text: #include "MultiBodyTree.hpp"
  
  #include <cmath>
  #include <limits>
  #include <vector>
  
  #include "IDMath.hpp"
  #include "details/MultiBodyTreeImpl.hpp"
  #include "details/MultiBodyTreeInitCache.hpp"
  
  namespace btInverseDynamics
  {
  MultiBodyTree::MultiBodyTree()
  	: m_is_finalized(false),
  	  m_mass_parameters_are_valid(true),
  	  m_accept_invalid_mass_parameters(false),
  	  m_impl(0x0),
  	  m_init_cache(0x0)
  {
  	m_init_cache = new InitCache();
  }
  
  MultiBodyTree::~MultiBodyTree()
  {
  	delete m_impl;
  	delete m_init_cache;
  }
  
  void MultiBodyTree::setAcceptInvalidMassParameters(bool flag)
  {
  	m_accept_invalid_mass_parameters = flag;
  }
  
  bool MultiBodyTree::getAcceptInvalidMassProperties() const
  {
  	return m_accept_invalid_mass_parameters;
  }
  
  int MultiBodyTree::getBodyOrigin(const int body_index, vec3 *world_origin) const
  {
  	return m_impl->getBodyOrigin(body_index, world_origin);
  }
  
  int MultiBodyTree::getBodyCoM(const int body_index, vec3 *world_com) const
  {
  	return m_impl->getBodyCoM(body_index, world_com);
  }
  
  int MultiBodyTree::getBodyTransform(const int body_index, mat33 *world_T_body) const
  {
  	return m_impl->getBodyTransform(body_index, world_T_body);
  }
  int MultiBodyTree::getBodyAngularVelocity(const int body_index, vec3 *world_omega) const
  {
  	return m_impl->getBodyAngularVelocity(body_index, world_omega);
  }
  int MultiBodyTree::getBodyLinearVelocity(const int body_index, vec3 *world_velocity) const
  {
  	return m_impl->getBodyLinearVelocity(body_index, world_velocity);
  }
  
  int MultiBodyTree::getBodyLinearVelocityCoM(const int body_index, vec3 *world_velocity) const
  {
  	return m_impl->getBodyLinearVelocityCoM(body_index, world_velocity);
  }
  
  int MultiBodyTree::getBodyAngularAcceleration(const int body_index, vec3 *world_dot_omega) const
  {
  	return m_impl->getBodyAngularAcceleration(body_index, world_dot_omega);
  }
  int MultiBodyTree::getBodyLinearAcceleration(const int body_index, vec3 *world_acceleration) const
  {
  	return m_impl->getBodyLinearAcceleration(body_index, world_acceleration);
  }
  
  int MultiBodyTree::getParentRParentBodyRef(const int body_index, vec3 *r) const
  {
  	return m_impl->getParentRParentBodyRef(body_index, r);
  }
  
  int MultiBodyTree::getBodyTParentRef(const int body_index, mat33 *T) const
  {
  	return m_impl->getBodyTParentRef(body_index, T);
  }
  
  int MultiBodyTree::getBodyAxisOfMotion(const int body_index, vec3 *axis) const
  {
  	return m_impl->getBodyAxisOfMotion(body_index, axis);
  }
  
  void MultiBodyTree::printTree() { m_impl->printTree(); }
  void MultiBodyTree::printTreeData() { m_impl->printTreeData(); }
  
  int MultiBodyTree::numBodies() const { return m_impl->m_num_bodies; }
  
  int MultiBodyTree::numDoFs() const { return m_impl->m_num_dofs; }
  
  int MultiBodyTree::calculateInverseDynamics(const vecx &q, const vecx &u, const vecx &dot_u,
  											vecx *joint_forces)
  {
  	if (false == m_is_finalized)
  	{
  		bt_id_error_message("system has not been initialized\n");
  		return -1;
  	}
  	if (-1 == m_impl->calculateInverseDynamics(q, u, dot_u, joint_forces))
  	{
  		bt_id_error_message("error in inverse dynamics calculation\n");
  		return -1;
  	}
  	return 0;
  }
  
  int MultiBodyTree::calculateMassMatrix(const vecx &q, const bool update_kinematics,
  									   const bool initialize_matrix,
  									   const bool set_lower_triangular_matrix, matxx *mass_matrix)
  {
  	if (false == m_is_finalized)
  	{
  		bt_id_error_message("system has not been initialized\n");
  		return -1;
  	}
  	if (-1 ==
  		m_impl->calculateMassMatrix(q, update_kinematics, initialize_matrix,
  									set_lower_triangular_matrix, mass_matrix))
  	{
  		bt_id_error_message("error in mass matrix calculation\n");
  		return -1;
  	}
  	return 0;
  }
  
  int MultiBodyTree::calculateMassMatrix(const vecx &q, matxx *mass_matrix)
  {
  	return calculateMassMatrix(q, true, true, true, mass_matrix);
  }
  
  int MultiBodyTree::calculateKinematics(const vecx &q, const vecx &u, const vecx &dot_u)
  {
  	vec3 world_gravity(m_impl->m_world_gravity);
  	// temporarily set gravity to zero, to ensure we get the actual accelerations
  	setZero(m_impl->m_world_gravity);
  
  	if (false == m_is_finalized)
  	{
  		bt_id_error_message("system has not been initialized\n");
  		return -1;
  	}
  	if (-1 == m_impl->calculateKinematics(q, u, dot_u,
  										  MultiBodyTree::MultiBodyImpl::POSITION_VELOCITY_ACCELERATION))
  	{
  		bt_id_error_message("error in kinematics calculation\n");
  		return -1;
  	}
  
  	m_impl->m_world_gravity = world_gravity;
  	return 0;
  }
  
  int MultiBodyTree::calculatePositionKinematics(const vecx &q)
  {
  	if (false == m_is_finalized)
  	{
  		bt_id_error_message("system has not been initialized\n");
  		return -1;
  	}
  	if (-1 == m_impl->calculateKinematics(q, q, q,
  										  MultiBodyTree::MultiBodyImpl::POSITION_VELOCITY))
  	{
  		bt_id_error_message("error in kinematics calculation\n");
  		return -1;
  	}
  	return 0;
  }
  
  int MultiBodyTree::calculatePositionAndVelocityKinematics(const vecx &q, const vecx &u)
  {
  	if (false == m_is_finalized)
  	{
  		bt_id_error_message("system has not been initialized\n");
  		return -1;
  	}
  	if (-1 == m_impl->calculateKinematics(q, u, u,
  										  MultiBodyTree::MultiBodyImpl::POSITION_VELOCITY))
  	{
  		bt_id_error_message("error in kinematics calculation\n");
  		return -1;
  	}
  	return 0;
  }
  
  #if (defined BT_ID_HAVE_MAT3X) && (defined BT_ID_WITH_JACOBIANS)
  int MultiBodyTree::calculateJacobians(const vecx &q, const vecx &u)
  {
  	if (false == m_is_finalized)
  	{
  		bt_id_error_message("system has not been initialized\n");
  		return -1;
  	}
  	if (-1 == m_impl->calculateJacobians(q, u,
  										 MultiBodyTree::MultiBodyImpl::POSITION_VELOCITY))
  	{
  		bt_id_error_message("error in jacobian calculation\n");
  		return -1;
  	}
  	return 0;
  }
  
  int MultiBodyTree::calculateJacobians(const vecx &q)
  {
  	if (false == m_is_finalized)
  	{
  		bt_id_error_message("system has not been initialized\n");
  		return -1;
  	}
  	if (-1 == m_impl->calculateJacobians(q, q,
  										 MultiBodyTree::MultiBodyImpl::POSITION_ONLY))
  	{
  		bt_id_error_message("error in jacobian calculation\n");
  		return -1;
  	}
  	return 0;
  }
  
  int MultiBodyTree::getBodyDotJacobianTransU(const int body_index, vec3 *world_dot_jac_trans_u) const
  {
  	return m_impl->getBodyDotJacobianTransU(body_index, world_dot_jac_trans_u);
  }
  
  int MultiBodyTree::getBodyDotJacobianRotU(const int body_index, vec3 *world_dot_jac_rot_u) const
  {
  	return m_impl->getBodyDotJacobianRotU(body_index, world_dot_jac_rot_u);
  }
  
  int MultiBodyTree::getBodyJacobianTrans(const int body_index, mat3x *world_jac_trans) const
  {
  	return m_impl->getBodyJacobianTrans(body_index, world_jac_trans);
  }
  
  int MultiBodyTree::getBodyJacobianRot(const int body_index, mat3x *world_jac_rot) const
  {
  	return m_impl->getBodyJacobianRot(body_index, world_jac_rot);
  }
  
  #endif
  
  int MultiBodyTree::addBody(int body_index, int parent_index, JointType joint_type,
  						   const vec3 &parent_r_parent_body_ref, const mat33 &body_T_parent_ref,
  						   const vec3 &body_axis_of_motion_, idScalar mass,
  						   const vec3 &body_r_body_com, const mat33 &body_I_body,
  						   const int user_int, void *user_ptr)
  {
  	if (body_index < 0)
  	{
  		bt_id_error_message("body index must be positive (got %d)\n", body_index);
  		return -1;
  	}
  	vec3 body_axis_of_motion(body_axis_of_motion_);
  	switch (joint_type)
  	{
  		case REVOLUTE:
  		case PRISMATIC:
  			// check if axis is unit vector
  			if (!isUnitVector(body_axis_of_motion))
  			{
  				bt_id_warning_message(
  					"axis of motion not a unit axis ([%f %f %f]), will use normalized vector\n",
  					body_axis_of_motion(0), body_axis_of_motion(1), body_axis_of_motion(2));
  				idScalar length = BT_ID_SQRT(BT_ID_POW(body_axis_of_motion(0), 2) +
  											 BT_ID_POW(body_axis_of_motion(1), 2) +
  											 BT_ID_POW(body_axis_of_motion(2), 2));
  				if (length < BT_ID_SQRT(std::numeric_limits<idScalar>::min()))
  				{
  					bt_id_error_message("axis of motion vector too short (%e)\n", length);
  					return -1;
  				}
  				body_axis_of_motion = (1.0 / length) * body_axis_of_motion;
  			}
  			break;
  		case FIXED:
  			break;
  		case FLOATING:
  			break;
  		case SPHERICAL:
  			break;
  		default:
  			bt_id_error_message("unknown joint type %d\n", joint_type);
  			return -1;
  	}
  
  	// sanity check for mass properties. Zero mass is OK.
  	if (mass < 0)
  	{
  		m_mass_parameters_are_valid = false;
  		bt_id_error_message("Body %d has invalid mass %e\n", body_index, mass);
  		if (!m_accept_invalid_mass_parameters)
  		{
  			return -1;
  		}
  	}
  
  	if (!isValidInertiaMatrix(body_I_body, body_index, FIXED == joint_type))
  	{
  		m_mass_parameters_are_valid = false;
  		// error message printed in function call
  		if (!m_accept_invalid_mass_parameters)
  		{
  			return -1;
  		}
  	}
  
  	if (!isValidTransformMatrix(body_T_parent_ref))
  	{
  		return -1;
  	}
  
  	return m_init_cache->addBody(body_index, parent_index, joint_type, parent_r_parent_body_ref,
  								 body_T_parent_ref, body_axis_of_motion, mass, body_r_body_com,
  								 body_I_body, user_int, user_ptr);
  }
  
  int MultiBodyTree::getParentIndex(const int body_index, int *parent_index) const
  {
  	return m_impl->getParentIndex(body_index, parent_index);
  }
  
  int MultiBodyTree::getUserInt(const int body_index, int *user_int) const
  {
  	return m_impl->getUserInt(body_index, user_int);
  }
  
  int MultiBodyTree::getUserPtr(const int body_index, void **user_ptr) const
  {
  	return m_impl->getUserPtr(body_index, user_ptr);
  }
  
  int MultiBodyTree::setUserInt(const int body_index, const int user_int)
  {
  	return m_impl->setUserInt(body_index, user_int);
  }
  
  int MultiBodyTree::setUserPtr(const int body_index, void *const user_ptr)
  {
  	return m_impl->setUserPtr(body_index, user_ptr);
  }
  
  int MultiBodyTree::finalize()
  {
  	const int &num_bodies = m_init_cache->numBodies();
  	const int &num_dofs = m_init_cache->numDoFs();
  
  	if (num_dofs < 0)
  	{
  		bt_id_error_message("Need num_dofs>=1, but num_dofs= %d\n", num_dofs);
  		//return -1;
  	}
  
  	// 1 allocate internal MultiBody structure
  	m_impl = new MultiBodyImpl(num_bodies, num_dofs);
  
  	// 2 build new index set assuring index(parent) < index(child)
  	if (-1 == m_init_cache->buildIndexSets())
  	{
  		return -1;
  	}
  	m_init_cache->getParentIndexArray(&m_impl->m_parent_index);
  
  	// 3 setup internal kinematic and dynamic data
  	for (int index = 0; index < num_bodies; index++)
  	{
  		InertiaData inertia;
  		JointData joint;
  		if (-1 == m_init_cache->getInertiaData(index, &inertia))
  		{
  			return -1;
  		}
  		if (-1 == m_init_cache->getJointData(index, &joint))
  		{
  			return -1;
  		}
  
  		RigidBody &rigid_body = m_impl->m_body_list[index];
  
  		rigid_body.m_mass = inertia.m_mass;
  		rigid_body.m_body_mass_com = inertia.m_mass * inertia.m_body_pos_body_com;
  		rigid_body.m_body_I_body = inertia.m_body_I_body;
  		rigid_body.m_joint_type = joint.m_type;
  		rigid_body.m_parent_pos_parent_body_ref = joint.m_parent_pos_parent_child_ref;
  		rigid_body.m_body_T_parent_ref = joint.m_child_T_parent_ref;
  		rigid_body.m_parent_pos_parent_body_ref = joint.m_parent_pos_parent_child_ref;
  		rigid_body.m_joint_type = joint.m_type;
  
  		int user_int;
  		if (-1 == m_init_cache->getUserInt(index, &user_int))
  		{
  			return -1;
  		}
  		if (-1 == m_impl->setUserInt(index, user_int))
  		{
  			return -1;
  		}
  
  		void *user_ptr;
  		if (-1 == m_init_cache->getUserPtr(index, &user_ptr))
  		{
  			return -1;
  		}
  		if (-1 == m_impl->setUserPtr(index, user_ptr))
  		{
  			return -1;
  		}
  
  		// Set joint Jacobians. Note that the dimension is always 3x1 here to avoid variable sized
  		// matrices.
  		switch (rigid_body.m_joint_type)
  		{
  			case REVOLUTE:
  				rigid_body.m_Jac_JR(0) = joint.m_child_axis_of_motion(0);
  				rigid_body.m_Jac_JR(1) = joint.m_child_axis_of_motion(1);
  				rigid_body.m_Jac_JR(2) = joint.m_child_axis_of_motion(2);
  				rigid_body.m_Jac_JT(0) = 0.0;
  				rigid_body.m_Jac_JT(1) = 0.0;
  				rigid_body.m_Jac_JT(2) = 0.0;
  				break;
  			case PRISMATIC:
  				rigid_body.m_Jac_JR(0) = 0.0;
  				rigid_body.m_Jac_JR(1) = 0.0;
  				rigid_body.m_Jac_JR(2) = 0.0;
  				rigid_body.m_Jac_JT(0) = joint.m_child_axis_of_motion(0);
  				rigid_body.m_Jac_JT(1) = joint.m_child_axis_of_motion(1);
  				rigid_body.m_Jac_JT(2) = joint.m_child_axis_of_motion(2);
  				break;
  			case FIXED:
  				// NOTE/TODO: dimension really should be zero ..
  				rigid_body.m_Jac_JR(0) = 0.0;
  				rigid_body.m_Jac_JR(1) = 0.0;
  				rigid_body.m_Jac_JR(2) = 0.0;
  				rigid_body.m_Jac_JT(0) = 0.0;
  				rigid_body.m_Jac_JT(1) = 0.0;
  				rigid_body.m_Jac_JT(2) = 0.0;
  				break;
  			case SPHERICAL:
  				// NOTE/TODO: this is not really correct.
  				// the Jacobians should be 3x3 matrices here !
  				rigid_body.m_Jac_JR(0) = 0.0;
  				rigid_body.m_Jac_JR(1) = 0.0;
  				rigid_body.m_Jac_JR(2) = 0.0;
  				rigid_body.m_Jac_JT(0) = 0.0;
  				rigid_body.m_Jac_JT(1) = 0.0;
  				rigid_body.m_Jac_JT(2) = 0.0;
  				break;
  			case FLOATING:
  				// NOTE/TODO: this is not really correct.
  				// the Jacobians should be 3x3 matrices here !
  				rigid_body.m_Jac_JR(0) = 0.0;
  				rigid_body.m_Jac_JR(1) = 0.0;
  				rigid_body.m_Jac_JR(2) = 0.0;
  				rigid_body.m_Jac_JT(0) = 0.0;
  				rigid_body.m_Jac_JT(1) = 0.0;
  				rigid_body.m_Jac_JT(2) = 0.0;
  				break;
  			default:
  				bt_id_error_message("unsupported joint type %d\n", rigid_body.m_joint_type);
  				return -1;
  		}
  	}
  
  	// 4 assign degree of freedom indices & build per-joint-type index arrays
  	if (-1 == m_impl->generateIndexSets())
  	{
  		bt_id_error_message("generating index sets\n");
  		return -1;
  	}
  
  	// 5 do some pre-computations ..
  	m_impl->calculateStaticData();
  
  	// 6. make sure all user forces are set to zero, as this might not happen
  	//	in the vector ctors.
  	m_impl->clearAllUserForcesAndMoments();
  
  	m_is_finalized = true;
  	return 0;
  }
  
  int MultiBodyTree::setGravityInWorldFrame(const vec3 &gravity)
  {
  	return m_impl->setGravityInWorldFrame(gravity);
  }
  
  int MultiBodyTree::getJointType(const int body_index, JointType *joint_type) const
  {
  	return m_impl->getJointType(body_index, joint_type);
  }
  
  int MultiBodyTree::getJointTypeStr(const int body_index, const char **joint_type) const
  {
  	return m_impl->getJointTypeStr(body_index, joint_type);
  }
  
  int MultiBodyTree::getDoFOffset(const int body_index, int *q_offset) const
  {
  	return m_impl->getDoFOffset(body_index, q_offset);
  }
  
  int MultiBodyTree::setBodyMass(const int body_index, idScalar mass)
  {
  	return m_impl->setBodyMass(body_index, mass);
  }
  
  int MultiBodyTree::setBodyFirstMassMoment(const int body_index, const vec3 &first_mass_moment)
  {
  	return m_impl->setBodyFirstMassMoment(body_index, first_mass_moment);
  }
  
  int MultiBodyTree::setBodySecondMassMoment(const int body_index, const mat33 &second_mass_moment)
  {
  	return m_impl->setBodySecondMassMoment(body_index, second_mass_moment);
  }
  
  int MultiBodyTree::getBodyMass(const int body_index, idScalar *mass) const
  {
  	return m_impl->getBodyMass(body_index, mass);
  }
  
  int MultiBodyTree::getBodyFirstMassMoment(const int body_index, vec3 *first_mass_moment) const
  {
  	return m_impl->getBodyFirstMassMoment(body_index, first_mass_moment);
  }
  
  int MultiBodyTree::getBodySecondMassMoment(const int body_index, mat33 *second_mass_moment) const
  {
  	return m_impl->getBodySecondMassMoment(body_index, second_mass_moment);
  }
  
  void MultiBodyTree::clearAllUserForcesAndMoments() { m_impl->clearAllUserForcesAndMoments(); }
  
  int MultiBodyTree::addUserForce(const int body_index, const vec3 &body_force)
  {
  	return m_impl->addUserForce(body_index, body_force);
  }
  
  int MultiBodyTree::addUserMoment(const int body_index, const vec3 &body_moment)
  {
  	return m_impl->addUserMoment(body_index, body_moment);
  }
  
  }  // namespace btInverseDynamics
  