public static float4 GetParticleVelocityAtPoint(float4 position, float4 prevPosition, quaternion orientation, quaternion prevOrientation, float4 point, float dt)
{
// calculate both linear and angular velocities:
float4 linearVelocity = BurstIntegration.DifferentiateLinear(position, prevPosition, dt);
float4 angularVelocity = BurstIntegration.DifferentiateAngular(orientation, prevOrientation, dt);
return(linearVelocity + new float4(math.cross(angularVelocity.xyz, (point - prevPosition).xyz), 0));
}
public void Update(float4 position, float4 scale, quaternion rotation, float dt)
{
prevFrame = frame;
float4 prevVelocity = velocity;
float4 prevAngularVelocity = angularVelocity;
frame.translation = position;
frame.rotation = rotation;
frame.scale = scale;
velocity = BurstIntegration.DifferentiateLinear(frame.translation, prevFrame.translation, dt);
angularVelocity = BurstIntegration.DifferentiateAngular(frame.rotation, prevFrame.rotation, dt);
acceleration = BurstIntegration.DifferentiateLinear(velocity, prevVelocity, dt);
angularAcceleration = BurstIntegration.DifferentiateLinear(angularVelocity, prevAngularVelocity, dt);
}
// The code actually running on the job
public void Execute(int index)
{
int i = activeParticles[index];
// Project particles on the XY plane if we are in 2D mode:
if (is2D)
{
// restrict position to the 2D plane
float4 pos = positions[i];
pos[2] = previousPositions[i][2];
positions[i] = pos;
// restrict rotation to the axis perpendicular to the 2D plane.
quaternion swing, twist;
BurstMath.SwingTwist(orientations[i], new float3(0, 0, 1), out swing, out twist);
orientations[i] = twist;
}
if (inverseMasses[i] > 0)
{
velocities[i] = BurstIntegration.DifferentiateLinear(positions[i], previousPositions[i], deltaTime);
}
else
{
velocities[i] = float4.zero;
}
if (inverseRotationalMasses[i] > 0)
{
angularVelocities[i] = BurstIntegration.DifferentiateAngular(orientations[i], previousOrientations[i], deltaTime);
}
else
{
angularVelocities[i] = float4.zero;
}
}
public static float4 GetParticleVelocityAtPoint(float4 position, float4 prevPosition, float4 point, float dt)
{
// no angular velocity, so calculate and return linear velocity only:
return(BurstIntegration.DifferentiateLinear(position, prevPosition, dt));
}
public void Execute(int workItemIndex)
{
int start, end;
batchData.GetConstraintRange(workItemIndex, out start, out end);
for (int i = start; i < end; ++i)
{
var contact = contacts[i];
int simplexStartA = simplexCounts.GetSimplexStartAndSize(contact.bodyA, out int simplexSizeA);
int simplexStartB = simplexCounts.GetSimplexStartAndSize(contact.bodyB, out int simplexSizeB);
// Combine collision materials:
BurstCollisionMaterial material = CombineCollisionMaterials(simplices[simplexStartA], simplices[simplexStartB]);
float4 prevPositionA = float4.zero;
float4 linearVelocityA = float4.zero;
float4 angularVelocityA = float4.zero;
float4 invInertiaTensorA = float4.zero;
quaternion orientationA = new quaternion(0, 0, 0, 0);
float simplexRadiusA = 0;
float4 prevPositionB = float4.zero;
float4 linearVelocityB = float4.zero;
float4 angularVelocityB = float4.zero;
float4 invInertiaTensorB = float4.zero;
quaternion orientationB = new quaternion(0, 0, 0, 0);
float simplexRadiusB = 0;
for (int j = 0; j < simplexSizeA; ++j)
{
int particleIndex = simplices[simplexStartA + j];
prevPositionA += prevPositions[particleIndex] * contact.pointA[j];
linearVelocityA += BurstIntegration.DifferentiateLinear(positions[particleIndex], prevPositions[particleIndex], substepTime) * contact.pointA[j];
angularVelocityA += BurstIntegration.DifferentiateAngular(orientations[particleIndex], prevOrientations[particleIndex], substepTime) * contact.pointA[j];
invInertiaTensorA += invInertiaTensors[particleIndex] * contact.pointA[j];
orientationA.value += orientations[particleIndex].value * contact.pointA[j];
simplexRadiusA += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
}
for (int j = 0; j < simplexSizeB; ++j)
{
int particleIndex = simplices[simplexStartB + j];
prevPositionB += prevPositions[particleIndex] * contact.pointB[j];
linearVelocityB += BurstIntegration.DifferentiateLinear(positions[particleIndex], prevPositions[particleIndex], substepTime) * contact.pointB[j];
angularVelocityB += BurstIntegration.DifferentiateAngular(orientations[particleIndex], prevOrientations[particleIndex], substepTime) * contact.pointB[j];
invInertiaTensorB += invInertiaTensors[particleIndex] * contact.pointB[j];
orientationB.value += orientations[particleIndex].value * contact.pointB[j];
simplexRadiusB += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointB[j];
}
float4 rA = float4.zero, rB = float4.zero;
// Consider angular velocities if rolling contacts are enabled:
if (material.rollingContacts > 0)
{
rA = -contact.normal * simplexRadiusA;
rB = contact.normal * simplexRadiusB;
linearVelocityA += new float4(math.cross(angularVelocityA.xyz, rA.xyz), 0);
linearVelocityB += new float4(math.cross(angularVelocityB.xyz, rB.xyz), 0);
}
// Calculate relative velocity:
float4 relativeVelocity = linearVelocityA - linearVelocityB;
// Calculate friction impulses (in the tangent and bitangent ddirections):
float2 impulses = contact.SolveFriction(relativeVelocity, material.staticFriction, material.dynamicFriction, substepTime);
// Apply friction impulses to both particles:
if (math.abs(impulses.x) > BurstMath.epsilon || math.abs(impulses.y) > BurstMath.epsilon)
{
float4 tangentImpulse = impulses.x * contact.tangent;
float4 bitangentImpulse = impulses.y * contact.bitangent;
float4 totalImpulse = tangentImpulse + bitangentImpulse;
float baryScale = BurstMath.BaryScale(contact.pointA);
for (int j = 0; j < simplexSizeA; ++j)
{
int particleIndex = simplices[simplexStartA + j];
deltas[particleIndex] += (tangentImpulse * contact.tangentInvMassA + bitangentImpulse * contact.bitangentInvMassA) * substepTime * contact.pointA[j] * baryScale;
counts[particleIndex]++;
}
baryScale = BurstMath.BaryScale(contact.pointB);
for (int j = 0; j < simplexSizeB; ++j)
{
int particleIndex = simplices[simplexStartB + j];
deltas[particleIndex] -= (tangentImpulse * contact.tangentInvMassB + bitangentImpulse * contact.bitangentInvMassB) * substepTime * contact.pointB[j] * baryScale;
counts[particleIndex]++;
}
// Rolling contacts:
if (material.rollingContacts > 0)
{
// Calculate angular velocity deltas due to friction impulse:
float4x4 solverInertiaA = BurstMath.TransformInertiaTensor(invInertiaTensorA, orientationA);
float4x4 solverInertiaB = BurstMath.TransformInertiaTensor(invInertiaTensorB, orientationB);
float4 angVelDeltaA = math.mul(solverInertiaA, new float4(math.cross(rA.xyz, totalImpulse.xyz), 0));
float4 angVelDeltaB = -math.mul(solverInertiaB, new float4(math.cross(rB.xyz, totalImpulse.xyz), 0));
// Final angular velocities, after adding the deltas:
angularVelocityA += angVelDeltaA;
angularVelocityB += angVelDeltaB;
// Calculate weights (inverse masses):
float invMassA = math.length(math.mul(solverInertiaA, math.normalizesafe(angularVelocityA)));
float invMassB = math.length(math.mul(solverInertiaB, math.normalizesafe(angularVelocityB)));
// Calculate rolling axis and angular velocity deltas:
float4 rollAxis = float4.zero;
float rollingImpulse = contact.SolveRollingFriction(angularVelocityA, angularVelocityB, material.rollingFriction, invMassA, invMassB, ref rollAxis);
angVelDeltaA += rollAxis * rollingImpulse * invMassA;
angVelDeltaB -= rollAxis * rollingImpulse * invMassB;
// Apply orientation deltas to particles:
quaternion orientationDeltaA = BurstIntegration.AngularVelocityToSpinQuaternion(orientationA, angVelDeltaA, substepTime);
quaternion orientationDeltaB = BurstIntegration.AngularVelocityToSpinQuaternion(orientationB, angVelDeltaB, substepTime);
for (int j = 0; j < simplexSizeA; ++j)
{
int particleIndex = simplices[simplexStartA + j];
quaternion qA = orientationDeltas[particleIndex];
qA.value += orientationDeltaA.value;
orientationDeltas[particleIndex] = qA;
orientationCounts[particleIndex]++;
}
for (int j = 0; j < simplexSizeB; ++j)
{
int particleIndex = simplices[simplexStartB + j];
quaternion qB = orientationDeltas[particleIndex];
qB.value += orientationDeltaB.value;
orientationDeltas[particleIndex] = qB;
orientationCounts[particleIndex]++;
}
}
}
contacts[i] = contact;
}
}
public void Execute()
{
for (int i = 0; i < contacts.Length; ++i)
{
var contact = contacts[i];
// Get the indices of the particle and collider involved in this contact:
int simplexStart = simplexCounts.GetSimplexStartAndSize(contact.bodyA, out int simplexSize);
int colliderIndex = contact.bodyB;
// Skip contacts involving triggers:
if (shapes[colliderIndex].flags > 0)
{
continue;
}
// Get the rigidbody index (might be < 0, in that case there's no rigidbody present)
int rigidbodyIndex = shapes[colliderIndex].rigidbodyIndex;
// Combine collision materials (use material from first particle in simplex)
BurstCollisionMaterial material = CombineCollisionMaterials(simplices[simplexStart], colliderIndex);
// Calculate relative velocity:
float4 rA = float4.zero, rB = float4.zero;
float4 prevPositionA = float4.zero;
float4 linearVelocityA = float4.zero;
float4 angularVelocityA = float4.zero;
float4 invInertiaTensorA = float4.zero;
quaternion orientationA = new quaternion(0, 0, 0, 0);
float simplexRadiusA = 0;
for (int j = 0; j < simplexSize; ++j)
{
int particleIndex = simplices[simplexStart + j];
prevPositionA += prevPositions[particleIndex] * contact.pointA[j];
linearVelocityA += BurstIntegration.DifferentiateLinear(positions[particleIndex], prevPositions[particleIndex], substepTime) * contact.pointA[j];
angularVelocityA += BurstIntegration.DifferentiateAngular(orientations[particleIndex], prevOrientations[particleIndex], substepTime) * contact.pointA[j];
invInertiaTensorA += invInertiaTensors[particleIndex] * contact.pointA[j];
orientationA.value += orientations[particleIndex].value * contact.pointA[j];
simplexRadiusA += BurstMath.EllipsoidRadius(contact.normal, prevOrientations[particleIndex], radii[particleIndex].xyz) * contact.pointA[j];
}
float4 relativeVelocity = linearVelocityA;
// Add particle angular velocity if rolling contacts are enabled:
if (material.rollingContacts > 0)
{
rA = -contact.normal * simplexRadiusA;
relativeVelocity += new float4(math.cross(angularVelocityA.xyz, rA.xyz), 0);
}
// Subtract rigidbody velocity:
if (rigidbodyIndex >= 0)
{
// Note: unlike rA, that is expressed in solver space, rB is expressed in world space.
rB = inertialFrame.frame.TransformPoint(contact.pointB) - rigidbodies[rigidbodyIndex].com;
relativeVelocity -= BurstMath.GetRigidbodyVelocityAtPoint(rigidbodyIndex, contact.pointB, rigidbodies, rigidbodyLinearDeltas, rigidbodyAngularDeltas, inertialFrame.frame);
}
// Determine impulse magnitude:
float2 impulses = contact.SolveFriction(relativeVelocity, material.staticFriction, material.dynamicFriction, stepTime);
if (math.abs(impulses.x) > BurstMath.epsilon || math.abs(impulses.y) > BurstMath.epsilon)
{
float4 tangentImpulse = impulses.x * contact.tangent;
float4 bitangentImpulse = impulses.y * contact.bitangent;
float4 totalImpulse = tangentImpulse + bitangentImpulse;
float baryScale = BurstMath.BaryScale(contact.pointA);
for (int j = 0; j < simplexSize; ++j)
{
int particleIndex = simplices[simplexStart + j];
//(tangentImpulse * contact.tangentInvMassA + bitangentImpulse * contact.bitangentInvMassA) * dt;
deltas[particleIndex] += (tangentImpulse * contact.tangentInvMassA + bitangentImpulse * contact.bitangentInvMassA) * substepTime * contact.pointA[j] * baryScale;
counts[particleIndex]++;
}
if (rigidbodyIndex >= 0)
{
BurstMath.ApplyImpulse(rigidbodyIndex, -totalImpulse, contact.pointB, rigidbodies, rigidbodyLinearDeltas, rigidbodyAngularDeltas, inertialFrame.frame);
}
// Rolling contacts:
if (material.rollingContacts > 0)
{
// Calculate angular velocity deltas due to friction impulse:
float4x4 solverInertiaA = BurstMath.TransformInertiaTensor(invInertiaTensorA, orientationA);
float4 angVelDeltaA = math.mul(solverInertiaA, new float4(math.cross(rA.xyz, totalImpulse.xyz), 0));
float4 angVelDeltaB = float4.zero;
// Final angular velocities, after adding the deltas:
angularVelocityA += angVelDeltaA;
float4 angularVelocityB = float4.zero;
// Calculate weights (inverse masses):
float invMassA = math.length(math.mul(solverInertiaA, math.normalizesafe(angularVelocityA)));
float invMassB = 0;
if (rigidbodyIndex >= 0)
{
angVelDeltaB = math.mul(-rigidbodies[rigidbodyIndex].inverseInertiaTensor, new float4(math.cross(rB.xyz, totalImpulse.xyz), 0));
angularVelocityB = rigidbodies[rigidbodyIndex].angularVelocity + angVelDeltaB;
invMassB = math.length(math.mul(rigidbodies[rigidbodyIndex].inverseInertiaTensor, math.normalizesafe(angularVelocityB)));
}
// Calculate rolling axis and angular velocity deltas:
float4 rollAxis = float4.zero;
float rollingImpulse = contact.SolveRollingFriction(angularVelocityA, angularVelocityB, material.rollingFriction, invMassA, invMassB, ref rollAxis);
angVelDeltaA += rollAxis * rollingImpulse * invMassA;
angVelDeltaB -= rollAxis * rollingImpulse * invMassB;
// Apply orientation delta to particles:
quaternion orientationDelta = BurstIntegration.AngularVelocityToSpinQuaternion(orientationA, angVelDeltaA, substepTime);
for (int j = 0; j < simplexSize; ++j)
{
int particleIndex = simplices[simplexStart + j];
quaternion qA = orientationDeltas[particleIndex];
qA.value += orientationDelta.value;
orientationDeltas[particleIndex] = qA;
orientationCounts[particleIndex]++;
}
// Apply angular velocity delta to rigidbody:
if (rigidbodyIndex >= 0)
{
float4 angularDelta = rigidbodyAngularDeltas[rigidbodyIndex];
angularDelta += angVelDeltaB;
rigidbodyAngularDeltas[rigidbodyIndex] = angularDelta;
}
}
}
contacts[i] = contact;
}
}
