number of rows (columns) of the symmetric matrix.
	- ``nband``: the number of bands under (over) the diagonal, inclusive of the diagonal.
	- ``ndense``: the number of dense rows (columns) at the bottom (right).

	The non-zeros are stored in memory as two contiguous row-major blocks, colored green and blue in the illustration
	below. The first block has size ``nband x (ntotal-ndense)`` and contains the diagonal and the bands below it. The
	second block has size ``ndense x ntotal`` and contains the dense part. Total required memory is the sum of the block
	sizes.

	.. figure:: /images/APIreference/arrowhead.svg
	:width: 750px
	:align: left

	For example, consider an arrowhead matrix with ``nband = 3``, ``ndense = 2`` and ``ntotal = 8``. In this example, the
	total memory required is ``3(8-2) + 28 = 34`` mjtNum's, laid out as follows:

	.. code-block::

	0 1 2
	3 4 5
	6 7 8
	9 10 11
	12 13 14
	15 16 17
	18 19 20 21 22 23 24 25
	26 27 28 29 30 31 32 33


	The diagonal elements are ``2, 5, 8, 11, 14, 17, 24, 33``.
	\|br\| Elements ``0, 1, 3, 25`` are present in memory but never touched.

	.. _mju_cholSolveBand:

	`mju_cholSolveBand <#mju_cholSolveBand>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_cholSolveBand

	Solve (matmat')res = vec where mat is a band-dense Cholesky factor.

	.. _mju_band2Dense:

	`mju_band2Dense <#mju_band2Dense>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_band2Dense

	Convert banded matrix to dense matrix, fill upper triangle if flg_sym>0.

	.. _mju_dense2Band:

	`mju_dense2Band <#mju_dense2Band>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_dense2Band

	Convert dense matrix to banded matrix.

	.. _mju_bandMulMatVec:

	`mju_bandMulMatVec <#mju_bandMulMatVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_bandMulMatVec

	Multiply band-diagonal matrix with nvec vectors, include upper triangle if flg_sym>0.

	.. _mju_bandDiag:

	`mju_bandDiag <#mju_bandDiag>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_bandDiag

	Address of diagonal element i in band-dense matrix representation.

	.. _mju_eig3:

	`mju_eig3 <#mju_eig3>`__
	~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_eig3

	Eigenvalue decomposition of symmetric 3x3 matrix, mat = eigvec * diag(eigval) * eigvec'.

	.. _mju_boxQP:

	`mju_boxQP <#mju_boxQP>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_boxQP

	Minimize :math:`\tfrac{1}{2} x^T H x + x^T g \quad \text{s.t.} \quad l \le x \le u`, return rank or -1 if failed.

	inputs:
	``n`` - problem dimension

	``H`` - SPD matrix ``n*n``

	``g`` - bias vector ``n``

	``lower`` - lower bounds ``n``

	``upper`` - upper bounds ``n``

	``res`` - solution warmstart ``n``

	return value:
	``nfree <= n`` - rank of unconstrained subspace, -1 if failure

	outputs (required):
	``res`` - solution ``n``

	``R`` - subspace Cholesky factor ``nfreenfree``, allocated: ``n(n+7)``

	outputs (optional):
	``index`` - set of free dimensions ``nfree``, allocated: ``n``

	notes:
	The initial value of ``res`` is used to warmstart the solver.
	``R`` must have allocated size ``n(n+7)``, but only ``nfreenfree`` values are used as output.
	``index`` (if given) must have allocated size ``n``, but only ``nfree`` values are used as output.
	The convenience function :ref:`mju_boxQPmalloc` allocates the required data structures.
	Only the lower triangles of H and R are read from and written to, respectively.

	.. _mju_boxQPmalloc:

	`mju_boxQPmalloc <#mju_boxQPmalloc>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mju_boxQPmalloc

	Allocate heap memory for box-constrained Quadratic Program.
	As in :ref:`mju_boxQP`, ``index``, ``lower``, and ``upper`` are optional.
	Free all pointers with ``mju_free()``.

	.. _Attachment:

	Attachment
	^^^^^^^^^^
	.. _mjs_attach:

	`mjs_attach <#mjs_attach>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_attach

	Attach child to a parent, return the attached element if success or NULL otherwise.

	.. _AddTreeElements:

	Tree elements
	^^^^^^^^^^^^^
	.. _mjs_addBody:

	`mjs_addBody <#mjs_addBody>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addBody

	Add child body to body, return child.

	.. _mjs_addSite:

	`mjs_addSite <#mjs_addSite>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addSite

	Add site to body, return site spec.

	.. _mjs_addJoint:

	`mjs_addJoint <#mjs_addJoint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addJoint

	Add joint to body.

	.. _mjs_addFreeJoint:

	`mjs_addFreeJoint <#mjs_addFreeJoint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addFreeJoint

	Add freejoint to body.

	.. _mjs_addGeom:

	`mjs_addGeom <#mjs_addGeom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addGeom

	Add geom to body.

	.. _mjs_addCamera:

	`mjs_addCamera <#mjs_addCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addCamera

	Add camera to body.

	.. _mjs_addLight:

	`mjs_addLight <#mjs_addLight>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addLight

	Add light to body.

	.. _mjs_addFrame:

	`mjs_addFrame <#mjs_addFrame>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addFrame

	Add frame to body.

	.. _mjs_delete:

	`mjs_delete <#mjs_delete>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_delete

	Remove object corresponding to the given element, return 0 on success.

	.. _AddNonTreeElements:

	Non-tree elements
	^^^^^^^^^^^^^^^^^
	.. _mjs_addActuator:

	`mjs_addActuator <#mjs_addActuator>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addActuator

	Add actuator.

	.. _mjs_addSensor:

	`mjs_addSensor <#mjs_addSensor>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addSensor

	Add sensor.

	.. _mjs_addFlex:

	`mjs_addFlex <#mjs_addFlex>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addFlex

	Add flex.

	.. _mjs_addPair:

	`mjs_addPair <#mjs_addPair>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addPair

	Add contact pair.

	.. _mjs_addExclude:

	`mjs_addExclude <#mjs_addExclude>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addExclude

	Add excluded body pair.

	.. _mjs_addEquality:

	`mjs_addEquality <#mjs_addEquality>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addEquality

	Add equality.

	.. _mjs_addTendon:

	`mjs_addTendon <#mjs_addTendon>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addTendon

	Add tendon.

	.. _mjs_wrapSite:

	`mjs_wrapSite <#mjs_wrapSite>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_wrapSite

	Wrap site using tendon.

	.. _mjs_wrapGeom:

	`mjs_wrapGeom <#mjs_wrapGeom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_wrapGeom

	Wrap geom using tendon.

	.. _mjs_wrapJoint:

	`mjs_wrapJoint <#mjs_wrapJoint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_wrapJoint

	Wrap joint using tendon.

	.. _mjs_wrapPulley:

	`mjs_wrapPulley <#mjs_wrapPulley>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_wrapPulley

	Wrap pulley using tendon.

	.. _mjs_addNumeric:

	`mjs_addNumeric <#mjs_addNumeric>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addNumeric

	Add numeric.

	.. _mjs_addText:

	`mjs_addText <#mjs_addText>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addText

	Add text.

	.. _mjs_addTuple:

	`mjs_addTuple <#mjs_addTuple>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addTuple

	Add tuple.

	.. _mjs_addKey:

	`mjs_addKey <#mjs_addKey>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addKey

	Add keyframe.

	.. _mjs_addPlugin:

	`mjs_addPlugin <#mjs_addPlugin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addPlugin

	Add plugin.

	.. _mjs_addDefault:

	`mjs_addDefault <#mjs_addDefault>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addDefault

	Add default.

	.. _AddAssets:

	Assets
	^^^^^^
	.. _mjs_addMesh:

	`mjs_addMesh <#mjs_addMesh>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addMesh

	Add mesh.

	.. _mjs_addHField:

	`mjs_addHField <#mjs_addHField>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addHField

	Add height field.

	.. _mjs_addSkin:

	`mjs_addSkin <#mjs_addSkin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addSkin

	Add skin.

	.. _mjs_addTexture:

	`mjs_addTexture <#mjs_addTexture>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addTexture

	Add texture.

	.. _mjs_addMaterial:

	`mjs_addMaterial <#mjs_addMaterial>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_addMaterial

	Add material.

	.. _FindAndGetUtilities:

	Find and get utilities
	^^^^^^^^^^^^^^^^^^^^^^
	.. _mjs_getSpec:

	`mjs_getSpec <#mjs_getSpec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getSpec

	Get spec from body.

	.. _mjs_findSpec:

	`mjs_findSpec <#mjs_findSpec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_findSpec

	Find spec (model asset) by name.

	.. _mjs_findBody:

	`mjs_findBody <#mjs_findBody>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_findBody

	Find body in spec by name.

	.. _mjs_findElement:

	`mjs_findElement <#mjs_findElement>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_findElement

	Find element in spec by name.

	.. _mjs_findChild:

	`mjs_findChild <#mjs_findChild>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_findChild

	Find child body by name.

	.. _mjs_getParent:

	`mjs_getParent <#mjs_getParent>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getParent

	Get parent body.

	.. _mjs_getFrame:

	`mjs_getFrame <#mjs_getFrame>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getFrame

	Get parent frame.

	.. _mjs_findFrame:

	`mjs_findFrame <#mjs_findFrame>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_findFrame

	Find frame by name.

	.. _mjs_getDefault:

	`mjs_getDefault <#mjs_getDefault>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getDefault

	Get default corresponding to an element.

	.. _mjs_findDefault:

	`mjs_findDefault <#mjs_findDefault>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_findDefault

	Find default in model by class name.

	.. _mjs_getSpecDefault:

	`mjs_getSpecDefault <#mjs_getSpecDefault>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getSpecDefault

	Get global default from model.

	.. _mjs_getId:

	`mjs_getId <#mjs_getId>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getId

	Get element id.

	.. _mjs_firstChild:

	`mjs_firstChild <#mjs_firstChild>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_firstChild

	Return body's first child of given type. If recurse is nonzero, also search the body's subtree.

	.. _mjs_nextChild:

	`mjs_nextChild <#mjs_nextChild>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_nextChild

	Return body's next child of the same type; return NULL if child is last.
	If recurse is nonzero, also search the body's subtree.

	.. _mjs_firstElement:

	`mjs_firstElement <#mjs_firstElement>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_firstElement

	Return spec's first element of selected type.

	.. _mjs_nextElement:

	`mjs_nextElement <#mjs_nextElement>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_nextElement

	Return spec's next element; return NULL if element is last.

	.. _AttributeSetters:

	Attribute setters
	^^^^^^^^^^^^^^^^^
	.. _mjs_setName:

	`mjs_setName <#mjs_setName>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setName

	Set element's name, return 0 on success.

	.. _mjs_setBuffer:

	`mjs_setBuffer <#mjs_setBuffer>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setBuffer

	Copy buffer.

	.. _mjs_setString:

	`mjs_setString <#mjs_setString>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setString

	Copy text to string.

	.. _mjs_setStringVec:

	`mjs_setStringVec <#mjs_setStringVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setStringVec

	Split text to entries and copy to string vector.

	.. _mjs_setInStringVec:

	`mjs_setInStringVec <#mjs_setInStringVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setInStringVec

	Set entry in string vector.

	.. _mjs_appendString:

	`mjs_appendString <#mjs_appendString>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_appendString

	Append text entry to string vector.

	.. _mjs_setInt:

	`mjs_setInt <#mjs_setInt>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setInt

	Copy int array to vector.

	.. _mjs_appendIntVec:

	`mjs_appendIntVec <#mjs_appendIntVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_appendIntVec

	Append int array to vector of arrays.

	.. _mjs_setFloat:

	`mjs_setFloat <#mjs_setFloat>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setFloat

	Copy float array to vector.

	.. _mjs_appendFloatVec:

	`mjs_appendFloatVec <#mjs_appendFloatVec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_appendFloatVec

	Append float array to vector of arrays.

	.. _mjs_setDouble:

	`mjs_setDouble <#mjs_setDouble>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setDouble

	Copy double array to vector.

	.. _mjs_setPluginAttributes:

	`mjs_setPluginAttributes <#mjs_setPluginAttributes>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setPluginAttributes

	Set plugin attributes.

	.. _AttributeGetters:

	Attribute getters
	^^^^^^^^^^^^^^^^^
	.. _mjs_getName:

	`mjs_getName <#mjs_getName>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getName

	Get element's name.

	.. _mjs_getString:

	`mjs_getString <#mjs_getString>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getString

	Get string contents.

	.. _mjs_getDouble:

	`mjs_getDouble <#mjs_getDouble>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getDouble

	Get double array contents and optionally its size.

	.. _mjs_getPluginAttributes:

	`mjs_getPluginAttributes <#mjs_getPluginAttributes>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getPluginAttributes

	Get plugin attributes.

	.. _SpecUtilities:

	Spec utilities
	^^^^^^^^^^^^^^
	.. _mjs_setDefault:

	`mjs_setDefault <#mjs_setDefault>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setDefault

	Set element's default.

	.. _mjs_setFrame:

	`mjs_setFrame <#mjs_setFrame>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setFrame

	Set element's enclosing frame, return 0 on success.

	.. _mjs_resolveOrientation:

	`mjs_resolveOrientation <#mjs_resolveOrientation>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_resolveOrientation

	Resolve alternative orientations to quat, return error if any.

	.. _mjs_bodyToFrame:

	`mjs_bodyToFrame <#mjs_bodyToFrame>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_bodyToFrame

	Transform body into a frame.

	.. _mjs_setUserValue:

	`mjs_setUserValue <#mjs_setUserValue>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setUserValue

	Set user payload, overriding the existing value for the specified key if present.

	.. _mjs_setUserValueWithCleanup:

	`mjs_setUserValueWithCleanup <#mjs_setUserValueWithCleanup>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_setUserValueWithCleanup

	Set user payload, overriding the existing value for the specified key if
	present. This version differs from mjs_setUserValue in that it takes a
	cleanup function that will be called when the user payload is deleted.

	.. _mjs_getUserValue:

	`mjs_getUserValue <#mjs_getUserValue>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_getUserValue

	Return user payload or NULL if none found.

	.. _mjs_deleteUserValue:

	`mjs_deleteUserValue <#mjs_deleteUserValue>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_deleteUserValue

	Delete user payload.

	.. _ElementInitialization:

	Element initialization
	^^^^^^^^^^^^^^^^^^^^^^
	.. _mjs_defaultSpec:

	`mjs_defaultSpec <#mjs_defaultSpec>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultSpec

	Default spec attributes.

	.. _mjs_defaultOrientation:

	`mjs_defaultOrientation <#mjs_defaultOrientation>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultOrientation

	Default orientation attributes.

	.. _mjs_defaultBody:

	`mjs_defaultBody <#mjs_defaultBody>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultBody

	Default body attributes.

	.. _mjs_defaultFrame:

	`mjs_defaultFrame <#mjs_defaultFrame>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultFrame

	Default frame attributes.

	.. _mjs_defaultJoint:

	`mjs_defaultJoint <#mjs_defaultJoint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultJoint

	Default joint attributes.

	.. _mjs_defaultGeom:

	`mjs_defaultGeom <#mjs_defaultGeom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultGeom

	Default geom attributes.

	.. _mjs_defaultSite:

	`mjs_defaultSite <#mjs_defaultSite>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultSite

	Default site attributes.

	.. _mjs_defaultCamera:

	`mjs_defaultCamera <#mjs_defaultCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultCamera

	Default camera attributes.

	.. _mjs_defaultLight:

	`mjs_defaultLight <#mjs_defaultLight>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultLight

	Default light attributes.

	.. _mjs_defaultFlex:

	`mjs_defaultFlex <#mjs_defaultFlex>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultFlex

	Default flex attributes.

	.. _mjs_defaultMesh:

	`mjs_defaultMesh <#mjs_defaultMesh>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultMesh

	Default mesh attributes.

	.. _mjs_defaultHField:

	`mjs_defaultHField <#mjs_defaultHField>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultHField

	Default height field attributes.

	.. _mjs_defaultSkin:

	`mjs_defaultSkin <#mjs_defaultSkin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultSkin

	Default skin attributes.

	.. _mjs_defaultTexture:

	`mjs_defaultTexture <#mjs_defaultTexture>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultTexture

	Default texture attributes.

	.. _mjs_defaultMaterial:

	`mjs_defaultMaterial <#mjs_defaultMaterial>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultMaterial

	Default material attributes.

	.. _mjs_defaultPair:

	`mjs_defaultPair <#mjs_defaultPair>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultPair

	Default pair attributes.

	.. _mjs_defaultEquality:

	`mjs_defaultEquality <#mjs_defaultEquality>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultEquality

	Default equality attributes.

	.. _mjs_defaultTendon:

	`mjs_defaultTendon <#mjs_defaultTendon>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultTendon

	Default tendon attributes.

	.. _mjs_defaultActuator:

	`mjs_defaultActuator <#mjs_defaultActuator>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultActuator

	Default actuator attributes.

	.. _mjs_defaultSensor:

	`mjs_defaultSensor <#mjs_defaultSensor>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultSensor

	Default sensor attributes.

	.. _mjs_defaultNumeric:

	`mjs_defaultNumeric <#mjs_defaultNumeric>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultNumeric

	Default numeric attributes.

	.. _mjs_defaultText:

	`mjs_defaultText <#mjs_defaultText>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultText

	Default text attributes.

	.. _mjs_defaultTuple:

	`mjs_defaultTuple <#mjs_defaultTuple>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultTuple

	Default tuple attributes.

	.. _mjs_defaultKey:

	`mjs_defaultKey <#mjs_defaultKey>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultKey

	Default keyframe attributes.

	.. _mjs_defaultPlugin:

	`mjs_defaultPlugin <#mjs_defaultPlugin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_defaultPlugin

	Default plugin attributes.

	.. _ElementCasting:

	Element casting
	^^^^^^^^^^^^^^^
	.. _mjs_asBody:

	`mjs_asBody <#mjs_asBody>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asBody

	Safely cast an element as mjsBody, or return NULL if the element is not an mjsBody.

	.. _mjs_asGeom:

	`mjs_asGeom <#mjs_asGeom>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asGeom

	Safely cast an element as mjsGeom, or return NULL if the element is not an mjsGeom.

	.. _mjs_asJoint:

	`mjs_asJoint <#mjs_asJoint>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asJoint

	Safely cast an element as mjsJoint, or return NULL if the element is not an mjsJoint.

	.. _mjs_asSite:

	`mjs_asSite <#mjs_asSite>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asSite

	Safely cast an element as mjsSite, or return NULL if the element is not an mjsSite.

	.. _mjs_asCamera:

	`mjs_asCamera <#mjs_asCamera>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asCamera

	Safely cast an element as mjsCamera, or return NULL if the element is not an mjsCamera.

	.. _mjs_asLight:

	`mjs_asLight <#mjs_asLight>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asLight

	Safely cast an element as mjsLight, or return NULL if the element is not an mjsLight.

	.. _mjs_asFrame:

	`mjs_asFrame <#mjs_asFrame>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asFrame

	Safely cast an element as mjsFrame, or return NULL if the element is not an mjsFrame.

	.. _mjs_asActuator:

	`mjs_asActuator <#mjs_asActuator>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asActuator

	Safely cast an element as mjsActuator, or return NULL if the element is not an mjsActuator.

	.. _mjs_asSensor:

	`mjs_asSensor <#mjs_asSensor>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asSensor

	Safely cast an element as mjsSensor, or return NULL if the element is not an mjsSensor.

	.. _mjs_asFlex:

	`mjs_asFlex <#mjs_asFlex>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asFlex

	Safely cast an element as mjsFlex, or return NULL if the element is not an mjsFlex.

	.. _mjs_asPair:

	`mjs_asPair <#mjs_asPair>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asPair

	Safely cast an element as mjsPair, or return NULL if the element is not an mjsPair.

	.. _mjs_asEquality:

	`mjs_asEquality <#mjs_asEquality>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asEquality

	Safely cast an element as mjsEquality, or return NULL if the element is not an mjsEquality.

	.. _mjs_asExclude:

	`mjs_asExclude <#mjs_asExclude>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asExclude

	Safely cast an element as mjsExclude, or return NULL if the element is not an mjsExclude.

	.. _mjs_asTendon:

	`mjs_asTendon <#mjs_asTendon>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asTendon

	Safely cast an element as mjsTendon, or return NULL if the element is not an mjsTendon.

	.. _mjs_asNumeric:

	`mjs_asNumeric <#mjs_asNumeric>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asNumeric

	Safely cast an element as mjsNumeric, or return NULL if the element is not an mjsNumeric.

	.. _mjs_asText:

	`mjs_asText <#mjs_asText>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asText

	Safely cast an element as mjsText, or return NULL if the element is not an mjsText.

	.. _mjs_asTuple:

	`mjs_asTuple <#mjs_asTuple>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asTuple

	Safely cast an element as mjsTuple, or return NULL if the element is not an mjsTuple.

	.. _mjs_asKey:

	`mjs_asKey <#mjs_asKey>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asKey

	Safely cast an element as mjsKey, or return NULL if the element is not an mjsKey.

	.. _mjs_asMesh:

	`mjs_asMesh <#mjs_asMesh>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asMesh

	Safely cast an element as mjsMesh, or return NULL if the element is not an mjsMesh.

	.. _mjs_asHField:

	`mjs_asHField <#mjs_asHField>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asHField

	Safely cast an element as mjsHField, or return NULL if the element is not an mjsHField.

	.. _mjs_asSkin:

	`mjs_asSkin <#mjs_asSkin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asSkin

	Safely cast an element as mjsSkin, or return NULL if the element is not an mjsSkin.

	.. _mjs_asTexture:

	`mjs_asTexture <#mjs_asTexture>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asTexture

	Safely cast an element as mjsTexture, or return NULL if the element is not an mjsTexture.

	.. _mjs_asMaterial:

	`mjs_asMaterial <#mjs_asMaterial>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asMaterial

	Safely cast an element as mjsMaterial, or return NULL if the element is not an mjsMaterial.

	.. _mjs_asPlugin:

	`mjs_asPlugin <#mjs_asPlugin>`__
	~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

	.. mujoco-include:: mjs_asPlugin

	Safely cast an element as mjsPlugin, or return NULL if the element is not an mjsPlugin.