/// Initialize the bodies, anchors, lengths, max lengths, and ratio using the world anchors.
// Pulley:
// length1 = norm(p1 - s1)
// length2 = norm(p2 - s2)
// C0 = (length1 + ratio * length2)_initial
// C = C0 - (length1 + ratio * length2)
// u1 = (p1 - s1) / norm(p1 - s1)
// u2 = (p2 - s2) / norm(p2 - s2)
// Cdot = -dot(u1, v1 + cross(w1, r1)) - ratio * dot(u2, v2 + cross(w2, r2))
// J = -[u1 cross(r1, u1) ratio * u2 ratio * cross(r2, u2)]
// K = J * invM * JT
// = invMass1 + invI1 * cross(r1, u1)^2 + ratio^2 * (invMass2 + invI2 * cross(r2, u2)^2)
public void Initialize(b2Body bA, b2Body bB, b2Vec2 groundA, b2Vec2 groundB, b2Vec2 anchorA, b2Vec2 anchorB, float r)
{
bodyA = bA;
bodyB = bB;
groundAnchorA = groundA;
groundAnchorB = groundB;
localAnchorA = bodyA.GetLocalPoint(anchorA);
localAnchorB = bodyB.GetLocalPoint(anchorB);
b2Vec2 dA = anchorA - groundA;
lengthA = dA.Length();
b2Vec2 dB = anchorB - groundB;
lengthB = dB.Length();
ratio = r;
Debug.Assert(ratio > float.Epsilon);
}
public override void SolveVelocityConstraints(b2SolverData data)
{
b2Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
// Cdot = v + cross(w, r)
b2Vec2 Cdot = vB + b2Math.b2Cross(wB, m_rB);
b2Vec2 impulse = b2Math.b2Mul(m_mass, -(Cdot + m_C + m_gamma * m_impulse));
b2Vec2 oldImpulse = m_impulse;
m_impulse += impulse;
float maxImpulse = data.step.dt * m_maxForce;
if (m_impulse.LengthSquared() > maxImpulse * maxImpulse)
{
m_impulse *= maxImpulse / m_impulse.Length();
}
impulse = m_impulse - oldImpulse;
vB += m_invMassB * impulse;
wB += m_invIB * b2Math.b2Cross(m_rB, impulse);
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
public virtual float GetLengthB()
{
b2Vec2 p = m_bodyB.GetWorldPoint(m_localAnchorB);
b2Vec2 s = m_groundAnchorB;
b2Vec2 d = p - s;
return(d.Length());
}
/// Get the current length of the segment attached to bodyB.
public float GetCurrentLengthB()
{
b2Vec2 p = m_bodyB.GetWorldPoint(m_localAnchorB);
b2Vec2 s = new b2Vec2(m_groundAnchorB);
b2Vec2 d = p - s;
return(d.Length());
}
/// Initialize the bodies, anchors, and length using the world
/// anchors.
// 1-D constrained system
// m (v2 - v1) = lambda
// v2 + (beta/h) * x1 + gamma * lambda = 0, gamma has units of inverse mass.
// x2 = x1 + h * v2
// 1-D mass-damper-spring system
// m (v2 - v1) + h * d * v2 + h * k *
// C = norm(p2 - p1) - L
// u = (p2 - p1) / norm(p2 - p1)
// Cdot = dot(u, v2 + cross(w2, r2) - v1 - cross(w1, r1))
// J = [-u -cross(r1, u) u cross(r2, u)]
// K = J * invM * JT
// = invMass1 + invI1 * cross(r1, u)^2 + invMass2 + invI2 * cross(r2, u)^2
public void Initialize(b2Body b1, b2Body b2, b2Vec2 anchor1, b2Vec2 anchor2)
{
bodyA = b1;
bodyB = b2;
localAnchorA = bodyA.GetLocalPoint(anchor1);
localAnchorB = bodyB.GetLocalPoint(anchor2);
b2Vec2 d = anchor2 - anchor1;
length = d.Length();
}
/// Initialize the bodies, anchors, lengths, max lengths, and ratio using the world anchors.
public void Initialize(b2Body bA, b2Body bB,
b2Vec2 groundA, b2Vec2 groundB,
b2Vec2 anchorA, b2Vec2 anchorB,
float r)
{
BodyA = bA;
BodyB = bB;
groundAnchorA = groundA;
groundAnchorB = groundB;
localAnchorA = BodyA.GetLocalPoint(anchorA);
localAnchorB = BodyB.GetLocalPoint(anchorB);
b2Vec2 dA = anchorA - groundA;
lengthA = dA.Length();
b2Vec2 dB = anchorB - groundB;
lengthB = dB.Length();
ratio = r;
System.Diagnostics.Debug.Assert(ratio > b2Settings.b2_epsilon);
}
public override void InitVelocityConstraints(b2SolverData data)
{
m_indexA = m_bodyA.IslandIndex;
m_indexB = m_bodyB.IslandIndex;
m_localCenterA = m_bodyA.Sweep.localCenter;
m_localCenterB = m_bodyB.Sweep.localCenter;
m_invMassA = m_bodyA.InvertedMass;
m_invMassB = m_bodyB.InvertedMass;
m_invIA = m_bodyA.InvertedI;
m_invIB = m_bodyB.InvertedI;
b2Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
b2Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
b2Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
b2Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
b2Rot qA = new b2Rot(aA);
b2Rot qB = new b2Rot(aB);
m_rA = b2Math.b2Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = b2Math.b2Mul(qB, m_localAnchorB - m_localCenterB);
m_u = cB + m_rB - cA - m_rA;
m_length = m_u.Length();
float C = m_length - m_maxLength;
if (C > 0.0f)
{
m_state = b2LimitState.e_atUpperLimit;
}
else
{
m_state = b2LimitState.e_inactiveLimit;
}
if (m_length > b2Settings.b2_linearSlop)
{
m_u *= 1.0f / m_length;
}
else
{
m_u.SetZero();
m_mass = 0.0f;
m_impulse = 0.0f;
return;
}
// Compute effective mass.
float crA = b2Math.b2Cross(m_rA, m_u);
float crB = b2Math.b2Cross(m_rB, m_u);
float invMass = m_invMassA + m_invIA * crA * crA + m_invMassB + m_invIB * crB * crB;
m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (data.step.warmStarting)
{
// Scale the impulse to support a variable time step.
m_impulse *= data.step.dtRatio;
b2Vec2 P = m_impulse * m_u;
vA -= m_invMassA * P;
wA -= m_invIA * b2Math.b2Cross(m_rA, P);
vB += m_invMassB * P;
wB += m_invIB * b2Math.b2Cross(m_rB, P);
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
public override bool SolvePositionConstraints(b2SolverData data)
{
b2Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
b2Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
b2Rot qA = new b2Rot(aA);
b2Rot qB = new b2Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
b2Vec2 rA = b2Math.b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Math.b2Mul(qB, m_localAnchorB - m_localCenterB);
float positionError, angularError;
b2Vec3 ex = new b2Vec3();
b2Vec3 ey = new b2Vec3();
b2Vec3 ez = new b2Vec3();
ex.x = mA + mB + rA.y * rA.y * iA + rB.y * rB.y * iB;
ey.x = -rA.y * rA.x * iA - rB.y * rB.x * iB;
ez.x = -rA.y * iA - rB.y * iB;
ex.y = ey.x;
ey.y = mA + mB + rA.x * rA.x * iA + rB.x * rB.x * iB;
ez.y = rA.x * iA + rB.x * iB;
ex.z = ez.x;
ey.z = ez.y;
ez.z = iA + iB;
b2Mat33 K = new b2Mat33(ex, ey, ez);
if (m_frequencyHz > 0.0f)
{
b2Vec2 C1 = cB + rB - cA - rA;
positionError = C1.Length();
angularError = 0.0f;
b2Vec2 P = -K.Solve22(C1);
cA -= mA * P;
aA -= iA * b2Math.b2Cross(rA, P);
cB += mB * P;
aB += iB * b2Math.b2Cross(rB, P);
}
else
{
b2Vec2 C1 = cB + rB - cA - rA;
float C2 = aB - aA - m_referenceAngle;
positionError = C1.Length();
angularError = b2Math.b2Abs(C2);
b2Vec3 C = new b2Vec3(C1.x, C1.y, C2);
b2Vec3 impulse = -K.Solve33(C);
b2Vec2 P = new b2Vec2(impulse.x, impulse.y);
cA -= mA * P;
aA -= iA * (b2Math.b2Cross(rA, P) + impulse.z);
cB += mB * P;
aB += iB * (b2Math.b2Cross(rB, P) + impulse.z);
}
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return(positionError <= b2Settings.b2_linearSlop && angularError <= b2Settings.b2_angularSlop);
}
public override void InitVelocityConstraints(b2SolverData data)
{
m_indexA = m_bodyA.IslandIndex;
m_indexB = m_bodyB.IslandIndex;
m_localCenterA = m_bodyA.Sweep.localCenter;
m_localCenterB = m_bodyB.Sweep.localCenter;
m_invMassA = m_bodyA.InvertedMass;
m_invMassB = m_bodyB.InvertedMass;
m_invIA = m_bodyA.InvertedI;
m_invIB = m_bodyB.InvertedI;
b2Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
b2Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
b2Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
b2Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
b2Rot qA = new b2Rot(aA);
b2Rot qB = new b2Rot(aB);
m_rA = b2Math.b2Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = b2Math.b2Mul(qB, m_localAnchorB - m_localCenterB);
// Get the pulley axes.
m_uA = cA + m_rA - m_groundAnchorA;
m_uB = cB + m_rB - m_groundAnchorB;
float lengthA = m_uA.Length();
float lengthB = m_uB.Length();
if (lengthA > 10.0f * b2Settings.b2_linearSlop)
{
m_uA *= 1.0f / lengthA;
}
else
{
m_uA.SetZero();
}
if (lengthB > 10.0f * b2Settings.b2_linearSlop)
{
m_uB *= 1.0f / lengthB;
}
else
{
m_uB.SetZero();
}
// Compute effective mass.
float ruA = b2Math.b2Cross(m_rA, m_uA);
float ruB = b2Math.b2Cross(m_rB, m_uB);
float mA = m_invMassA + m_invIA * ruA * ruA;
float mB = m_invMassB + m_invIB * ruB * ruB;
m_mass = mA + m_ratio * m_ratio * mB;
if (m_mass > 0.0f)
{
m_mass = 1.0f / m_mass;
}
if (data.step.warmStarting)
{
// Scale impulses to support variable time steps.
m_impulse *= data.step.dtRatio;
// Warm starting.
b2Vec2 PA = -(m_impulse) * m_uA;
b2Vec2 PB = (-m_ratio * m_impulse) * m_uB;
vA += m_invMassA * PA;
wA += m_invIA * b2Math.b2Cross(m_rA, PA);
vB += m_invMassB * PB;
wB += m_invIB * b2Math.b2Cross(m_rB, PB);
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
public override bool SolvePositionConstraints(b2SolverData data)
{
b2Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
b2Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
b2Rot qA = new b2Rot(aA);
b2Rot qB = new b2Rot(aB);
b2Vec2 rA = b2Math.b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Math.b2Mul(qB, m_localAnchorB - m_localCenterB);
// Get the pulley axes.
b2Vec2 uA = cA + rA - m_groundAnchorA;
b2Vec2 uB = cB + rB - m_groundAnchorB;
float lengthA = uA.Length();
float lengthB = uB.Length();
if (lengthA > 10.0f * b2Settings.b2_linearSlop)
{
uA *= 1.0f / lengthA;
}
else
{
uA.SetZero();
}
if (lengthB > 10.0f * b2Settings.b2_linearSlop)
{
uB *= 1.0f / lengthB;
}
else
{
uB.SetZero();
}
// Compute effective mass.
float ruA = b2Math.b2Cross(rA, uA);
float ruB = b2Math.b2Cross(rB, uB);
float mA = m_invMassA + m_invIA * ruA * ruA;
float mB = m_invMassB + m_invIB * ruB * ruB;
float mass = mA + m_ratio * m_ratio * mB;
if (mass > 0.0f)
{
mass = 1.0f / mass;
}
float C = m_constant - lengthA - m_ratio * lengthB;
float linearError = b2Math.b2Abs(C);
float impulse = -mass * C;
b2Vec2 PA = -impulse * uA;
b2Vec2 PB = -m_ratio * impulse * uB;
cA += m_invMassA * PA;
aA += m_invIA * b2Math.b2Cross(rA, PA);
cB += m_invMassB * PB;
aB += m_invIB * b2Math.b2Cross(rB, PB);
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return(linearError < b2Settings.b2_linearSlop);
}
public static float Distance(b2Vec2 a, b2Vec2 b)
{
b2Vec2 c = a - b;
return(c.Length());
}
internal override bool SolvePositionConstraints(b2SolverData data)
{
b2Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
b2Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
b2Rot qA = new b2Rot(aA);
b2Rot qB = new b2Rot(aB);
float angularError = 0.0f;
float positionError = 0.0f;
bool fixedRotation = (m_invIA + m_invIB == 0.0f);
// Solve angular limit constraint.
if (m_enableLimit && m_limitState != b2LimitState.e_inactiveLimit && fixedRotation == false)
{
float angle = aB - aA - m_referenceAngle;
float limitImpulse = 0.0f;
if (m_limitState == b2LimitState.e_equalLimits)
{
// Prevent large angular corrections
float C = Utils.b2Clamp(angle - m_lowerAngle, -Settings.b2_maxAngularCorrection, Settings.b2_maxAngularCorrection);
limitImpulse = -m_motorMass * C;
angularError = Utils.b2Abs(C);
}
else if (m_limitState == b2LimitState.e_atLowerLimit)
{
float C = angle - m_lowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = Utils.b2Clamp(C + Settings.b2_angularSlop, -Settings.b2_maxAngularCorrection, 0.0f);
limitImpulse = -m_motorMass * C;
}
else if (m_limitState == b2LimitState.e_atUpperLimit)
{
float C = angle - m_upperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = Utils.b2Clamp(C - Settings.b2_angularSlop, 0.0f, Settings.b2_maxAngularCorrection);
limitImpulse = -m_motorMass * C;
}
aA -= m_invIA * limitImpulse;
aB += m_invIB * limitImpulse;
}
{
// Solve point-to-point constraint.
qA.Set(aA);
qB.Set(aB);
b2Vec2 rA = Utils.b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = Utils.b2Mul(qB, m_localAnchorB - m_localCenterB);
b2Vec2 C = cB + rB - cA - rA;
positionError = C.Length();
float mA = m_invMassA;
float mB = m_invMassB;
float iA = m_invIA;
float iB = m_invIB;
b2Mat22 K = new b2Mat22();
K.ex.x = mA + mB + iA * rA.y * rA.y + iB * rB.y * rB.y;
K.ex.y = -iA * rA.x * rA.y - iB * rB.x * rB.y;
K.ey.x = K.ex.y;
K.ey.y = mA + mB + iA * rA.x * rA.x + iB * rB.x * rB.x;
b2Vec2 impulse = -K.Solve(C);
cA -= mA * impulse;
aA -= iA * Utils.b2Cross(rA, impulse);
cB += mB * impulse;
aB += iB * Utils.b2Cross(rB, impulse);
}
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return(positionError <= Settings.b2_linearSlop && angularError <= Settings.b2_angularSlop);
}
public void SolveTOI(b2TimeStep subStep, int toiIndexA, int toiIndexB)
{
Debug.Assert(toiIndexA < m_bodyCount);
Debug.Assert(toiIndexB < m_bodyCount);
// Initialize the body state.
for (int i = 0; i < m_bodyCount; ++i)
{
b2Body b = m_bodies[i];
m_positions[i].c = b.m_sweep.c;
m_positions[i].a = b.m_sweep.a;
m_velocities[i].v = b.m_linearVelocity;
m_velocities[i].w = b.m_angularVelocity;
}
b2ContactSolverDef contactSolverDef = new b2ContactSolverDef();
contactSolverDef.contacts = m_contacts;
contactSolverDef.count = m_contactCount;
contactSolverDef.step = subStep;
contactSolverDef.positions = m_positions;
contactSolverDef.velocities = m_velocities;
b2ContactSolver contactSolver = new b2ContactSolver(contactSolverDef);
// Solve position constraints.
for (int i = 0; i < subStep.positionIterations; ++i)
{
bool contactsOkay = contactSolver.SolveTOIPositionConstraints(toiIndexA, toiIndexB);
if (contactsOkay)
{
break;
}
}
#if false
// // Is the new position really safe?
// for (int32 i = 0; i < m_contactCount; ++i)
// {
// b2Contact* c = m_contacts[i];
// b2Fixture* fA = c->GetFixtureA();
// b2Fixture* fB = c->GetFixtureB();
//
// b2Body* bA = fA->GetBody();
// b2Body* bB = fB->GetBody();
//
// int32 indexA = c->GetChildIndexA();
// int32 indexB = c->GetChildIndexB();
//
// b2DistanceInput input;
// input.proxyA.Set(fA->GetShape(), indexA);
// input.proxyB.Set(fB->GetShape(), indexB);
// input.transformA = bA->GetTransform();
// input.transformB = bB->GetTransform();
// input.useRadii = false;
//
// b2DistanceOutput output;
// b2SimplexCache cache;
// cache.count = 0;
// b2Distance(&output, &cache, &input);
//
// if (output.distance == 0 || cache.count == 3)
// {
// cache.count += 0;
// }
// }
#endif
// Leap of faith to new safe state.
m_bodies[toiIndexA].m_sweep.c0 = m_positions[toiIndexA].c;
m_bodies[toiIndexA].m_sweep.a0 = m_positions[toiIndexA].a;
m_bodies[toiIndexB].m_sweep.c0 = m_positions[toiIndexB].c;
m_bodies[toiIndexB].m_sweep.a0 = m_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 < subStep.velocityIterations; ++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 < m_bodyCount; ++i)
{
b2Vec2 c = m_positions[i].c;
float a = m_positions[i].a;
b2Vec2 v = m_velocities[i].v;
float w = m_velocities[i].w;
// Check for large velocities
b2Vec2 translation = h * v;
if (Utils.b2Dot(translation, translation) > (Settings.b2_maxTranslationSquared))
{
float ratio = Settings.b2_maxTranslation / translation.Length();
v *= ratio;
}
float rotation = h * w;
if (rotation * rotation > Settings.b2_maxRotationSquared)
{
float ratio = (0.5f * Settings.b2_pi) / Utils.b2Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
m_positions[i].c = c;
m_positions[i].a = a;
m_velocities[i].v = v;
m_velocities[i].w = w;
// Sync bodies
b2Body body = m_bodies[i];
body.m_sweep.c = c;
body.m_sweep.a = a;
body.m_linearVelocity = v;
body.m_angularVelocity = w;
body.SynchronizeTransform();
}
Report(contactSolver.m_velocityConstraints);
}
public void Solve(b2Profile profile, b2TimeStep step, b2Vec2 gravity, bool allowSleep)
{
b2Timer timer = new b2Timer();
float h = step.dt;
// Integrate velocities and apply damping. Initialize the body state.
for (int i = 0; i < m_bodyCount; ++i)
{
b2Body b = m_bodies[i];
b2Vec2 c = new b2Vec2(b.m_sweep.c);
float a = b.m_sweep.a;
b2Vec2 v = new b2Vec2(b.m_linearVelocity);
float w = b.m_angularVelocity;
// Store positions for continuous collision.
b.m_sweep.c0 = b.m_sweep.c;
b.m_sweep.a0 = b.m_sweep.a;
if (b.m_type == BodyType.b2_dynamicBody)
{
// Integrate velocities.
v += h * (b.m_gravityScale * gravity + b.m_invMass * b.m_force);
w += h * b.m_invI * b.m_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
// Pade approximation:
// v2 = v1 * 1 / (1 + c * dt)
v *= 1.0f / (1.0f + h * b.m_linearDamping);
w *= 1.0f / (1.0f + h * b.m_angularDamping);
}
m_positions[i].c = c;
m_positions[i].a = a;
m_velocities[i].v = v;
m_velocities[i].w = w;
}
timer.Reset();
// Solver data
b2SolverData solverData = new b2SolverData();
solverData.step = step;
solverData.positions = m_positions;
solverData.velocities = m_velocities;
// Initialize velocity constraints.
b2ContactSolverDef contactSolverDef = new b2ContactSolverDef();
contactSolverDef.step = step;
contactSolverDef.contacts = m_contacts;
contactSolverDef.count = m_contactCount;
contactSolverDef.positions = m_positions;
contactSolverDef.velocities = m_velocities;
b2ContactSolver contactSolver = new b2ContactSolver(contactSolverDef);
contactSolver.InitializeVelocityConstraints();
if (step.warmStarting)
{
contactSolver.WarmStart();
}
for (int i = 0; i < m_jointCount; ++i)
{
m_joints[i].InitVelocityConstraints(solverData);
}
profile.solveInit = timer.GetMilliseconds();
// Solve velocity constraints
timer.Reset();
for (int i = 0; i < step.velocityIterations; ++i)
{
for (int j = 0; j < m_jointCount; ++j)
{
m_joints[j].SolveVelocityConstraints(solverData);
}
contactSolver.SolveVelocityConstraints();
}
// Store impulses for warm starting
contactSolver.StoreImpulses();
profile.solveVelocity = timer.GetMilliseconds();
// Integrate positions
for (int i = 0; i < m_bodyCount; ++i)
{
b2Vec2 c = m_positions[i].c;
float a = m_positions[i].a;
b2Vec2 v = m_velocities[i].v;
float w = m_velocities[i].w;
// Check for large velocities
b2Vec2 translation = h * v;
if (Utils.b2Dot(translation, translation) > (Settings.b2_maxTranslation * Settings.b2_maxTranslation))
{
float ratio = Settings.b2_maxTranslation / translation.Length();
v *= ratio;
}
float rotation = h * w;
if (rotation * rotation > Settings.b2_maxRotationSquared)
{
float ratio = (0.5f * Settings.b2_pi) / Utils.b2Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
m_positions[i].c = c;
m_positions[i].a = a;
m_velocities[i].v = v;
m_velocities[i].w = w;
}
// Solve position constraints
timer.Reset();
bool positionSolved = false;
for (int i = 0; i < step.positionIterations; ++i)
{
bool contactsOkay = contactSolver.SolvePositionConstraints();
bool jointsOkay = true;
for (int j = 0; j < m_jointCount; ++j)
{
bool jointOkay = m_joints[j].SolvePositionConstraints(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 < m_bodyCount; ++i)
{
b2Body body = m_bodies[i];
body.m_sweep.c = m_positions[i].c;
body.m_sweep.a = m_positions[i].a;
body.m_linearVelocity = m_velocities[i].v;
body.m_angularVelocity = m_velocities[i].w;
body.SynchronizeTransform();
}
profile.solvePosition = timer.GetMilliseconds();
Report(contactSolver.m_velocityConstraints);
if (allowSleep)
{
float minSleepTime = float.MaxValue;
const float linTolSqr = Settings.b2_linearSleepTolerance * Settings.b2_linearSleepTolerance;
float angTolSqr = Settings.b2_angularSlop * Settings.b2_angularSlop;
for (int i = 0; i < m_bodyCount; ++i)
{
b2Body b = m_bodies[i];
if (b.GetType() == BodyType.b2_staticBody)
{
continue;
}
if ((b.m_flags & b2Body.BodyFlags.e_autoSleepFlag) == 0 || b.m_angularVelocity * b.m_angularVelocity > angTolSqr || Utils.b2Dot(b.m_linearVelocity, b.m_linearVelocity) > linTolSqr)
{
b.m_sleepTime = 0.0f;
minSleepTime = 0.0f;
}
else
{
b.m_sleepTime += h;
minSleepTime = Utils.b2Min(minSleepTime, b.m_sleepTime);
}
}
if (minSleepTime >= Settings.b2_timeToSleep && positionSolved)
{
for (int i = 0; i < m_bodyCount; ++i)
{
b2Body b = m_bodies[i];
b.SetAwake(false);
}
}
}
}
public override void InitVelocityConstraints(b2SolverData data)
{
m_indexA = m_bodyA.IslandIndex;
m_indexB = m_bodyB.IslandIndex;
m_localCenterA = m_bodyA.Sweep.localCenter;
m_localCenterB = m_bodyB.Sweep.localCenter;
m_invMassA = m_bodyA.InvertedMass;
m_invMassB = m_bodyB.InvertedMass;
m_invIA = m_bodyA.InvertedI;
m_invIB = m_bodyB.InvertedI;
b2Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
b2Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
b2Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
b2Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
b2Rot qA = new b2Rot(aA);
b2Rot qB = new b2Rot(aB);
m_rA = b2Math.b2Mul(qA, m_localAnchorA - m_localCenterA);
m_rB = b2Math.b2Mul(qB, m_localAnchorB - m_localCenterB);
m_u = cB + m_rB - cA - m_rA;
// Handle singularity.
float length = m_u.Length();
if (length > b2Settings.b2_linearSlop)
{
m_u *= 1.0f / length;
}
else
{
m_u.Set(0.0f, 0.0f);
}
float crAu = b2Math.b2Cross(m_rA, m_u);
float crBu = b2Math.b2Cross(m_rB, m_u);
float invMass = m_invMassA + m_invIA * crAu * crAu + m_invMassB + m_invIB * crBu * crBu;
// Compute the effective mass matrix.
m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (m_frequencyHz > 0.0f)
{
float C = length - m_length;
// Frequency
float omega = 2.0f * (float)Math.PI * m_frequencyHz;
// Damping coefficient
float d = 2.0f * m_mass * m_dampingRatio * omega;
// Spring stiffness
float k = m_mass * omega * omega;
// magic formulas
float h = data.step.dt;
m_gamma = h * (d + h * k);
m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
m_bias = C * h * k * m_gamma;
invMass += m_gamma;
m_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
}
else
{
m_gamma = 0.0f;
m_bias = 0.0f;
}
if (data.step.warmStarting)
{
// Scale the impulse to support a variable time step.
m_impulse *= data.step.dtRatio;
b2Vec2 P = m_impulse * m_u;
vA -= m_invMassA * P;
wA -= m_invIA * b2Math.b2Cross(m_rA, P);
vB += m_invMassB * P;
wB += m_invIB * b2Math.b2Cross(m_rB, P);
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
public void Solve(ref b2Profile profile, b2TimeStep step, b2Vec2 gravity, bool allowSleep)
{
b2Timer timer = new b2Timer();
float h = step.dt;
// Integrate velocities and apply damping. Initialize the body state.
for (int i = 0; i < m_bodyCount; ++i)
{
b2Body b = m_bodies[i];
b2Vec2 c = b.Sweep.c;
float a = b.Sweep.a;
b2Vec2 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 == b2BodyType.b2_dynamicBody)
{
// Integrate velocities.
v += h * (b.GravityScale * gravity + b.InvertedMass * b.Force);
w += h * b.InvertedI * 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 *= b2Math.b2Clamp(1.0f - h * b.LinearDamping, 0.0f, 1.0f);
w *= b2Math.b2Clamp(1.0f - h * b.AngularDamping, 0.0f, 1.0f);
}
m_positions[i].c = c;
m_positions[i].a = a;
m_velocities[i].v = v;
m_velocities[i].w = w;
}
timer.Reset();
// Solver data
b2SolverData solverData = new b2SolverData();
solverData.step = step;
solverData.positions = m_positions;
solverData.velocities = m_velocities;
// Initialize velocity constraints.
b2ContactSolverDef contactSolverDef;
contactSolverDef.step = step;
contactSolverDef.contacts = m_contacts;
contactSolverDef.count = m_contactCount;
contactSolverDef.positions = m_positions;
contactSolverDef.velocities = m_velocities;
b2ContactSolver contactSolver = new b2ContactSolver(contactSolverDef);
contactSolver.InitializeVelocityConstraints();
if (step.warmStarting)
{
contactSolver.WarmStart();
}
for (int i = 0; i < m_jointCount; ++i)
{
m_joints[i].InitVelocityConstraints(solverData);
}
profile.solveInit = timer.GetMilliseconds();
// Solve velocity constraints
timer.Reset();
for (int i = 0; i < step.velocityIterations; ++i)
{
for (int j = 0; j < m_jointCount; ++j)
{
m_joints[j].SolveVelocityConstraints(solverData);
}
contactSolver.SolveVelocityConstraints();
}
// Store impulses for warm starting
contactSolver.StoreImpulses();
profile.solveVelocity = timer.GetMilliseconds();
// Integrate positions
for (int i = 0; i < m_bodyCount; ++i)
{
b2Vec2 c = m_positions[i].c;
float a = m_positions[i].a;
b2Vec2 v = m_velocities[i].v;
float w = m_velocities[i].w;
// Check for large velocities
b2Vec2 translation = h * v;
if (b2Math.b2Dot(translation, translation) > b2Settings.b2_maxTranslationSquared)
{
float ratio = b2Settings.b2_maxTranslation / translation.Length();
v *= ratio;
}
float rotation = h * w;
if (rotation * rotation > b2Settings.b2_maxRotationSquared)
{
float ratio = b2Settings.b2_maxRotation / Math.Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
m_positions[i].c = c;
m_positions[i].a = a;
m_velocities[i].v = v;
m_velocities[i].w = w;
}
// Solve position constraints
timer.Reset();
bool positionSolved = false;
for (int i = 0; i < step.positionIterations; ++i)
{
bool contactsOkay = contactSolver.SolvePositionConstraints();
bool jointsOkay = true;
for (int i2 = 0; i2 < m_jointCount; ++i2)
{
bool jointOkay = m_joints[i2].SolvePositionConstraints(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 < m_bodyCount; ++i)
{
b2Body body = m_bodies[i];
body.Sweep.c = m_positions[i].c;
body.Sweep.a = m_positions[i].a;
body.LinearVelocity = m_velocities[i].v;
body.AngularVelocity = m_velocities[i].w;
body.SynchronizeTransform();
}
profile.solvePosition = timer.GetMilliseconds();
Report(contactSolver.m_velocityConstraints);
if (allowSleep)
{
float minSleepTime = b2Settings.b2_maxFloat;
float linTolSqr = b2Settings.b2_linearSleepTolerance * b2Settings.b2_linearSleepTolerance;
float angTolSqr = b2Settings.b2_angularSleepTolerance * b2Settings.b2_angularSleepTolerance;
for (int i = 0; i < m_bodyCount; ++i)
{
b2Body b = m_bodies[i];
if (b.BodyType == b2BodyType.b2_staticBody)
{
continue;
}
if (!(b.BodyFlags.HasFlag(b2BodyFlags.e_autoSleepFlag)) ||
b.AngularVelocity * b.AngularVelocity > angTolSqr ||
b2Math.b2Dot(b.LinearVelocity, b.LinearVelocity) > linTolSqr)
{
b.SleepTime = 0.0f;
minSleepTime = 0.0f;
}
else
{
b.SleepTime += h;
minSleepTime = Math.Min(minSleepTime, b.SleepTime);
}
}
if (minSleepTime >= b2Settings.b2_timeToSleep && positionSolved)
{
for (int i = 0; i < m_bodyCount; ++i)
{
b2Body b = m_bodies[i];
b.SetAwake(false);
}
}
}
}