public void Solve(ref TimeStep step, ref FPVector2 gravity)
{
FP h = step.dt;
// Integrate velocities and apply damping. Initialize the body state.
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
FPVector2 c = b._sweep.C;
FP a = b._sweep.A;
FPVector2 v = b._linearVelocity;
FP w = b._angularVelocity;
// Store positions for continuous collision.
b._sweep.C0 = b._sweep.C;
b._sweep.A0 = b._sweep.A;
if (b.BodyType == BodyType.Dynamic)
{
// Integrate velocities.
// FPE: Only apply gravity if the body wants it.
if (b.IgnoreGravity)
{
v += h * (b._invMass * b._force);
}
else
{
v += h * (b.GravityScale * gravity + b._invMass * b._force);
}
w += h * b._invI * b._torque;
// Apply damping.
// ODE: dv/dt + c * v = 0
// Solution: v(t) = v0 * exp(-c * t)
// Time step: v(t + dt) = v0 * exp(-c * (t + dt)) = v0 * exp(-c * t) * exp(-c * dt) = v * exp(-c * dt)
// v2 = exp(-c * dt) * v1
// Taylor expansion:
// v2 = (1.0f - c * dt) * v1
//v *= MathUtils.Clamp(1.0f - h * b.LinearDamping, 0.0f, 1.0f);
//w *= MathUtils.Clamp(1.0f - h * b.AngularDamping, 0.0f, 1.0f);
v *= 1 / (1 + h * b.LinearDamping);
w *= 1 / (1 + h * b.AngularDamping);
}
_positions[i].c = c;
_positions[i].a = a;
_velocities[i].v = v;
_velocities[i].w = w;
}
// Solver data
SolverData solverData = new SolverData();
solverData.step = step;
solverData.positions = _positions;
solverData.velocities = _velocities;
_contactSolver.Reset(step, ContactCount, _contacts, _positions, _velocities);
_contactSolver.InitializeVelocityConstraints();
if (Settings.EnableWarmstarting)
{
_contactSolver.WarmStart();
}
for (int i = 0; i < JointCount; ++i)
{
if (_joints[i].Enabled)
{
_joints[i].InitVelocityConstraints(ref solverData);
}
}
// Solve velocity constraints.
for (int i = 0; i < Settings.VelocityIterations; ++i)
{
for (int j = 0; j < JointCount; ++j)
{
Joint2D joint = _joints[j];
if (!joint.Enabled)
{
continue;
}
joint.SolveVelocityConstraints(ref solverData);
joint.Validate(step.inv_dt);
}
_contactSolver.SolveVelocityConstraints();
}
// Store impulses for warm starting.
_contactSolver.StoreImpulses();
// Integrate positions
for (int i = 0; i < BodyCount; ++i)
{
FPVector2 c = _positions[i].c;
FP a = _positions[i].a;
FPVector2 v = _velocities[i].v;
FP w = _velocities[i].w;
// Check for large velocities
FPVector2 translation = h * v;
if (FPVector2.Dot(translation, translation) > Settings.MaxTranslationSquared)
{
FP ratio = Settings.MaxTranslation / translation.magnitude;
v *= ratio;
}
FP rotation = h * w;
if (rotation * rotation > Settings.MaxRotationSquared)
{
FP ratio = Settings.MaxRotation / FP.Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
_positions[i].c = c;
_positions[i].a = a;
_velocities[i].v = v;
_velocities[i].w = w;
}
// Solve position constraints
bool positionSolved = false;
for (int i = 0; i < Settings.PositionIterations; ++i)
{
bool contactsOkay = _contactSolver.SolvePositionConstraints();
bool jointsOkay = true;
for (int j = 0; j < JointCount; ++j)
{
Joint2D joint = _joints[j];
if (!joint.Enabled)
{
continue;
}
bool jointOkay = joint.SolvePositionConstraints(ref solverData);
jointsOkay = jointsOkay && jointOkay;
}
if (contactsOkay && jointsOkay)
{
// Exit early if the position errors are small.
positionSolved = true;
break;
}
}
// Copy state buffers back to the bodies
for (int i = 0; i < BodyCount; ++i)
{
Body body = Bodies[i];
body._sweep.C = _positions[i].c;
body._sweep.A = _positions[i].a;
body._linearVelocity = _velocities[i].v;
body._angularVelocity = _velocities[i].w;
body.SynchronizeTransform();
}
Report(_contactSolver._velocityConstraints);
if (Settings.AllowSleep)
{
FP minSleepTime = Settings.MaxFP;
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
if (b.BodyType == BodyType.Static)
{
continue;
}
if (!b.SleepingAllowed || b._angularVelocity * b._angularVelocity > AngTolSqr || FPVector2.Dot(b._linearVelocity, b._linearVelocity) > LinTolSqr)
{
b._sleepTime = 0.0f;
minSleepTime = 0.0f;
}
else
{
b._sleepTime += h;
minSleepTime = KBEngine.FPMath.Min(minSleepTime, b._sleepTime);
}
}
if (minSleepTime >= Settings.TimeToSleep && positionSolved)
{
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
b.Awake = false;
}
}
}
}
public void Reset(TimeStep step, int count, Contact[] contacts, Position[] positions, Velocity[] velocities, bool warmstarting = Settings.EnableWarmstarting)
{
_step = step;
_count = count;
_positions = positions;
_velocities = velocities;
_contacts = contacts;
// grow the array
if (_velocityConstraints == null || _velocityConstraints.Length < count)
{
_velocityConstraints = new ContactVelocityConstraint[count * 2];
_positionConstraints = new ContactPositionConstraint[count * 2];
for (int i = 0; i < _velocityConstraints.Length; i++)
{
_velocityConstraints[i] = new ContactVelocityConstraint();
}
for (int i = 0; i < _positionConstraints.Length; i++)
{
_positionConstraints[i] = new ContactPositionConstraint();
}
}
// Initialize position independent portions of the constraints.
for (int i = 0; i < _count; ++i)
{
Contact contact = contacts[i];
Fixture fixtureA = contact.FixtureA;
Fixture fixtureB = contact.FixtureB;
Shape shapeA = fixtureA.Shape;
Shape shapeB = fixtureB.Shape;
FP radiusA = shapeA.Radius;
FP radiusB = shapeB.Radius;
Body bodyA = fixtureA.Body;
Body bodyB = fixtureB.Body;
Manifold manifold = contact.Manifold;
int pointCount = manifold.PointCount;
Debug.Assert(pointCount > 0);
ContactVelocityConstraint vc = _velocityConstraints[i];
vc.friction = contact.Friction;
vc.restitution = contact.Restitution;
vc.tangentSpeed = contact.TangentSpeed;
vc.indexA = bodyA.IslandIndex;
vc.indexB = bodyB.IslandIndex;
vc.invMassA = bodyA._invMass;
vc.invMassB = bodyB._invMass;
vc.invIA = bodyA._invI;
vc.invIB = bodyB._invI;
vc.contactIndex = i;
vc.pointCount = pointCount;
vc.K.SetZero();
vc.normalMass.SetZero();
ContactPositionConstraint pc = _positionConstraints[i];
pc.indexA = bodyA.IslandIndex;
pc.indexB = bodyB.IslandIndex;
pc.invMassA = bodyA._invMass;
pc.invMassB = bodyB._invMass;
pc.localCenterA = bodyA._sweep.LocalCenter;
pc.localCenterB = bodyB._sweep.LocalCenter;
pc.invIA = bodyA._invI;
pc.invIB = bodyB._invI;
pc.localNormal = manifold.LocalNormal;
pc.localPoint = manifold.LocalPoint;
pc.pointCount = pointCount;
pc.radiusA = radiusA;
pc.radiusB = radiusB;
pc.type = manifold.Type;
for (int j = 0; j < pointCount; ++j)
{
ManifoldPoint cp = manifold.Points[j];
VelocityConstraintPoint vcp = vc.points[j];
if (Settings.EnableWarmstarting)
{
vcp.normalImpulse = _step.dtRatio * cp.NormalImpulse;
vcp.tangentImpulse = _step.dtRatio * cp.TangentImpulse;
}
else
{
vcp.normalImpulse = 0.0f;
vcp.tangentImpulse = 0.0f;
}
vcp.rA = FPVector2.zero;
vcp.rB = FPVector2.zero;
vcp.normalMass = 0.0f;
vcp.tangentMass = 0.0f;
vcp.velocityBias = 0.0f;
pc.localPoints[j] = cp.LocalPoint;
}
}
}
internal void SolveTOI(ref TimeStep subStep, int toiIndexA, int toiIndexB, bool warmstarting)
{
Debug.Assert(toiIndexA < BodyCount);
Debug.Assert(toiIndexB < BodyCount);
// Initialize the body state.
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
_positions[i].c = b._sweep.C;
_positions[i].a = b._sweep.A;
_velocities[i].v = b._linearVelocity;
_velocities[i].w = b._angularVelocity;
}
_contactSolver.Reset(subStep, ContactCount, _contacts, _positions, _velocities, warmstarting);
// Solve position constraints.
for (int i = 0; i < Settings.TOIPositionIterations; ++i)
{
bool contactsOkay = _contactSolver.SolveTOIPositionConstraints(toiIndexA, toiIndexB);
if (contactsOkay)
{
break;
}
}
// Leap of faith to new safe state.
Bodies[toiIndexA]._sweep.C0 = _positions[toiIndexA].c;
Bodies[toiIndexA]._sweep.A0 = _positions[toiIndexA].a;
Bodies[toiIndexB]._sweep.C0 = _positions[toiIndexB].c;
Bodies[toiIndexB]._sweep.A0 = _positions[toiIndexB].a;
// No warm starting is needed for TOI events because warm
// starting impulses were applied in the discrete solver.
_contactSolver.InitializeVelocityConstraints();
// Solve velocity constraints.
for (int i = 0; i < Settings.TOIVelocityIterations; ++i)
{
_contactSolver.SolveVelocityConstraints();
}
// Don't store the TOI contact forces for warm starting
// because they can be quite large.
FP h = subStep.dt;
// Integrate positions.
for (int i = 0; i < BodyCount; ++i)
{
FPVector2 c = _positions[i].c;
FP a = _positions[i].a;
FPVector2 v = _velocities[i].v;
FP w = _velocities[i].w;
// Check for large velocities
FPVector2 translation = h * v;
if (FPVector2.Dot(translation, translation) > Settings.MaxTranslationSquared)
{
FP ratio = Settings.MaxTranslation / translation.magnitude;
v *= ratio;
}
FP rotation = h * w;
if (rotation * rotation > Settings.MaxRotationSquared)
{
FP ratio = Settings.MaxRotation / FP.Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
_positions[i].c = c;
_positions[i].a = a;
_velocities[i].v = v;
_velocities[i].w = w;
// Sync bodies
Body body = Bodies[i];
body._sweep.C = c;
body._sweep.A = a;
body._linearVelocity = v;
body._angularVelocity = w;
body.SynchronizeTransform();
}
Report(_contactSolver._velocityConstraints);
}