public void solve(ref TimeStep step, ref Vector2 gravity)
{
float h = step.dt;
// Integrate velocities and apply damping. Initialize the body state.
for (int i = 0; i < BodyCount; ++i)
{
var b = Bodies[i];
var c = b._sweep.c;
float a = b._sweep.a;
var v = b._linearVelocity;
float 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);
}
_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();
}
if (Settings.enableDiagnostics)
{
_watch.Start();
}
for (int i = 0; i < JointCount; ++i)
{
if (_joints[i].enabled)
{
_joints[i].initVelocityConstraints(ref solverData);
}
}
if (Settings.enableDiagnostics)
{
_watch.Stop();
}
// Solve velocity constraints.
for (int i = 0; i < Settings.velocityIterations; ++i)
{
for (int j = 0; j < JointCount; ++j)
{
Joint joint = _joints[j];
if (!joint.enabled)
{
continue;
}
if (Settings.enableDiagnostics)
{
_watch.Start();
}
joint.solveVelocityConstraints(ref solverData);
joint.validate(step.inv_dt);
if (Settings.enableDiagnostics)
{
_watch.Stop();
}
}
_contactSolver.solveVelocityConstraints();
}
// Store impulses for warm starting.
_contactSolver.storeImpulses();
// Integrate positions
for (int i = 0; i < BodyCount; ++i)
{
Vector2 c = _positions[i].c;
float a = _positions[i].a;
Vector2 v = _velocities[i].v;
float w = _velocities[i].w;
// Check for large velocities
Vector2 translation = h * v;
if (Vector2.Dot(translation, translation) > Settings.maxTranslationSquared)
{
float ratio = Settings.maxTranslation / translation.Length();
v *= ratio;
}
float rotation = h * w;
if (rotation * rotation > Settings.maxRotationSquared)
{
float ratio = Settings.maxRotation / Math.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)
{
Joint joint = _joints[j];
if (!joint.enabled)
{
continue;
}
if (Settings.enableDiagnostics)
{
_watch.Start();
}
bool jointOkay = joint.solvePositionConstraints(ref solverData);
if (Settings.enableDiagnostics)
{
_watch.Stop();
}
jointsOkay = jointsOkay && jointOkay;
}
if (contactsOkay && jointsOkay)
{
// Exit early if the position errors are small.
positionSolved = true;
break;
}
}
if (Settings.enableDiagnostics)
{
JointUpdateTime = _watch.ElapsedTicks;
_watch.Reset();
}
// 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)
{
float minSleepTime = Settings.maxFloat;
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
if (b.bodyType == BodyType.Static)
{
continue;
}
if (!b.isSleepingAllowed || b._angularVelocity * b._angularVelocity > AngTolSqr || Vector2.Dot(b._linearVelocity, b._linearVelocity) > LinTolSqr)
{
b._sleepTime = 0.0f;
minSleepTime = 0.0f;
}
else
{
b._sleepTime += h;
minSleepTime = Math.Min(minSleepTime, b._sleepTime);
}
}
if (minSleepTime >= Settings.timeToSleep && positionSolved)
{
for (int i = 0; i < BodyCount; ++i)
{
Body b = Bodies[i];
b.isAwake = false;
}
}
}
}
internal void solveTOI(ref TimeStep subStep, int toiIndexA, int toiIndexB)
{
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);
// 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.
float h = subStep.dt;
// Integrate positions.
for (int i = 0; i < BodyCount; ++i)
{
Vector2 c = _positions[i].c;
float a = _positions[i].a;
Vector2 v = _velocities[i].v;
float w = _velocities[i].w;
// Check for large velocities
Vector2 translation = h * v;
if (Vector2.Dot(translation, translation) > Settings.maxTranslationSquared)
{
float ratio = Settings.maxTranslation / translation.Length();
v *= ratio;
}
float rotation = h * w;
if (rotation * rotation > Settings.maxRotationSquared)
{
float ratio = Settings.maxRotation / Math.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);
}
