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)
{
Body b = Bodies[i];
Vector2 c = b._sweep.C;
float a = b._sweep.A;
Vector2 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.SleepingAllowed || 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.Awake = false;
}
}
}
}
private void SolveTOI(ref TimeStep step)
{
Island.Reset(2 * Settings.MaxTOIContacts, Settings.MaxTOIContacts, 0, ContactManager);
if (_stepComplete)
{
for (int i = 0; i < BodyList.Count; i++)
{
BodyList[i]._flags &= ~BodyFlags.IslandFlag;
BodyList[i]._sweep.Alpha0 = 0.0f;
}
for (int i = 0; i < ContactManager.ContactList.Count; i++)
{
Contact c = ContactManager.ContactList[i];
// Invalidate TOI
c._flags &= ~ContactFlags.IslandFlag;
c._flags &= ~ContactFlags.TOIFlag;
c._toiCount = 0;
c._toi = 1.0f;
}
}
// Find TOI events and solve them.
for (;;)
{
// Find the first TOI.
Contact minContact = null;
float minAlpha = 1.0f;
for (int i = 0; i < ContactManager.ContactList.Count; i++)
{
Contact c = ContactManager.ContactList[i];
// Is this contact disabled?
if (c.Enabled == false)
{
continue;
}
// Prevent excessive sub-stepping.
if (c._toiCount > Settings.MaxSubSteps)
{
continue;
}
float alpha;
if (c.TOIFlag)
{
// This contact has a valid cached TOI.
alpha = c._toi;
}
else
{
Fixture fA = c.FixtureA;
Fixture fB = c.FixtureB;
// Is there a sensor?
if (fA.IsSensor || fB.IsSensor)
{
continue;
}
Body bA = fA.Body;
Body bB = fB.Body;
BodyType typeA = bA.BodyType;
BodyType typeB = bB.BodyType;
Debug.Assert(typeA == BodyType.Dynamic || typeB == BodyType.Dynamic);
bool activeA = bA.Awake && typeA != BodyType.Static;
bool activeB = bB.Awake && typeB != BodyType.Static;
// Is at least one body active (awake and dynamic or kinematic)?
if (activeA == false && activeB == false)
{
continue;
}
bool collideA = (bA.IsBullet || typeA != BodyType.Dynamic) && (fA.IgnoreCCDWith & fB.CollisionCategories) == 0 && !bA.IgnoreCCD;
bool collideB = (bB.IsBullet || typeB != BodyType.Dynamic) && (fB.IgnoreCCDWith & fA.CollisionCategories) == 0 && !bB.IgnoreCCD;
// Are these two non-bullet dynamic bodies?
if (collideA == false && collideB == false)
{
continue;
}
// Compute the TOI for this contact.
// Put the sweeps onto the same time interval.
float alpha0 = bA._sweep.Alpha0;
if (bA._sweep.Alpha0 < bB._sweep.Alpha0)
{
alpha0 = bB._sweep.Alpha0;
bA._sweep.Advance(alpha0);
}
else if (bB._sweep.Alpha0 < bA._sweep.Alpha0)
{
alpha0 = bA._sweep.Alpha0;
bB._sweep.Advance(alpha0);
}
Debug.Assert(alpha0 < 1.0f);
// Compute the time of impact in interval [0, minTOI]
TOIInput input = new TOIInput();
input.ProxyA = new DistanceProxy(fA.Shape, c.ChildIndexA);
input.ProxyB = new DistanceProxy(fB.Shape, c.ChildIndexB);
input.SweepA = bA._sweep;
input.SweepB = bB._sweep;
input.TMax = 1.0f;
TOIOutput output;
TimeOfImpact.CalculateTimeOfImpact(ref input, out output);
// Beta is the fraction of the remaining portion of the .
float beta = output.T;
if (output.State == TOIOutputState.Touching)
{
alpha = Math.Min(alpha0 + (1.0f - alpha0) * beta, 1.0f);
}
else
{
alpha = 1.0f;
}
c._toi = alpha;
c._flags &= ~ContactFlags.TOIFlag;
}
if (alpha < minAlpha)
{
// This is the minimum TOI found so far.
minContact = c;
minAlpha = alpha;
}
}
if (minContact == null || 1.0f - 10.0f * Settings.Epsilon < minAlpha)
{
// No more TOI events. Done!
_stepComplete = true;
break;
}
// Advance the bodies to the TOI.
Fixture fA1 = minContact.FixtureA;
Fixture fB1 = minContact.FixtureB;
Body bA0 = fA1.Body;
Body bB0 = fB1.Body;
Sweep backup1 = bA0._sweep;
Sweep backup2 = bB0._sweep;
bA0.Advance(minAlpha);
bB0.Advance(minAlpha);
// The TOI contact likely has some new contact points.
minContact.Update(ContactManager);
minContact._flags &= ~ContactFlags.TOIFlag;
++minContact._toiCount;
// Is the contact solid?
if (minContact.Enabled == false || minContact.IsTouching == false)
{
// Restore the sweeps.
minContact._flags &= ~ContactFlags.EnabledFlag;
bA0._sweep = backup1;
bB0._sweep = backup2;
bA0.SynchronizeTransform();
bB0.SynchronizeTransform();
continue;
}
bA0.Awake = true;
bB0.Awake = true;
// Build the island
Island.Clear();
Island.Add(bA0);
Island.Add(bB0);
Island.Add(minContact);
bA0._flags |= BodyFlags.IslandFlag;
bB0._flags |= BodyFlags.IslandFlag;
minContact._flags &= ~ContactFlags.IslandFlag;
// Get contacts on bodyA and bodyB.
Body[] bodies = { bA0, bB0 };
for (int i = 0; i < 2; ++i)
{
Body body = bodies[i];
if (body.BodyType == BodyType.Dynamic)
{
for (ContactEdge ce = body.ContactList; ce != null; ce = ce.Next)
{
Contact contact = ce.Contact;
if (Island.BodyCount == Island.BodyCapacity)
{
break;
}
if (Island.ContactCount == Island.ContactCapacity)
{
break;
}
// Has this contact already been added to the island?
if (contact.IslandFlag)
{
continue;
}
// Only add static, kinematic, or bullet bodies.
Body other = ce.Other;
if (other.BodyType == BodyType.Dynamic &&
body.IsBullet == false && other.IsBullet == false)
{
continue;
}
// Skip sensors.
if (contact.FixtureA.IsSensor || contact.FixtureB.IsSensor)
{
continue;
}
// Tentatively advance the body to the TOI.
Sweep backup = other._sweep;
if (!other.IsIsland)
{
other.Advance(minAlpha);
}
// Update the contact points
contact.Update(ContactManager);
// Was the contact disabled by the user?
if (contact.Enabled == false)
{
other._sweep = backup;
other.SynchronizeTransform();
continue;
}
// Are there contact points?
if (contact.IsTouching == false)
{
other._sweep = backup;
other.SynchronizeTransform();
continue;
}
// Add the contact to the island
minContact._flags |= ContactFlags.IslandFlag;
Island.Add(contact);
// Has the other body already been added to the island?
if (other.IsIsland)
{
continue;
}
// Add the other body to the island.
other._flags |= BodyFlags.IslandFlag;
if (other.BodyType != BodyType.Static)
{
other.Awake = true;
}
Island.Add(other);
}
}
}
TimeStep subStep;
subStep.dt = (1.0f - minAlpha) * step.dt;
subStep.inv_dt = 1.0f / subStep.dt;
subStep.dtRatio = 1.0f;
Island.SolveTOI(ref subStep, bA0.IslandIndex, bB0.IslandIndex);
// Reset island flags and synchronize broad-phase proxies.
for (int i = 0; i < Island.BodyCount; ++i)
{
Body body = Island.Bodies[i];
body._flags &= ~BodyFlags.IslandFlag;
if (body.BodyType != BodyType.Dynamic)
{
continue;
}
body.SynchronizeFixtures();
// Invalidate all contact TOIs on this displaced body.
for (ContactEdge ce = body.ContactList; ce != null; ce = ce.Next)
{
ce.Contact._flags &= ~ContactFlags.TOIFlag;
ce.Contact._flags &= ~ContactFlags.IslandFlag;
}
}
// Commit fixture proxy movements to the broad-phase so that new contacts are created.
// Also, some contacts can be destroyed.
ContactManager.FindNewContacts();
if (Settings.EnableSubStepping)
{
_stepComplete = false;
break;
}
}
}
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.
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);
}