godot/servers/physics/joints/hinge_joint_sw.cpp

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/*  hinge_joint_sw.cpp                                                   */
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/*
Adapted to Godot from the Bullet library.
See corresponding header file for licensing info.
*/

#include "hinge_joint_sw.h"

static void plane_space(const Vector3& n, Vector3& p, Vector3& q) {

  if (Math::abs(n.z) > 0.707106781186547524400844362) {
    // choose p in y-z plane
    real_t a = n[1]*n[1] + n[2]*n[2];
    real_t k = 1.0/Math::sqrt(a);
    p=Vector3(0,-n[2]*k,n[1]*k);
    // set q = n x p
    q=Vector3(a*k,-n[0]*p[2],n[0]*p[1]);
  }
  else {
    // choose p in x-y plane
    real_t a = n.x*n.x + n.y*n.y;
    real_t k = 1.0/Math::sqrt(a);
    p=Vector3(-n.y*k,n.x*k,0);
    // set q = n x p
    q=Vector3(-n.z*p.y,n.z*p.x,a*k);
  }
}

HingeJointSW::HingeJointSW(BodySW* rbA,BodySW* rbB, const Transform& frameA, const Transform& frameB) :  JointSW(_arr,2) {

	A=rbA;
	B=rbB;

	m_rbAFrame=frameA;
	m_rbBFrame=frameB;
	// flip axis
	m_rbBFrame.basis[0][2] *= real_t(-1.);
	m_rbBFrame.basis[1][2] *= real_t(-1.);
	m_rbBFrame.basis[2][2] *= real_t(-1.);


	//start with free
	m_lowerLimit = Math_PI;
	m_upperLimit = -Math_PI;


	m_useLimit = false;
	m_biasFactor = 0.3f;
	m_relaxationFactor = 1.0f;
	m_limitSoftness = 0.9f;
	m_solveLimit = false;

	tau=0.3;

	m_angularOnly=false;
	m_enableAngularMotor=false;

	A->add_constraint(this,0);
	B->add_constraint(this,1);

}

HingeJointSW::HingeJointSW(BodySW* rbA,BodySW* rbB, const Vector3& pivotInA,const Vector3& pivotInB,
									const  Vector3& axisInA,const Vector3& axisInB) :  JointSW(_arr,2) {

	A=rbA;
	B=rbB;

	m_rbAFrame.origin = pivotInA;

	// since no frame is given, assume this to be zero angle and just pick rb transform axis
	Vector3 rbAxisA1 = rbA->get_transform().basis.get_axis(0);

	Vector3 rbAxisA2;
	real_t projection = axisInA.dot(rbAxisA1);
	if (projection >= 1.0f - CMP_EPSILON) {
		rbAxisA1 = -rbA->get_transform().basis.get_axis(2);
		rbAxisA2 = rbA->get_transform().basis.get_axis(1);
	} else if (projection <= -1.0f + CMP_EPSILON) {
		rbAxisA1 = rbA->get_transform().basis.get_axis(2);
		rbAxisA2 = rbA->get_transform().basis.get_axis(1);
	} else {
		rbAxisA2 = axisInA.cross(rbAxisA1);
		rbAxisA1 = rbAxisA2.cross(axisInA);
	}

	m_rbAFrame.basis=Matrix3( rbAxisA1.x,rbAxisA2.x,axisInA.x,
									rbAxisA1.y,rbAxisA2.y,axisInA.y,
									rbAxisA1.z,rbAxisA2.z,axisInA.z );

	Quat rotationArc = Quat(axisInA,axisInB);
	Vector3 rbAxisB1 =  rotationArc.xform(rbAxisA1);
	Vector3 rbAxisB2 =  axisInB.cross(rbAxisB1);

	m_rbBFrame.origin = pivotInB;
	m_rbBFrame.basis=Matrix3( rbAxisB1.x,rbAxisB2.x,-axisInB.x,
									rbAxisB1.y,rbAxisB2.y,-axisInB.y,
									rbAxisB1.z,rbAxisB2.z,-axisInB.z );

	//start with free
	m_lowerLimit = Math_PI;
	m_upperLimit = -Math_PI;


	m_useLimit = false;
	m_biasFactor = 0.3f;
	m_relaxationFactor = 1.0f;
	m_limitSoftness = 0.9f;
	m_solveLimit = false;

	tau=0.3;

	m_angularOnly=false;
	m_enableAngularMotor=false;

	A->add_constraint(this,0);
	B->add_constraint(this,1);

}



bool HingeJointSW::setup(float p_step) {

	m_appliedImpulse = real_t(0.);

	if (!m_angularOnly)
	{
		Vector3 pivotAInW = A->get_transform().xform(m_rbAFrame.origin);
		Vector3 pivotBInW = B->get_transform().xform(m_rbBFrame.origin);
		Vector3 relPos = pivotBInW - pivotAInW;

		Vector3 normal[3];
		if (relPos.length_squared() > CMP_EPSILON)
		{
			normal[0] = relPos.normalized();
		}
		else
		{
			normal[0]=Vector3(real_t(1.0),0,0);
		}

		plane_space(normal[0], normal[1], normal[2]);

		for (int i=0;i<3;i++)
		{
			memnew_placement(&m_jac[i], JacobianEntrySW(
				A->get_transform().basis.transposed(),
				B->get_transform().basis.transposed(),
				pivotAInW - A->get_transform().origin,
				pivotBInW - B->get_transform().origin,
				normal[i],
				A->get_inv_inertia(),
				A->get_inv_mass(),
				B->get_inv_inertia(),
				B->get_inv_mass()) );
		}
	}

	//calculate two perpendicular jointAxis, orthogonal to hingeAxis
	//these two jointAxis require equal angular velocities for both bodies

	//this is unused for now, it's a todo
	Vector3 jointAxis0local;
	Vector3 jointAxis1local;

	plane_space(m_rbAFrame.basis.get_axis(2),jointAxis0local,jointAxis1local);

	A->get_transform().basis.xform( m_rbAFrame.basis.get_axis(2) );
	Vector3 jointAxis0 = A->get_transform().basis.xform( jointAxis0local );
	Vector3 jointAxis1 = A->get_transform().basis.xform( jointAxis1local );
	Vector3 hingeAxisWorld = A->get_transform().basis.xform( m_rbAFrame.basis.get_axis(2) );

	memnew_placement(&m_jacAng[0],	JacobianEntrySW(jointAxis0,
		A->get_transform().basis.transposed(),
		B->get_transform().basis.transposed(),
		A->get_inv_inertia(),
		B->get_inv_inertia()));

	memnew_placement(&m_jacAng[1],	JacobianEntrySW(jointAxis1,
		A->get_transform().basis.transposed(),
		B->get_transform().basis.transposed(),
		A->get_inv_inertia(),
		B->get_inv_inertia()));

	memnew_placement(&m_jacAng[2],	JacobianEntrySW(hingeAxisWorld,
		A->get_transform().basis.transposed(),
		B->get_transform().basis.transposed(),
		A->get_inv_inertia(),
		B->get_inv_inertia()));


	// Compute limit information
	real_t hingeAngle = get_hinge_angle();

//	print_line("angle: "+rtos(hingeAngle));
	//set bias, sign, clear accumulator
	m_correction = real_t(0.);
	m_limitSign = real_t(0.);
	m_solveLimit = false;
	m_accLimitImpulse = real_t(0.);



	/*if (m_useLimit) {
		print_line("low: "+rtos(m_lowerLimit));
		print_line("hi: "+rtos(m_upperLimit));
	}*/

//	if (m_lowerLimit < m_upperLimit)
	if (m_useLimit && m_lowerLimit <= m_upperLimit)
	{
//		if (hingeAngle <= m_lowerLimit*m_limitSoftness)
		if (hingeAngle <= m_lowerLimit)
		{
			m_correction = (m_lowerLimit - hingeAngle);
			m_limitSign = 1.0f;
			m_solveLimit = true;
		}
//		else if (hingeAngle >= m_upperLimit*m_limitSoftness)
		else if (hingeAngle >= m_upperLimit)
		{
			m_correction = m_upperLimit - hingeAngle;
			m_limitSign = -1.0f;
			m_solveLimit = true;
		}
	}

	//Compute K = J*W*J' for hinge axis
	Vector3 axisA =  A->get_transform().basis.xform(  m_rbAFrame.basis.get_axis(2) );
	m_kHinge =   1.0f / (A->compute_angular_impulse_denominator(axisA) +
				     B->compute_angular_impulse_denominator(axisA));

	return true;
}

void HingeJointSW::solve(float p_step) {

	Vector3 pivotAInW = A->get_transform().xform(m_rbAFrame.origin);
	Vector3 pivotBInW = B->get_transform().xform(m_rbBFrame.origin);

	//real_t tau = real_t(0.3);

	//linear part
	if (!m_angularOnly)
	{
		Vector3 rel_pos1 = pivotAInW - A->get_transform().origin;
		Vector3 rel_pos2 = pivotBInW - B->get_transform().origin;

		Vector3 vel1 = A->get_velocity_in_local_point(rel_pos1);
		Vector3 vel2 = B->get_velocity_in_local_point(rel_pos2);
		Vector3 vel = vel1 - vel2;

		for (int i=0;i<3;i++)
		{
			const Vector3& normal = m_jac[i].m_linearJointAxis;
			real_t jacDiagABInv = real_t(1.) / m_jac[i].getDiagonal();

			real_t rel_vel;
			rel_vel = normal.dot(vel);
			//positional error (zeroth order error)
			real_t depth = -(pivotAInW - pivotBInW).dot(normal); //this is the error projected on the normal
			real_t impulse = depth*tau/p_step  * jacDiagABInv -  rel_vel * jacDiagABInv;
			m_appliedImpulse += impulse;
			Vector3 impulse_vector = normal * impulse;
			A->apply_impulse(pivotAInW - A->get_transform().origin,impulse_vector);
			B->apply_impulse(pivotBInW - B->get_transform().origin,-impulse_vector);
		}
	}


	{
		///solve angular part

		// get axes in world space
		Vector3 axisA =  A->get_transform().basis.xform(  m_rbAFrame.basis.get_axis(2) );
		Vector3 axisB =  B->get_transform().basis.xform(  m_rbBFrame.basis.get_axis(2) );

		const Vector3& angVelA = A->get_angular_velocity();
		const Vector3& angVelB = B->get_angular_velocity();

		Vector3 angVelAroundHingeAxisA = axisA * axisA.dot(angVelA);
		Vector3 angVelAroundHingeAxisB = axisB * axisB.dot(angVelB);

		Vector3 angAorthog = angVelA - angVelAroundHingeAxisA;
		Vector3 angBorthog = angVelB - angVelAroundHingeAxisB;
		Vector3 velrelOrthog = angAorthog-angBorthog;
		{
			//solve orthogonal angular velocity correction
			real_t relaxation = real_t(1.);
			real_t len = velrelOrthog.length();
			if (len > real_t(0.00001))
			{
				Vector3 normal = velrelOrthog.normalized();
				real_t denom = A->compute_angular_impulse_denominator(normal) +
					B->compute_angular_impulse_denominator(normal);
				// scale for mass and relaxation
				velrelOrthog *= (real_t(1.)/denom) * m_relaxationFactor;
			}

			//solve angular positional correction
			Vector3 angularError = -axisA.cross(axisB) *(real_t(1.)/p_step);
			real_t len2 = angularError.length();
			if (len2>real_t(0.00001))
			{
				Vector3 normal2 = angularError.normalized();
				real_t denom2 = A->compute_angular_impulse_denominator(normal2) +
						B->compute_angular_impulse_denominator(normal2);
				angularError *= (real_t(1.)/denom2) * relaxation;
			}

			A->apply_torque_impulse(-velrelOrthog+angularError);
			B->apply_torque_impulse(velrelOrthog-angularError);

			// solve limit
			if (m_solveLimit)
			{
				real_t amplitude = ( (angVelB - angVelA).dot( axisA )*m_relaxationFactor + m_correction* (real_t(1.)/p_step)*m_biasFactor  ) * m_limitSign;

				real_t impulseMag = amplitude * m_kHinge;

				// Clamp the accumulated impulse
				real_t temp = m_accLimitImpulse;
				m_accLimitImpulse = MAX(m_accLimitImpulse + impulseMag, real_t(0) );
				impulseMag = m_accLimitImpulse - temp;


				Vector3 impulse = axisA * impulseMag * m_limitSign;
				A->apply_torque_impulse(impulse);
				B->apply_torque_impulse(-impulse);
			}
		}

		//apply motor
		if (m_enableAngularMotor)
		{
			//todo: add limits too
			Vector3 angularLimit(0,0,0);

			Vector3 velrel = angVelAroundHingeAxisA - angVelAroundHingeAxisB;
			real_t projRelVel = velrel.dot(axisA);

			real_t desiredMotorVel = m_motorTargetVelocity;
			real_t motor_relvel = desiredMotorVel - projRelVel;

			real_t unclippedMotorImpulse = m_kHinge * motor_relvel;;
			//todo: should clip against accumulated impulse
			real_t clippedMotorImpulse = unclippedMotorImpulse > m_maxMotorImpulse ? m_maxMotorImpulse : unclippedMotorImpulse;
			clippedMotorImpulse = clippedMotorImpulse < -m_maxMotorImpulse ? -m_maxMotorImpulse : clippedMotorImpulse;
			Vector3 motorImp = clippedMotorImpulse * axisA;

			A->apply_torque_impulse(motorImp+angularLimit);
			B->apply_torque_impulse(-motorImp-angularLimit);

		}
	}

}
/*
void	HingeJointSW::updateRHS(real_t	timeStep)
{
	(void)timeStep;

}
*/

static _FORCE_INLINE_ real_t atan2fast(real_t y, real_t x)
{
	real_t coeff_1 = Math_PI / 4.0f;
	real_t coeff_2 = 3.0f * coeff_1;
	real_t abs_y = Math::abs(y);
	real_t angle;
	if (x >= 0.0f) {
		real_t r = (x - abs_y) / (x + abs_y);
		angle = coeff_1 - coeff_1 * r;
	} else {
		real_t r = (x + abs_y) / (abs_y - x);
		angle = coeff_2 - coeff_1 * r;
	}
	return (y < 0.0f) ? -angle : angle;
}


real_t HingeJointSW::get_hinge_angle() {
	const Vector3 refAxis0  = A->get_transform().basis.xform( m_rbAFrame.basis.get_axis(0) );
	const Vector3 refAxis1  = A->get_transform().basis.xform( m_rbAFrame.basis.get_axis(1) );
	const Vector3 swingAxis = B->get_transform().basis.xform( m_rbBFrame.basis.get_axis(1) );

	return atan2fast( swingAxis.dot(refAxis0), swingAxis.dot(refAxis1)  );
}


void HingeJointSW::set_param(PhysicsServer::HingeJointParam p_param, float p_value) {

	switch (p_param) {

		case PhysicsServer::HINGE_JOINT_BIAS: tau=p_value; break;
		case PhysicsServer::HINGE_JOINT_LIMIT_UPPER: m_upperLimit=p_value; break;
		case PhysicsServer::HINGE_JOINT_LIMIT_LOWER: m_lowerLimit=p_value; break;
		case PhysicsServer::HINGE_JOINT_LIMIT_BIAS: m_biasFactor=p_value; break;
		case PhysicsServer::HINGE_JOINT_LIMIT_SOFTNESS: m_limitSoftness=p_value; break;
		case PhysicsServer::HINGE_JOINT_LIMIT_RELAXATION: m_relaxationFactor=p_value; break;
		case PhysicsServer::HINGE_JOINT_MOTOR_TARGET_VELOCITY: m_motorTargetVelocity=p_value; break;
		case PhysicsServer::HINGE_JOINT_MOTOR_MAX_IMPULSE: m_maxMotorImpulse=p_value; break;

	}
}

float HingeJointSW::get_param(PhysicsServer::HingeJointParam p_param) const{

	switch (p_param) {

		case PhysicsServer::HINGE_JOINT_BIAS: return tau;
		case PhysicsServer::HINGE_JOINT_LIMIT_UPPER: return m_upperLimit;
		case PhysicsServer::HINGE_JOINT_LIMIT_LOWER: return m_lowerLimit;
		case PhysicsServer::HINGE_JOINT_LIMIT_BIAS: return m_biasFactor;
		case PhysicsServer::HINGE_JOINT_LIMIT_SOFTNESS: return m_limitSoftness;
		case PhysicsServer::HINGE_JOINT_LIMIT_RELAXATION: return m_relaxationFactor;
		case PhysicsServer::HINGE_JOINT_MOTOR_TARGET_VELOCITY: return m_motorTargetVelocity;
		case PhysicsServer::HINGE_JOINT_MOTOR_MAX_IMPULSE: return m_maxMotorImpulse;

	}

	return 0;
}

void HingeJointSW::set_flag(PhysicsServer::HingeJointFlag p_flag, bool p_value){

	switch (p_flag) {
		case PhysicsServer::HINGE_JOINT_FLAG_USE_LIMIT: m_useLimit=p_value; break;
		case PhysicsServer::HINGE_JOINT_FLAG_ENABLE_MOTOR: m_enableAngularMotor=p_value; break;
	}

}
bool HingeJointSW::get_flag(PhysicsServer::HingeJointFlag p_flag) const{

	switch (p_flag) {
		case PhysicsServer::HINGE_JOINT_FLAG_USE_LIMIT: return m_useLimit;
		case PhysicsServer::HINGE_JOINT_FLAG_ENABLE_MOTOR:return m_enableAngularMotor;
	}

	return false;
}