reactphysics3d/src/systems/SolveSliderJointSystem.cpp
2020-05-27 16:15:35 +02:00

962 lines
51 KiB
C++

/********************************************************************************
* ReactPhysics3D physics library, http://www.reactphysics3d.com *
* Copyright (c) 2010-2020 Daniel Chappuis *
*********************************************************************************
* *
* This software is provided 'as-is', without any express or implied warranty. *
* In no event will the authors be held liable for any damages arising from the *
* use of this software. *
* *
* Permission is granted to anyone to use this software for any purpose, *
* including commercial applications, and to alter it and redistribute it *
* freely, subject to the following restrictions: *
* *
* 1. The origin of this software must not be misrepresented; you must not claim *
* that you wrote the original software. If you use this software in a *
* product, an acknowledgment in the product documentation would be *
* appreciated but is not required. *
* *
* 2. Altered source versions must be plainly marked as such, and must not be *
* misrepresented as being the original software. *
* *
* 3. This notice may not be removed or altered from any source distribution. *
* *
********************************************************************************/
// Libraries
#include <reactphysics3d/systems/SolveSliderJointSystem.h>
#include <reactphysics3d/engine/PhysicsWorld.h>
#include <reactphysics3d/body/RigidBody.h>
using namespace reactphysics3d;
// Static variables definition
const decimal SolveSliderJointSystem::BETA = decimal(0.2);
// Constructor
SolveSliderJointSystem::SolveSliderJointSystem(PhysicsWorld& world, RigidBodyComponents& rigidBodyComponents,
TransformComponents& transformComponents,
JointComponents& jointComponents,
SliderJointComponents& sliderJointComponents)
:mWorld(world), mRigidBodyComponents(rigidBodyComponents), mTransformComponents(transformComponents),
mJointComponents(jointComponents), mSliderJointComponents(sliderJointComponents),
mTimeStep(0), mIsWarmStartingActive(true) {
}
// Initialize before solving the constraint
void SolveSliderJointSystem::initBeforeSolve() {
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
assert(!mRigidBodyComponents.getIsEntityDisabled(body1Entity));
assert(!mRigidBodyComponents.getIsEntityDisabled(body2Entity));
// Get the inertia tensor of bodies
mSliderJointComponents.mI1[i] = RigidBody::getWorldInertiaTensorInverse(mWorld, body1Entity);
mSliderJointComponents.mI2[i] = RigidBody::getWorldInertiaTensorInverse(mWorld, body2Entity);
}
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const Quaternion& orientationBody1 = mTransformComponents.getTransform(body1Entity).getOrientation();
const Quaternion& orientationBody2 = mTransformComponents.getTransform(body2Entity).getOrientation();
// Vector from body center to the anchor point
mSliderJointComponents.mR1[i] = orientationBody1 * mSliderJointComponents.mLocalAnchorPointBody1[i];
mSliderJointComponents.mR2[i] = orientationBody2 * mSliderJointComponents.mLocalAnchorPointBody2[i];
}
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Quaternion& orientationBody1 = mTransformComponents.getTransform(body1Entity).getOrientation();
// Compute the two orthogonal vectors to the slider axis in world-space
mSliderJointComponents.mSliderAxisWorld[i] = orientationBody1 * mSliderJointComponents.mSliderAxisBody1[i];
mSliderJointComponents.mSliderAxisWorld[i].normalize();
}
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
mSliderJointComponents.mN1[i] = mSliderJointComponents.mSliderAxisWorld[i].getOneUnitOrthogonalVector();
mSliderJointComponents.mN2[i] = mSliderJointComponents.mSliderAxisWorld[i].cross(mSliderJointComponents.mN1[i]);
}
const decimal biasFactor = (BETA / mTimeStep);
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const uint32 componentIndexBody1 = mRigidBodyComponents.getEntityIndex(body1Entity);
const uint32 componentIndexBody2 = mRigidBodyComponents.getEntityIndex(body2Entity);
const Vector3& x1 = mRigidBodyComponents.mCentersOfMassWorld[componentIndexBody1];
const Vector3& x2 = mRigidBodyComponents.mCentersOfMassWorld[componentIndexBody2];
const Vector3& r1 = mSliderJointComponents.mR1[i];
const Vector3& r2 = mSliderJointComponents.mR2[i];
// Compute the vector u (difference between anchor points)
const Vector3 u = x2 + r2 - x1 - r1;
// Compute the cross products used in the Jacobians
const Vector3 r1PlusU = mSliderJointComponents.mR1[i] + u;
mSliderJointComponents.mR1PlusUCrossN1[i] = r1PlusU.cross(mSliderJointComponents.mN1[i]);
mSliderJointComponents.mR1PlusUCrossN2[i] = r1PlusU.cross(mSliderJointComponents.mN2[i]);
mSliderJointComponents.mR1PlusUCrossSliderAxis[i] = r1PlusU.cross(mSliderJointComponents.mSliderAxisWorld[i]);
// Check if the limit constraints are violated or not
decimal uDotSliderAxis = u.dot(mSliderJointComponents.mSliderAxisWorld[i]);
decimal lowerLimitError = uDotSliderAxis - mSliderJointComponents.mLowerLimit[i];
decimal upperLimitError = mSliderJointComponents.mUpperLimit[i] - uDotSliderAxis;
bool oldIsLowerLimitViolated = mSliderJointComponents.mIsLowerLimitViolated[i];
mSliderJointComponents.mIsLowerLimitViolated[i] = lowerLimitError <= 0;
if (!mSliderJointComponents.mIsLowerLimitViolated[i] || mSliderJointComponents.mIsLowerLimitViolated[i] != oldIsLowerLimitViolated) {
mSliderJointComponents.mImpulseLowerLimit[i] = decimal(0.0);
}
bool oldIsUpperLimitViolated = mSliderJointComponents.mIsUpperLimitViolated[i];
mSliderJointComponents.mIsUpperLimitViolated[i] = upperLimitError <= 0;
if (!mSliderJointComponents.mIsUpperLimitViolated[i] || mSliderJointComponents.mIsUpperLimitViolated[i] != oldIsUpperLimitViolated) {
mSliderJointComponents.mImpulseUpperLimit[i] = decimal(0.0);
}
// Compute the bias "b" of the translation constraint
mSliderJointComponents.mBiasTranslation[i].setToZero();
if (mJointComponents.getPositionCorrectionTechnique(jointEntity) == JointsPositionCorrectionTechnique::BAUMGARTE_JOINTS) {
mSliderJointComponents.mBiasTranslation[i].x = u.dot(mSliderJointComponents.mN1[i]);
mSliderJointComponents.mBiasTranslation[i].y = u.dot(mSliderJointComponents.mN2[i]);
mSliderJointComponents.mBiasTranslation[i] *= biasFactor;
}
// If the limits are enabled
if (mSliderJointComponents.mIsLimitEnabled[i] && (mSliderJointComponents.mIsLowerLimitViolated[i] ||
mSliderJointComponents.mIsUpperLimitViolated[i])) {
const Vector3& r2CrossSliderAxis = mSliderJointComponents.mR2CrossSliderAxis[i];
const Vector3& r1PlusUCrossSliderAxis = mSliderJointComponents.mR1PlusUCrossSliderAxis[i];
const decimal body1MassInverse = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
const decimal body2MassInverse = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
const decimal sumInverseMass = body1MassInverse + body2MassInverse;
// Compute the inverse of the mass matrix K=JM^-1J^t for the limits (1x1 matrix)
mSliderJointComponents.mInverseMassMatrixLimit[i] = sumInverseMass +
r1PlusUCrossSliderAxis.dot(mSliderJointComponents.mI1[i] * r1PlusUCrossSliderAxis) +
r2CrossSliderAxis.dot(mSliderJointComponents.mI2[i] * r2CrossSliderAxis);
mSliderJointComponents.mInverseMassMatrixLimit[i] = (mSliderJointComponents.mInverseMassMatrixLimit[i] > decimal(0.0)) ?
decimal(1.0) / mSliderJointComponents.mInverseMassMatrixLimit[i] : decimal(0.0);
// Compute the bias "b" of the lower limit constraint
mSliderJointComponents.mBLowerLimit[i] = decimal(0.0);
if (mJointComponents.getPositionCorrectionTechnique(jointEntity) == JointsPositionCorrectionTechnique::BAUMGARTE_JOINTS) {
mSliderJointComponents.mBLowerLimit[i] = biasFactor * lowerLimitError;
}
// Compute the bias "b" of the upper limit constraint
mSliderJointComponents.mBUpperLimit[i] = decimal(0.0);
if (mJointComponents.getPositionCorrectionTechnique(jointEntity) == JointsPositionCorrectionTechnique::BAUMGARTE_JOINTS) {
mSliderJointComponents.mBUpperLimit[i] = biasFactor * upperLimitError;
}
}
}
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
// Compute the cross products used in the Jacobians
mSliderJointComponents.mR2CrossN1[i] = mSliderJointComponents.mR2[i].cross(mSliderJointComponents.mN1[i]);
mSliderJointComponents.mR2CrossN2[i] = mSliderJointComponents.mR2[i].cross(mSliderJointComponents.mN2[i]);
mSliderJointComponents.mR2CrossSliderAxis[i] = mSliderJointComponents.mR2[i].cross(mSliderJointComponents.mSliderAxisWorld[i]);
}
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const Vector3& r2CrossN1 = mSliderJointComponents.mR2CrossN1[i];
const Vector3& r2CrossN2 = mSliderJointComponents.mR2CrossN2[i];
const Vector3& r1PlusUCrossN1 = mSliderJointComponents.mR1PlusUCrossN1[i];
const Vector3& r1PlusUCrossN2 = mSliderJointComponents.mR1PlusUCrossN2[i];
const Matrix3x3& i1 = mSliderJointComponents.mI1[i];
const Matrix3x3& i2 = mSliderJointComponents.mI2[i];
const uint32 componentIndexBody1 = mRigidBodyComponents.getEntityIndex(body1Entity);
const uint32 componentIndexBody2 = mRigidBodyComponents.getEntityIndex(body2Entity);
// Compute the inverse of the mass matrix K=JM^-1J^t for the 2 translation
// constraints (2x2 matrix)
const decimal body1MassInverse = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
const decimal body2MassInverse = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
const decimal sumInverseMass = body1MassInverse + body2MassInverse;
Vector3 I1R1PlusUCrossN1 = i1 * r1PlusUCrossN1;
Vector3 I1R1PlusUCrossN2 = i1 * r1PlusUCrossN2;
Vector3 I2R2CrossN1 = i2 * r2CrossN1;
Vector3 I2R2CrossN2 = i2 * r2CrossN2;
const decimal el11 = sumInverseMass + r1PlusUCrossN1.dot(I1R1PlusUCrossN1) +
r2CrossN1.dot(I2R2CrossN1);
const decimal el12 = r1PlusUCrossN1.dot(I1R1PlusUCrossN2) +
r2CrossN1.dot(I2R2CrossN2);
const decimal el21 = r1PlusUCrossN2.dot(I1R1PlusUCrossN1) +
r2CrossN2.dot(I2R2CrossN1);
const decimal el22 = sumInverseMass + r1PlusUCrossN2.dot(I1R1PlusUCrossN2) +
r2CrossN2.dot(I2R2CrossN2);
Matrix2x2 matrixKTranslation(el11, el12, el21, el22);
mSliderJointComponents.mInverseMassMatrixTranslation[i].setToZero();
if (mRigidBodyComponents.mBodyTypes[componentIndexBody1] == BodyType::DYNAMIC ||
mRigidBodyComponents.mBodyTypes[componentIndexBody2] == BodyType::DYNAMIC) {
mSliderJointComponents.mInverseMassMatrixTranslation[i] = matrixKTranslation.getInverse();
}
// Compute the inverse of the mass matrix K=JM^-1J^t for the 3 rotation
// contraints (3x3 matrix)
mSliderJointComponents.mInverseMassMatrixRotation[i] = i1 + i2;
if (mRigidBodyComponents.mBodyTypes[componentIndexBody1] == BodyType::DYNAMIC ||
mRigidBodyComponents.mBodyTypes[componentIndexBody2] == BodyType::DYNAMIC) {
mSliderJointComponents.mInverseMassMatrixRotation[i] = mSliderJointComponents.mInverseMassMatrixRotation[i].getInverse();
}
}
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const Quaternion& orientationBody1 = mTransformComponents.getTransform(body1Entity).getOrientation();
const Quaternion& orientationBody2 = mTransformComponents.getTransform(body2Entity).getOrientation();
// Compute the bias "b" of the rotation constraint
mSliderJointComponents.mBiasRotation[i].setToZero();
if (mJointComponents.getPositionCorrectionTechnique(jointEntity) == JointsPositionCorrectionTechnique::BAUMGARTE_JOINTS) {
const Quaternion qError = orientationBody2 * mSliderJointComponents.mInitOrientationDifferenceInv[i] * orientationBody1.getInverse();
mSliderJointComponents.mBiasRotation[i] = biasFactor * decimal(2.0) * qError.getVectorV();
}
// If the motor is enabled
if (mSliderJointComponents.mIsMotorEnabled[i]) {
const decimal body1MassInverse = mRigidBodyComponents.getMassInverse(body1Entity);
const decimal body2MassInverse = mRigidBodyComponents.getMassInverse(body2Entity);
const decimal sumInverseMass = body1MassInverse + body2MassInverse;
// Compute the inverse of mass matrix K=JM^-1J^t for the motor (1x1 matrix)
mSliderJointComponents.mInverseMassMatrixMotor[i] = sumInverseMass;
mSliderJointComponents.mInverseMassMatrixMotor[i] = (mSliderJointComponents.mInverseMassMatrixMotor[i] > decimal(0.0)) ?
decimal(1.0) / mSliderJointComponents.mInverseMassMatrixMotor[i] : decimal(0.0);
}
}
// If warm-starting is not enabled
if (!mIsWarmStartingActive) {
// For each joint
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
// Reset all the accumulated impulses
mSliderJointComponents.mImpulseTranslation[i].setToZero();
mSliderJointComponents.mImpulseRotation[i].setToZero();
mSliderJointComponents.mImpulseLowerLimit[i] = decimal(0.0);
mSliderJointComponents.mImpulseUpperLimit[i] = decimal(0.0);
mSliderJointComponents.mImpulseMotor[i] = decimal(0.0);
}
}
}
// Warm start the constraint (apply the previous impulse at the beginning of the step)
void SolveSliderJointSystem::warmstart() {
// For each joint component
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const uint32 componentIndexBody1 = mRigidBodyComponents.getEntityIndex(body1Entity);
const uint32 componentIndexBody2 = mRigidBodyComponents.getEntityIndex(body2Entity);
// Get the velocities
Vector3& v1 = mRigidBodyComponents.mConstrainedLinearVelocities[componentIndexBody1];
Vector3& v2 = mRigidBodyComponents.mConstrainedLinearVelocities[componentIndexBody2];
Vector3& w1 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody1];
Vector3& w2 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody2];
// Get the inverse mass and inverse inertia tensors of the bodies
const decimal inverseMassBody1 = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
const decimal inverseMassBody2 = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
const Vector3& n1 = mSliderJointComponents.mN1[i];
const Vector3& n2 = mSliderJointComponents.mN2[i];
// Compute the impulse P=J^T * lambda for the lower and upper limits constraints of body 1
decimal impulseLimits = mSliderJointComponents.mImpulseUpperLimit[i] - mSliderJointComponents.mImpulseLowerLimit[i];
Vector3 linearImpulseLimits = impulseLimits * mSliderJointComponents.mSliderAxisWorld[i];
// Compute the impulse P=J^T * lambda for the motor constraint of body 1
Vector3 impulseMotor = mSliderJointComponents.mImpulseMotor[i] * mSliderJointComponents.mSliderAxisWorld[i];
const Vector2& impulseTranslation = mSliderJointComponents.mImpulseTranslation[i];
const Vector3& impulseRotation = mSliderJointComponents.mImpulseRotation[i];
// Compute the impulse P=J^T * lambda for the 2 translation constraints of body 1
Vector3 linearImpulseBody1 = -n1 * impulseTranslation.x - n2 * impulseTranslation.y;
Vector3 angularImpulseBody1 = -mSliderJointComponents.mR1PlusUCrossN1[i] * impulseTranslation.x -
mSliderJointComponents.mR1PlusUCrossN2[i] * impulseTranslation.y;
// Compute the impulse P=J^T * lambda for the 3 rotation constraints of body 1
angularImpulseBody1 += -impulseRotation;
// Compute the impulse P=J^T * lambda for the lower and upper limits constraints of body 1
linearImpulseBody1 += linearImpulseLimits;
angularImpulseBody1 += impulseLimits * mSliderJointComponents.mR1PlusUCrossSliderAxis[i];
// Compute the impulse P=J^T * lambda for the motor constraint of body 1
linearImpulseBody1 += impulseMotor;
// Apply the impulse to the body 1
v1 += inverseMassBody1 * linearImpulseBody1;
w1 += mSliderJointComponents.mI1[i] * angularImpulseBody1;
// Compute the impulse P=J^T * lambda for the 2 translation constraints of body 2
Vector3 linearImpulseBody2 = n1 * impulseTranslation.x + n2 * impulseTranslation.y;
Vector3 angularImpulseBody2 = mSliderJointComponents.mR2CrossN1[i] * impulseTranslation.x +
mSliderJointComponents.mR2CrossN2[i] * impulseTranslation.y;
// Compute the impulse P=J^T * lambda for the 3 rotation constraints of body 2
angularImpulseBody2 += impulseRotation;
// Compute the impulse P=J^T * lambda for the lower and upper limits constraints of body 2
linearImpulseBody2 += -linearImpulseLimits;
angularImpulseBody2 += -impulseLimits * mSliderJointComponents.mR2CrossSliderAxis[i];
// Compute the impulse P=J^T * lambda for the motor constraint of body 2
linearImpulseBody2 += -impulseMotor;
// Apply the impulse to the body 2
v2 += inverseMassBody2 * linearImpulseBody2;
w2 += mSliderJointComponents.mI2[i] * angularImpulseBody2;
}
}
// Solve the velocity constraint
void SolveSliderJointSystem::solveVelocityConstraint() {
// For each joint component
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const uint32 componentIndexBody1 = mRigidBodyComponents.getEntityIndex(body1Entity);
const uint32 componentIndexBody2 = mRigidBodyComponents.getEntityIndex(body2Entity);
// Get the velocities
Vector3& v1 = mRigidBodyComponents.mConstrainedLinearVelocities[componentIndexBody1];
Vector3& v2 = mRigidBodyComponents.mConstrainedLinearVelocities[componentIndexBody2];
Vector3& w1 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody1];
Vector3& w2 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody2];
const Matrix3x3& i1 = mSliderJointComponents.mI1[i];
const Matrix3x3& i2 = mSliderJointComponents.mI2[i];
const Vector3& n1 = mSliderJointComponents.mN1[i];
const Vector3& n2 = mSliderJointComponents.mN2[i];
const Vector3& r2CrossN1 = mSliderJointComponents.mR2CrossN1[i];
const Vector3& r2CrossN2 = mSliderJointComponents.mR2CrossN2[i];
const Vector3& r1PlusUCrossN1 = mSliderJointComponents.mR1PlusUCrossN1[i];
const Vector3& r1PlusUCrossN2 = mSliderJointComponents.mR1PlusUCrossN2[i];
// Get the inverse mass and inverse inertia tensors of the bodies
decimal inverseMassBody1 = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
decimal inverseMassBody2 = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
// --------------- Translation Constraints --------------- //
// Compute J*v for the 2 translation constraints
const decimal el1 = -n1.dot(v1) - w1.dot(r1PlusUCrossN1) +
n1.dot(v2) + w2.dot(r2CrossN1);
const decimal el2 = -n2.dot(v1) - w1.dot(r1PlusUCrossN2) +
n2.dot(v2) + w2.dot(r2CrossN2);
const Vector2 JvTranslation(el1, el2);
// Compute the Lagrange multiplier lambda for the 2 translation constraints
Vector2 deltaLambda = mSliderJointComponents.mInverseMassMatrixTranslation[i] * (-JvTranslation - mSliderJointComponents.mBiasTranslation[i]);
mSliderJointComponents.mImpulseTranslation[i] += deltaLambda;
// Compute the impulse P=J^T * lambda for the 2 translation constraints of body 1
const Vector3 linearImpulseBody1 = -n1 * deltaLambda.x - n2 * deltaLambda.y;
Vector3 angularImpulseBody1 = -r1PlusUCrossN1 * deltaLambda.x -
r1PlusUCrossN2 * deltaLambda.y;
// Apply the impulse to the body 1
v1 += inverseMassBody1 * linearImpulseBody1;
w1 += i1 * angularImpulseBody1;
// Compute the impulse P=J^T * lambda for the 2 translation constraints of body 2
const Vector3 linearImpulseBody2 = n1 * deltaLambda.x + n2 * deltaLambda.y;
Vector3 angularImpulseBody2 = r2CrossN1 * deltaLambda.x + r2CrossN2 * deltaLambda.y;
// Apply the impulse to the body 2
v2 += inverseMassBody2 * linearImpulseBody2;
w2 += i2 * angularImpulseBody2;
}
// For each joint component
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const uint32 componentIndexBody1 = mRigidBodyComponents.getEntityIndex(body1Entity);
const uint32 componentIndexBody2 = mRigidBodyComponents.getEntityIndex(body2Entity);
// --------------- Rotation Constraints --------------- //
Vector3& w1 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody1];
Vector3& w2 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody2];
// Compute J*v for the 3 rotation constraints
const Vector3 JvRotation = w2 - w1;
// Compute the Lagrange multiplier lambda for the 3 rotation constraints
Vector3 deltaLambda2 = mSliderJointComponents.mInverseMassMatrixRotation[i] *
(-JvRotation - mSliderJointComponents.getBiasRotation(jointEntity));
mSliderJointComponents.mImpulseRotation[i] += deltaLambda2;
// Compute the impulse P=J^T * lambda for the 3 rotation constraints of body 1
Vector3 angularImpulseBody1 = -deltaLambda2;
// Apply the impulse to the body to body 1
w1 += mSliderJointComponents.mI1[i] * angularImpulseBody1;
// Compute the impulse P=J^T * lambda for the 3 rotation constraints of body 2
Vector3 angularImpulseBody2 = deltaLambda2;
// Apply the impulse to the body 2
w2 += mSliderJointComponents.mI2[i] * angularImpulseBody2;
}
// For each joint component
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const uint32 componentIndexBody1 = mRigidBodyComponents.getEntityIndex(body1Entity);
const uint32 componentIndexBody2 = mRigidBodyComponents.getEntityIndex(body2Entity);
Vector3& v1 = mRigidBodyComponents.mConstrainedLinearVelocities[componentIndexBody1];
Vector3& v2 = mRigidBodyComponents.mConstrainedLinearVelocities[componentIndexBody2];
decimal inverseMassBody1 = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
decimal inverseMassBody2 = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
const Vector3& r2CrossSliderAxis = mSliderJointComponents.mR2CrossSliderAxis[i];
const Vector3& r1PlusUCrossSliderAxis = mSliderJointComponents.mR1PlusUCrossSliderAxis[i];
const Vector3& sliderAxisWorld = mSliderJointComponents.mSliderAxisWorld[i];
// --------------- Limits Constraints --------------- //
if (mSliderJointComponents.mIsLimitEnabled[i]) {
Vector3& w1 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody1];
Vector3& w2 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody2];
const decimal inverseMassMatrixLimit = mSliderJointComponents.mInverseMassMatrixLimit[i];
// If the lower limit is violated
if (mSliderJointComponents.mIsLowerLimitViolated[i]) {
// Compute J*v for the lower limit constraint
const decimal JvLowerLimit = sliderAxisWorld.dot(v2) + r2CrossSliderAxis.dot(w2) -
sliderAxisWorld.dot(v1) - r1PlusUCrossSliderAxis.dot(w1);
// Compute the Lagrange multiplier lambda for the lower limit constraint
decimal deltaLambdaLower = inverseMassMatrixLimit * (-JvLowerLimit - mSliderJointComponents.mBLowerLimit[i]);
decimal lambdaTemp = mSliderJointComponents.mImpulseLowerLimit[i];
mSliderJointComponents.mImpulseLowerLimit[i] = std::max(mSliderJointComponents.mImpulseLowerLimit[i] + deltaLambdaLower, decimal(0.0));
deltaLambdaLower = mSliderJointComponents.mImpulseLowerLimit[i] - lambdaTemp;
// Compute the impulse P=J^T * lambda for the lower limit constraint of body 1
const Vector3 linearImpulseBody1 = -deltaLambdaLower * sliderAxisWorld;
const Vector3 angularImpulseBody1 = -deltaLambdaLower * r1PlusUCrossSliderAxis;
// Apply the impulse to the body 1
v1 += inverseMassBody1 * linearImpulseBody1;
w1 += mSliderJointComponents.mI1[i] * angularImpulseBody1;
// Compute the impulse P=J^T * lambda for the lower limit constraint of body 2
const Vector3 linearImpulseBody2 = deltaLambdaLower * sliderAxisWorld;
const Vector3 angularImpulseBody2 = deltaLambdaLower * r2CrossSliderAxis;
// Apply the impulse to the body 2
v2 += inverseMassBody2 * linearImpulseBody2;
w2 += mSliderJointComponents.mI2[i] * angularImpulseBody2;
}
// If the upper limit is violated
if (mSliderJointComponents.mIsUpperLimitViolated[i]) {
// Compute J*v for the upper limit constraint
const decimal JvUpperLimit = sliderAxisWorld.dot(v1) + r1PlusUCrossSliderAxis.dot(w1)
- sliderAxisWorld.dot(v2) - r2CrossSliderAxis.dot(w2);
// Compute the Lagrange multiplier lambda for the upper limit constraint
decimal deltaLambdaUpper = inverseMassMatrixLimit * (-JvUpperLimit -mSliderJointComponents.mBUpperLimit[i]);
decimal lambdaTemp = mSliderJointComponents.mImpulseUpperLimit[i];
mSliderJointComponents.mImpulseUpperLimit[i] = std::max(mSliderJointComponents.mImpulseUpperLimit[i] + deltaLambdaUpper, decimal(0.0));
deltaLambdaUpper = mSliderJointComponents.mImpulseUpperLimit[i] - lambdaTemp;
// Compute the impulse P=J^T * lambda for the upper limit constraint of body 1
const Vector3 linearImpulseBody1 = deltaLambdaUpper * sliderAxisWorld;
const Vector3 angularImpulseBody1 = deltaLambdaUpper * r1PlusUCrossSliderAxis;
// Apply the impulse to the body 1
v1 += inverseMassBody1 * linearImpulseBody1;
w1 += mSliderJointComponents.mI1[i] * angularImpulseBody1;
// Compute the impulse P=J^T * lambda for the upper limit constraint of body 2
const Vector3 linearImpulseBody2 = -deltaLambdaUpper * sliderAxisWorld;
const Vector3 angularImpulseBody2 = -deltaLambdaUpper * r2CrossSliderAxis;
// Apply the impulse to the body 2
v2 += inverseMassBody2 * linearImpulseBody2;
w2 += mSliderJointComponents.mI2[i] * angularImpulseBody2;
}
}
// --------------- Motor --------------- //
if (mSliderJointComponents.mIsMotorEnabled[i]) {
// Compute J*v for the motor
const decimal JvMotor = sliderAxisWorld.dot(v1) - sliderAxisWorld.dot(v2);
// Compute the Lagrange multiplier lambda for the motor
const decimal maxMotorImpulse = mSliderJointComponents.mMaxMotorForce[i] * mTimeStep;
decimal deltaLambdaMotor = mSliderJointComponents.mInverseMassMatrixMotor[i] * (-JvMotor - mSliderJointComponents.mMotorSpeed[i]);
decimal lambdaTemp = mSliderJointComponents.mImpulseMotor[i];
mSliderJointComponents.mImpulseMotor[i] = clamp(mSliderJointComponents.mImpulseMotor[i] + deltaLambdaMotor, -maxMotorImpulse, maxMotorImpulse);
deltaLambdaMotor = mSliderJointComponents.mImpulseMotor[i] - lambdaTemp;
// Compute the impulse P=J^T * lambda for the motor of body 1
const Vector3 linearImpulseBody1 = deltaLambdaMotor * sliderAxisWorld;
// Apply the impulse to the body 1
v1 += inverseMassBody1 * linearImpulseBody1;
// Compute the impulse P=J^T * lambda for the motor of body 2
const Vector3 linearImpulseBody2 = -deltaLambdaMotor * sliderAxisWorld;
// Apply the impulse to the body 2
v2 += inverseMassBody2 * linearImpulseBody2;
}
}
}
// Solve the position constraint (for position error correction)
void SolveSliderJointSystem::solvePositionConstraint() {
// For each joint component
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// If the error position correction technique is not the non-linear-gauss-seidel, we do
// do not execute this method
if (mJointComponents.getPositionCorrectionTechnique(jointEntity) != JointsPositionCorrectionTechnique::NON_LINEAR_GAUSS_SEIDEL) return;
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
// Recompute the inverse inertia tensors
mSliderJointComponents.mI1[i] = RigidBody::getWorldInertiaTensorInverse(mWorld, body1Entity);
mSliderJointComponents.mI2[i] = RigidBody::getWorldInertiaTensorInverse(mWorld, body2Entity);
}
// For each joint component
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// If the error position correction technique is not the non-linear-gauss-seidel, we do
// do not execute this method
if (mJointComponents.getPositionCorrectionTechnique(jointEntity) != JointsPositionCorrectionTechnique::NON_LINEAR_GAUSS_SEIDEL) return;
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const Quaternion& q1 = mRigidBodyComponents.getConstrainedOrientation(body1Entity);
const Quaternion& q2 = mRigidBodyComponents.getConstrainedOrientation(body2Entity);
// Vector from body center to the anchor point
mSliderJointComponents.mR1[i] = q1 * mSliderJointComponents.mLocalAnchorPointBody1[i];
mSliderJointComponents.mR2[i] = q2 * mSliderJointComponents.mLocalAnchorPointBody2[i];
}
// For each joint component
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// If the error position correction technique is not the non-linear-gauss-seidel, we do
// do not execute this method
if (mJointComponents.getPositionCorrectionTechnique(jointEntity) != JointsPositionCorrectionTechnique::NON_LINEAR_GAUSS_SEIDEL) return;
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const uint32 componentIndexBody1 = mRigidBodyComponents.getEntityIndex(body1Entity);
const uint32 componentIndexBody2 = mRigidBodyComponents.getEntityIndex(body2Entity);
// Get the inverse mass and inverse inertia tensors of the bodies
const decimal inverseMassBody1 = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
const decimal inverseMassBody2 = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
const Vector3& r1 = mSliderJointComponents.mR1[i];
const Vector3& r2 = mSliderJointComponents.mR2[i];
const Vector3& n1 = mSliderJointComponents.mN1[i];
const Vector3& n2 = mSliderJointComponents.mN2[i];
Vector3& x1 = mRigidBodyComponents.mConstrainedPositions[componentIndexBody1];
Vector3& x2 = mRigidBodyComponents.mConstrainedPositions[componentIndexBody2];
// Compute the vector u (difference between anchor points)
const Vector3 u = x2 + r2 - x1 - r1;
Quaternion& q1 = mRigidBodyComponents.mConstrainedOrientations[componentIndexBody1];
Quaternion& q2 = mRigidBodyComponents.mConstrainedOrientations[componentIndexBody2];
// Compute the two orthogonal vectors to the slider axis in world-space
mSliderJointComponents.mSliderAxisWorld[i] = q1 * mSliderJointComponents.mSliderAxisBody1[i];
mSliderJointComponents.mSliderAxisWorld[i].normalize();
mSliderJointComponents.mN1[i] = mSliderJointComponents.mSliderAxisWorld[i].getOneUnitOrthogonalVector();
mSliderJointComponents.mN2[i] = mSliderJointComponents.mSliderAxisWorld[i].cross(n1);
// Check if the limit constraints are violated or not
decimal uDotSliderAxis = u.dot(mSliderJointComponents.mSliderAxisWorld[i]);
decimal lowerLimitError = uDotSliderAxis - mSliderJointComponents.getLowerLimit(jointEntity);
decimal upperLimitError = mSliderJointComponents.getUpperLimit(jointEntity) - uDotSliderAxis;
mSliderJointComponents.mIsLowerLimitViolated[i] = lowerLimitError <= 0;
mSliderJointComponents.mIsUpperLimitViolated[i] = upperLimitError <= 0;
// Compute the cross products used in the Jacobians
mSliderJointComponents.mR2CrossN1[i] = r2.cross(n1);
mSliderJointComponents.mR2CrossN2[i] = r2.cross(n2);
mSliderJointComponents.mR2CrossSliderAxis[i] = r2.cross(mSliderJointComponents.mSliderAxisWorld[i]);
const Vector3 r1PlusU = r1 + u;
mSliderJointComponents.mR1PlusUCrossN1[i] = r1PlusU.cross(n1);
mSliderJointComponents.mR1PlusUCrossN2[i] = r1PlusU.cross(n2);
mSliderJointComponents.mR1PlusUCrossSliderAxis[i] = r1PlusU.cross(mSliderJointComponents.mSliderAxisWorld[i]);
const Vector3& r2CrossN1 = mSliderJointComponents.mR2CrossN1[i];
const Vector3& r2CrossN2 = mSliderJointComponents.mR2CrossN2[i];
const Vector3& r1PlusUCrossN1 = mSliderJointComponents.mR1PlusUCrossN1[i];
const Vector3& r1PlusUCrossN2 = mSliderJointComponents.mR1PlusUCrossN2[i];
// --------------- Translation Constraints --------------- //
const Matrix3x3& i1 = mSliderJointComponents.getI1(jointEntity);
const Matrix3x3& i2 = mSliderJointComponents.getI2(jointEntity);
// Recompute the inverse of the mass matrix K=JM^-1J^t for the 2 translation
// constraints (2x2 matrix)
const decimal body1MassInverse = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
const decimal body2MassInverse = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
decimal sumInverseMass = body1MassInverse + body2MassInverse;
Vector3 I1R1PlusUCrossN1 = i1 * r1PlusUCrossN1;
Vector3 I1R1PlusUCrossN2 = i1 * r1PlusUCrossN2;
Vector3 I2R2CrossN1 = i2 * r2CrossN1;
Vector3 I2R2CrossN2 = i2 * r2CrossN2;
const decimal el11 = sumInverseMass + r1PlusUCrossN1.dot(I1R1PlusUCrossN1) +
r2CrossN1.dot(I2R2CrossN1);
const decimal el12 = r1PlusUCrossN1.dot(I1R1PlusUCrossN2) +
r2CrossN1.dot(I2R2CrossN2);
const decimal el21 = r1PlusUCrossN2.dot(I1R1PlusUCrossN1) +
r2CrossN2.dot(I2R2CrossN1);
const decimal el22 = sumInverseMass + r1PlusUCrossN2.dot(I1R1PlusUCrossN2) +
r2CrossN2.dot(I2R2CrossN2);
Matrix2x2 matrixKTranslation(el11, el12, el21, el22);
mSliderJointComponents.mInverseMassMatrixTranslation[i].setToZero();
if (mRigidBodyComponents.mBodyTypes[componentIndexBody1] == BodyType::DYNAMIC || mRigidBodyComponents.mBodyTypes[componentIndexBody2] == BodyType::DYNAMIC) {
mSliderJointComponents.mInverseMassMatrixTranslation[i] = matrixKTranslation.getInverse();
}
// Compute the position error for the 2 translation constraints
const Vector2 translationError(u.dot(n1), u.dot(n2));
// Compute the Lagrange multiplier lambda for the 2 translation constraints
Vector2 lambdaTranslation = mSliderJointComponents.mInverseMassMatrixTranslation[i] * (-translationError);
// Compute the impulse P=J^T * lambda for the 2 translation constraints of body 1
const Vector3 linearImpulseBody1 = -n1 * lambdaTranslation.x - n2 * lambdaTranslation.y;
Vector3 angularImpulseBody1 = -r1PlusUCrossN1 * lambdaTranslation.x -
r1PlusUCrossN2 * lambdaTranslation.y;
// Apply the impulse to the body 1
const Vector3 v1 = inverseMassBody1 * linearImpulseBody1;
Vector3 w1 = i1 * angularImpulseBody1;
// Update the body position/orientation of body 1
x1 += v1;
q1 += Quaternion(0, w1) * q1 * decimal(0.5);
q1.normalize();
// Compute the impulse P=J^T * lambda for the 2 translation constraints of body 2
const Vector3 linearImpulseBody2 = n1 * lambdaTranslation.x + n2 * lambdaTranslation.y;
Vector3 angularImpulseBody2 = r2CrossN1 * lambdaTranslation.x + r2CrossN2 * lambdaTranslation.y;
// Apply the impulse to the body 2
const Vector3 v2 = inverseMassBody2 * linearImpulseBody2;
Vector3 w2 = i2 * angularImpulseBody2;
// Update the body position/orientation of body 2
x2 += v2;
q2 += Quaternion(0, w2) * q2 * decimal(0.5);
q2.normalize();
}
// For each joint component
for (uint32 i=0; i < mSliderJointComponents.getNbEnabledComponents(); i++) {
const Entity jointEntity = mSliderJointComponents.mJointEntities[i];
// If the error position correction technique is not the non-linear-gauss-seidel, we do
// do not execute this method
if (mJointComponents.getPositionCorrectionTechnique(jointEntity) != JointsPositionCorrectionTechnique::NON_LINEAR_GAUSS_SEIDEL) return;
// Get the bodies entities
const Entity body1Entity = mJointComponents.getBody1Entity(jointEntity);
const Entity body2Entity = mJointComponents.getBody2Entity(jointEntity);
const uint32 componentIndexBody1 = mRigidBodyComponents.getEntityIndex(body1Entity);
const uint32 componentIndexBody2 = mRigidBodyComponents.getEntityIndex(body2Entity);
Quaternion& q1 = mRigidBodyComponents.mConstrainedOrientations[componentIndexBody1];
Quaternion& q2 = mRigidBodyComponents.mConstrainedOrientations[componentIndexBody2];
// Get the velocities
Vector3& w1 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody1];
Vector3& w2 = mRigidBodyComponents.mConstrainedAngularVelocities[componentIndexBody2];
// --------------- Rotation Constraints --------------- //
// Compute the inverse of the mass matrix K=JM^-1J^t for the 3 rotation
// contraints (3x3 matrix)
mSliderJointComponents.mInverseMassMatrixRotation[i] = mSliderJointComponents.mI1[i] + mSliderJointComponents.mI2[i];
if (mRigidBodyComponents.mBodyTypes[componentIndexBody1] == BodyType::DYNAMIC || mRigidBodyComponents.mBodyTypes[componentIndexBody2] == BodyType::DYNAMIC) {
mSliderJointComponents.mInverseMassMatrixRotation[i] = mSliderJointComponents.mInverseMassMatrixRotation[i].getInverse();
}
// Calculate difference in rotation
//
// The rotation should be:
//
// q2 = q1 r0
//
// But because of drift the actual rotation is:
//
// q2 = qError q1 r0
// <=> qError = q2 r0^-1 q1^-1
//
// Where:
// q1 = current rotation of body 1
// q2 = current rotation of body 2
// qError = error that needs to be reduced to zero
Quaternion qError = q2 * mSliderJointComponents.mInitOrientationDifferenceInv[i] * q1.getInverse();
// A quaternion can be seen as:
//
// q = [sin(theta / 2) * v, cos(theta/2)]
//
// Where:
// v = rotation vector
// theta = rotation angle
//
// If we assume theta is small (error is small) then sin(x) = x so an approximation of the error angles is:
const Vector3 errorRotation = decimal(2.0) * qError.getVectorV();
// Compute the Lagrange multiplier lambda for the 3 rotation constraints
Vector3 lambdaRotation = mSliderJointComponents.mInverseMassMatrixRotation[i] * (-errorRotation);
// Compute the impulse P=J^T * lambda for the 3 rotation constraints of body 1
Vector3 angularImpulseBody1 = -lambdaRotation;
// Apply the impulse to the body 1
w1 = mSliderJointComponents.mI1[i] * angularImpulseBody1;
// Update the body position/orientation of body 1
q1 += Quaternion(0, w1) * q1 * decimal(0.5);
q1.normalize();
// Compute the impulse P=J^T * lambda for the 3 rotation constraints of body 2
Vector3 angularImpulseBody2 = lambdaRotation;
// Apply the impulse to the body 2
w2 = mSliderJointComponents.mI2[i] * angularImpulseBody2;
// Update the body position/orientation of body 2
q2 += Quaternion(0, w2) * q2 * decimal(0.5);
q2.normalize();
// --------------- Limits Constraints --------------- //
if (mSliderJointComponents.mIsLimitEnabled[i]) {
Vector3& x1 = mRigidBodyComponents.mConstrainedPositions[componentIndexBody1];
Vector3& x2 = mRigidBodyComponents.mConstrainedPositions[componentIndexBody2];
const Vector3& r2CrossSliderAxis = mSliderJointComponents.mR2CrossSliderAxis[i];
const Vector3& r1PlusUCrossSliderAxis = mSliderJointComponents.mR1PlusUCrossSliderAxis[i];
if (mSliderJointComponents.mIsLowerLimitViolated[i] || mSliderJointComponents.mIsUpperLimitViolated[i]) {
// Compute the inverse of the mass matrix K=JM^-1J^t for the limits (1x1 matrix)
const decimal body1MassInverse = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
const decimal body2MassInverse = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
mSliderJointComponents.mInverseMassMatrixLimit[i] = body1MassInverse + body2MassInverse +
r1PlusUCrossSliderAxis.dot(mSliderJointComponents.mI1[i] * r1PlusUCrossSliderAxis) +
r2CrossSliderAxis.dot(mSliderJointComponents.mI2[i] * r2CrossSliderAxis);
mSliderJointComponents.mInverseMassMatrixLimit[i] = (mSliderJointComponents.mInverseMassMatrixLimit[i] > decimal(0.0)) ?
decimal(1.0) / mSliderJointComponents.mInverseMassMatrixLimit[i] : decimal(0.0);
}
const decimal inverseMassBody1 = mRigidBodyComponents.mInverseMasses[componentIndexBody1];
const decimal inverseMassBody2 = mRigidBodyComponents.mInverseMasses[componentIndexBody2];
// If the lower limit is violated
if (mSliderJointComponents.mIsLowerLimitViolated[i]) {
const Vector3& r1 = mSliderJointComponents.mR1[i];
const Vector3& r2 = mSliderJointComponents.mR2[i];
const Vector3 u = x2 + r2 - x1 - r1;
decimal uDotSliderAxis = u.dot(mSliderJointComponents.mSliderAxisWorld[i]);
decimal lowerLimitError = uDotSliderAxis - mSliderJointComponents.mLowerLimit[i];
// Compute the Lagrange multiplier lambda for the lower limit constraint
decimal lambdaLowerLimit = mSliderJointComponents.mInverseMassMatrixLimit[i] * (-lowerLimitError);
// Compute the impulse P=J^T * lambda for the lower limit constraint of body 1
const Vector3 linearImpulseBody1 = -lambdaLowerLimit * mSliderJointComponents.mSliderAxisWorld[i];
const Vector3 angularImpulseBody1 = -lambdaLowerLimit * r1PlusUCrossSliderAxis;
// Apply the impulse to the body 1
const Vector3 v1 = inverseMassBody1 * linearImpulseBody1;
const Vector3 w1 = mSliderJointComponents.mI1[i] * angularImpulseBody1;
// Update the body position/orientation of body 1
x1 += v1;
q1 += Quaternion(0, w1) * q1 * decimal(0.5);
q1.normalize();
// Compute the impulse P=J^T * lambda for the lower limit constraint of body 2
const Vector3 linearImpulseBody2 = lambdaLowerLimit * mSliderJointComponents.mSliderAxisWorld[i];
const Vector3 angularImpulseBody2 = lambdaLowerLimit * r2CrossSliderAxis;
// Apply the impulse to the body 2
const Vector3 v2 = inverseMassBody2 * linearImpulseBody2;
const Vector3 w2 = mSliderJointComponents.mI2[i] * angularImpulseBody2;
// Update the body position/orientation of body 2
x2 += v2;
q2 += Quaternion(0, w2) * q2 * decimal(0.5);
q2.normalize();
}
// If the upper limit is violated
if (mSliderJointComponents.mIsUpperLimitViolated[i]) {
const Vector3& r1 = mSliderJointComponents.mR1[i];
const Vector3& r2 = mSliderJointComponents.mR2[i];
const Vector3 u = x2 + r2 - x1 - r1;
decimal uDotSliderAxis = u.dot(mSliderJointComponents.mSliderAxisWorld[i]);
decimal upperLimitError = mSliderJointComponents.mUpperLimit[i] - uDotSliderAxis;
// Compute the Lagrange multiplier lambda for the upper limit constraint
decimal lambdaUpperLimit = mSliderJointComponents.mInverseMassMatrixLimit[i] * (-upperLimitError);
// Compute the impulse P=J^T * lambda for the upper limit constraint of body 1
const Vector3 linearImpulseBody1 = lambdaUpperLimit * mSliderJointComponents.mSliderAxisWorld[i];
const Vector3 angularImpulseBody1 = lambdaUpperLimit * r1PlusUCrossSliderAxis;
// Apply the impulse to the body 1
const Vector3 v1 = inverseMassBody1 * linearImpulseBody1;
const Vector3 w1 = mSliderJointComponents.mI1[i] * angularImpulseBody1;
// Update the body position/orientation of body 1
x1 += v1;
q1 += Quaternion(0, w1) * q1 * decimal(0.5);
q1.normalize();
// Compute the impulse P=J^T * lambda for the upper limit constraint of body 2
const Vector3 linearImpulseBody2 = -lambdaUpperLimit * mSliderJointComponents.mSliderAxisWorld[i];
const Vector3 angularImpulseBody2 = -lambdaUpperLimit * r2CrossSliderAxis;
// Apply the impulse to the body 2
const Vector3 v2 = inverseMassBody2 * linearImpulseBody2;
const Vector3 w2 = mSliderJointComponents.mI2[i] * angularImpulseBody2;
// Update the body position/orientation of body 2
x2 += v2;
q2 += Quaternion(0, w2) * q2 * decimal(0.5);
q2.normalize();
}
}
}
}