/*************************************************************************/
/*  hinge_joint_sw.cpp                                                   */
/*************************************************************************/
/*                       This file is part of:                           */
/*                           GODOT ENGINE                                */
/*                    http://www.godotengine.org                         */
/*************************************************************************/
/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
/*                                                                       */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the       */
/* "Software"), to deal in the Software without restriction, including   */
/* without limitation the rights to use, copy, modify, merge, publish,   */
/* distribute, sublicense, and/or sell copies of the Software, and to    */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions:                                             */
/*                                                                       */
/* The above copyright notice and this permission notice shall be        */
/* included in all copies or substantial portions of the Software.       */
/*                                                                       */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
/*************************************************************************/

/*
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;
}