internal override void InitVelocityConstraints(ref SolverData data)
{
_jointError = BodyA.Sweep.A - TargetAngle;
_bias = -BiasFactor * data.step.inv_dt * _jointError;
_massFactor = (1 - Softness) / (BodyA.InvI);
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
//GABS: NOT A BOTTLENECK
float p = (_bias - BodyB.AngularVelocity + BodyA.AngularVelocity) * _massFactor;
BodyA.AngularVelocity -= BodyA.InvI * Math.Sign(p) * Math.Min(Math.Abs(p), MaxImpulse);
BodyB.AngularVelocity += BodyB.InvI * Math.Sign(p) * Math.Min(Math.Abs(p), MaxImpulse);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
Body b1 = BodyA;
Body b2 = BodyB;
Transform xf1, xf2;
b1.GetTransform(out xf1);
b2.GetTransform(out xf2);
// Compute the effective mass matrix.
FVector2 r1 = MathUtils.Mul(ref xf1.q, LocalAnchorA - b1.LocalCenter);
FVector2 r2 = MathUtils.Mul(ref xf2.q, LocalAnchorB - b2.LocalCenter);
_u = b2.Sweep.C + r2 - b1.Sweep.C - r1;
// Handle singularity.
float length = _u.Length();
if (length < MaxLength && length > MinLength)
{
return;
}
if (length > Settings.LinearSlop)
{
_u *= 1.0f / length;
}
else
{
_u = FVector2.Zero;
}
float cr1u = MathUtils.Cross(r1, _u);
float cr2u = MathUtils.Cross(r2, _u);
float invMass = b1.InvMass + b1.InvI * cr1u * cr1u + b2.InvMass + b2.InvI * cr2u * cr2u;
Debug.Assert(invMass > Settings.Epsilon);
_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (Frequency > 0.0f)
{
float C = length - MaxLength;
// Frequency
float omega = 2.0f * Settings.Pi * Frequency;
// Damping coefficient
float d = 2.0f * _mass * DampingRatio * omega;
// Spring stiffness
float k = _mass * omega * omega;
// magic formulas
_gamma = data.step.dt * (d + data.step.dt * k);
_gamma = _gamma != 0.0f ? 1.0f / _gamma : 0.0f;
_bias = C * data.step.dt * k * _gamma;
_mass = invMass + _gamma;
_mass = _mass != 0.0f ? 1.0f / _mass : 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Scale the impulse to support a variable time step.
_impulse *= data.step.dtRatio;
FVector2 P = _impulse * _u;
b1.LinearVelocityInternal -= b1.InvMass * P;
b1.AngularVelocityInternal -= b1.InvI * MathUtils.Cross(r1, P);
b2.LinearVelocityInternal += b2.InvMass * P;
b2.AngularVelocityInternal += b2.InvI * MathUtils.Cross(r2, P);
}
else
{
_impulse = 0.0f;
}
}
public override void solveVelocityConstraints(SolverData data)
{
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Vec2 temp = pool.popVec2();
// Solve linear motor constraint.
if (m_enableMotor && m_limitState != LimitState.EQUAL)
{
temp.set_Renamed(vB).subLocal(vA);
float Cdot = Vec2.dot(m_axis, temp) + m_a2 * wB - m_a1 * wA;
float impulse = m_motorMass * (m_motorSpeed - Cdot);
float oldImpulse = m_motorImpulse;
float maxImpulse = data.step.dt * m_maxMotorForce;
m_motorImpulse = MathUtils.clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
Vec2 P = pool.popVec2();
P.set_Renamed(m_axis).mulLocal(impulse);
float LA = impulse * m_a1;
float LB = impulse * m_a2;
vA.x -= mA * P.x;
vA.y -= mA * P.y;
wA -= iA * LA;
vB.x += mB * P.x;
vB.y += mB * P.y;
wB += iB * LB;
pool.pushVec2(1);
}
Vec2 Cdot1 = pool.popVec2();
temp.set_Renamed(vB).subLocal(vA);
Cdot1.x = Vec2.dot(m_perp, temp) + m_s2 * wB - m_s1 * wA;
Cdot1.y = wB - wA;
// System.out.println(Cdot1);
if (m_enableLimit && m_limitState != LimitState.INACTIVE)
{
// Solve prismatic and limit constraint in block form.
float Cdot2;
temp.set_Renamed(vB).subLocal(vA);
Cdot2 = Vec2.dot(m_axis, temp) + m_a2 * wB - m_a1 * wA;
Vec3 Cdot = pool.popVec3();
Cdot.set_Renamed(Cdot1.x, Cdot1.y, Cdot2);
Cdot.negateLocal();
Vec3 f1 = pool.popVec3();
Vec3 df = pool.popVec3();
f1.set_Renamed(m_impulse);
m_K.solve33ToOut(Cdot.negateLocal(), df);
//Cdot.negateLocal(); not used anymore
m_impulse.addLocal(df);
if (m_limitState == LimitState.AT_LOWER)
{
m_impulse.z = MathUtils.max(m_impulse.z, 0.0f);
}
else if (m_limitState == LimitState.AT_UPPER)
{
m_impulse.z = MathUtils.min(m_impulse.z, 0.0f);
}
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) +
// f1(1:2)
Vec2 b = pool.popVec2();
Vec2 f2r = pool.popVec2();
temp.set_Renamed(m_K.ez.x, m_K.ez.y).mulLocal(m_impulse.z - f1.z);
b.set_Renamed(Cdot1).negateLocal().subLocal(temp);
temp.set_Renamed(f1.x, f1.y);
m_K.solve22ToOut(b, f2r);
f2r.addLocal(temp);
m_impulse.x = f2r.x;
m_impulse.y = f2r.y;
df.set_Renamed(m_impulse).subLocal(f1);
Vec2 P = pool.popVec2();
temp.set_Renamed(m_axis).mulLocal(df.z);
P.set_Renamed(m_perp).mulLocal(df.x).addLocal(temp);
float LA = df.x * m_s1 + df.y + df.z * m_a1;
float LB = df.x * m_s2 + df.y + df.z * m_a2;
vA.x -= mA * P.x;
vA.y -= mA * P.y;
wA -= iA * LA;
vB.x += mB * P.x;
vB.y += mB * P.y;
wB += iB * LB;
pool.pushVec2(3);
pool.pushVec3(3);
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
Vec2 df = pool.popVec2();
m_K.solve22ToOut(Cdot1.negateLocal(), df);
Cdot1.negateLocal();
m_impulse.x += df.x;
m_impulse.y += df.y;
Vec2 P = pool.popVec2();
P.set_Renamed(m_perp).mulLocal(df.x);
float LA = df.x * m_s1 + df.y;
float LB = df.x * m_s2 + df.y;
vA.x -= mA * P.x;
vA.y -= mA * P.y;
wA -= iA * LA;
vB.x += mB * P.x;
vB.y += mB * P.y;
wB += iB * LB;
Vec2 Cdot10 = pool.popVec2();
Cdot10.set_Renamed(Cdot1);
Cdot1.x = Vec2.dot(m_perp, temp.set_Renamed(vB).subLocal(vA)) + m_s2 * wB - m_s1 * wA;
Cdot1.y = wB - wA;
if (MathUtils.abs(Cdot1.x) > 0.01f || MathUtils.abs(Cdot1.y) > 0.01f)
{
// djm note: what's happening here?
Mat33.mul22ToOutUnsafe(m_K, df, temp);
Cdot1.x += 0.0f;
}
pool.pushVec2(3);
}
data.velocities[m_indexA].v.set_Renamed(vA);
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v.set_Renamed(vB);
data.velocities[m_indexB].w = wB;
pool.pushVec2(2);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Vector2 cA = data.Positions[_indexA].C;
float aA = data.Positions[_indexA].A;
Vector2 vA = data.Velocities[_indexA].V;
float wA = data.Velocities[_indexA].W;
Vector2 cB = data.Positions[_indexB].C;
float aB = data.Positions[_indexB].A;
Vector2 vB = data.Velocities[_indexB].V;
float wB = data.Velocities[_indexB].W;
Rot qA = new Rot(aA), qB = new Rot(aB);
// Compute the effective masses.
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
Vector2 d1 = cB + rB - cA - rA;
// Point to line constraint
{
_ay = MathUtils.Mul(qA, _localYAxis);
_sAy = MathUtils.Cross(d1 + rA, _ay);
_sBy = MathUtils.Cross(rB, _ay);
_mass = mA + mB + iA * _sAy * _sAy + iB * _sBy * _sBy;
if (_mass > 0.0f)
{
_mass = 1.0f / _mass;
}
}
// Spring constraint
_springMass = 0.0f;
_bias = 0.0f;
_gamma = 0.0f;
if (Frequency > 0.0f)
{
_ax = MathUtils.Mul(qA, LocalXAxis);
_sAx = MathUtils.Cross(d1 + rA, _ax);
_sBx = MathUtils.Cross(rB, _ax);
float invMass = mA + mB + iA * _sAx * _sAx + iB * _sBx * _sBx;
if (invMass > 0.0f)
{
_springMass = 1.0f / invMass;
float C = Vector2.Dot(d1, _ax);
// Frequency
float omega = 2.0f * Settings.Pi * Frequency;
// Damping coefficient
float d = 2.0f * _springMass * DampingRatio * omega;
// Spring stiffness
float k = _springMass * omega * omega;
// magic formulas
float h = data.Step.dt;
_gamma = h * (d + h * k);
if (_gamma > 0.0f)
{
_gamma = 1.0f / _gamma;
}
_bias = C * h * k * _gamma;
_springMass = invMass + _gamma;
if (_springMass > 0.0f)
{
_springMass = 1.0f / _springMass;
}
}
}
else
{
_springImpulse = 0.0f;
}
// Rotational motor
if (_enableMotor)
{
_motorMass = iA + iB;
if (_motorMass > 0.0f)
{
_motorMass = 1.0f / _motorMass;
}
}
else
{
_motorMass = 0.0f;
_motorImpulse = 0.0f;
}
#pragma warning disable 162
// ReSharper disable once ConditionIsAlwaysTrueOrFalse
if (Settings.EnableWarmstarting)
{
// Account for variable time step.
_impulse *= data.Step.dtRatio;
_springImpulse *= data.Step.dtRatio;
_motorImpulse *= data.Step.dtRatio;
Vector2 P = _impulse * _ay + _springImpulse * _ax;
float LA = _impulse * _sAy + _springImpulse * _sAx + _motorImpulse;
float LB = _impulse * _sBy + _springImpulse * _sBx + _motorImpulse;
vA -= _invMassA * P;
wA -= _invIA * LA;
vB += _invMassB * P;
wB += _invIB * LB;
}
else
{
_impulse = 0.0f;
_springImpulse = 0.0f;
_motorImpulse = 0.0f;
}
#pragma warning restore 162
data.Velocities[_indexA].V = vA;
data.Velocities[_indexA].W = wA;
data.Velocities[_indexB].V = vB;
data.Velocities[_indexB].W = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA.Sweep.LocalCenter;
_localCenterB = BodyB.Sweep.LocalCenter;
_invMassA = BodyA.InvMass;
_invMassB = BodyB.InvMass;
_invIA = BodyA.InvI;
_invIB = BodyB.InvI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Rot qA = new Rot(aA), qB = new Rot(aB);
_rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
_rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
_u = cB + _rB - cA - _rA;
_length = _u.Length();
float C = _length - MaxLength;
if (C > 0.0f)
{
_state = LimitState.AtUpper;
}
else
{
_state = LimitState.Inactive;
}
if (_length > Settings.LinearSlop)
{
_u *= 1.0f / _length;
}
else
{
_u = Vector2.Zero;
_mass = 0.0f;
_impulse = 0.0f;
return;
}
// Compute effective mass.
float crA = MathUtils.Cross(_rA, _u);
float crB = MathUtils.Cross(_rB, _u);
float invMass = _invMassA + _invIA * crA * crA + _invMassB + _invIB * crB * crB;
_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (Settings.EnableWarmstarting)
{
// Scale the impulse to support a variable time step.
_impulse *= data.step.dtRatio;
Vector2 P = _impulse * _u;
vA -= _invMassA * P;
wA -= _invIA * MathUtils.Cross(_rA, P);
vB += _invMassB * P;
wB += _invIB * MathUtils.Cross(_rB, P);
}
else
{
_impulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
if (Frequency > 0.0f)
{
// There is no position correction for soft distance constraints.
return true;
}
Body b1 = BodyA;
Body b2 = BodyB;
Transform xf1, xf2;
b1.GetTransform(out xf1);
b2.GetTransform(out xf2);
Vector2 r1 = MathUtils.Mul(ref xf1.q, LocalAnchorA - b1.LocalCenter);
Vector2 r2 = MathUtils.Mul(ref xf2.q, LocalAnchorB - b2.LocalCenter);
Vector2 d = b2.Sweep.C + r2 - b1.Sweep.C - r1;
float length = d.Length();
if (length < MaxLength && length > MinLength)
{
return true;
}
if (length == 0.0f)
return true;
d /= length;
float C = length - MaxLength;
C = MathUtils.Clamp(C, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
float impulse = -_mass * C;
_u = d;
Vector2 P = impulse * _u;
b1.Sweep.C -= b1.InvMass * P;
b1.Sweep.A -= b1.InvI * MathUtils.Cross(r1, P);
b2.Sweep.C += b2.InvMass * P;
b2.Sweep.A += b2.InvI * MathUtils.Cross(r2, P);
b1.SynchronizeTransform();
b2.SynchronizeTransform();
return Math.Abs(C) < Settings.LinearSlop;
}
public override bool solvePositionConstraints(SolverData data)
{
Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 temp = pool.popVec2();
qA.set(aA);
qB.set(aB);
temp.set(m_localAnchorA);
temp.subLocal(m_localCenterA);
Rot.mulToOut(qA, temp, ref rA);
temp.set(m_localAnchorB);
temp.subLocal(m_localCenterB);
Rot.mulToOut(qB, temp , ref rB);
d.set(cB);
d.subLocal(cA);
d.addLocal(rB);
d.subLocal(rA);
Vec2 ay = pool.popVec2();
Rot.mulToOut(qA, m_localYAxisA, ref ay);
temp.set(d);
temp.addLocal(rA);
float sAy = Vec2.cross(temp, ay);
float sBy = Vec2.cross(rB, ay);
float C = Vec2.dot(d, ay);
float k = m_invMassA + m_invMassB + m_invIA*m_sAy*m_sAy + m_invIB*m_sBy*m_sBy;
float impulse;
if (k != 0.0f)
{
impulse = -C/k;
}
else
{
impulse = 0.0f;
}
Vec2 P = pool.popVec2();
P.x = impulse*ay.x;
P.y = impulse*ay.y;
float LA = impulse*sAy;
float LB = impulse*sBy;
cA.x -= m_invMassA*P.x;
cA.y -= m_invMassA*P.y;
aA -= m_invIA*LA;
cB.x += m_invMassB*P.x;
cB.y += m_invMassB*P.y;
aB += m_invIB*LB;
pool.pushVec2(3);
pool.pushRot(2);
// 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 MathUtils.abs(C) <= Settings.linearSlop;
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Vector2 vC = data.velocities[_indexC].v;
float wC = data.velocities[_indexC].w;
Vector2 vD = data.velocities[_indexD].v;
float wD = data.velocities[_indexD].w;
float Cdot = Vector2.Dot(_JvAC, vA - vC) + Vector2.Dot(_JvBD, vB - vD);
Cdot += (_JwA * wA - _JwC * wC) + (_JwB * wB - _JwD * wD);
float impulse = -_mass * Cdot;
_impulse += impulse;
vA += (_mA * impulse) * _JvAC;
wA += _iA * impulse * _JwA;
vB += (_mB * impulse) * _JvBD;
wB += _iB * impulse * _JwB;
vC -= (_mC * impulse) * _JvAC;
wC -= _iC * impulse * _JwC;
vD -= (_mD * impulse) * _JvBD;
wD -= _iD * impulse * _JwD;
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
data.velocities[_indexC].v = vC;
data.velocities[_indexC].w = wC;
data.velocities[_indexD].v = vD;
data.velocities[_indexD].w = wD;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
_rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
_rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
// Get the pulley axes.
_uA = cA + _rA - WorldAnchorA;
_uB = cB + _rB - WorldAnchorB;
float lengthA = _uA.Length();
float lengthB = _uB.Length();
if (lengthA > 10.0f * Settings.LinearSlop)
{
_uA *= 1.0f / lengthA;
}
else
{
_uA = Vector2.Zero;
}
if (lengthB > 10.0f * Settings.LinearSlop)
{
_uB *= 1.0f / lengthB;
}
else
{
_uB = Vector2.Zero;
}
// Compute effective mass.
float ruA = MathUtils.Cross(ref _rA, ref _uA);
float ruB = MathUtils.Cross(ref _rB, ref _uB);
float mA = _invMassA + _invIA * ruA * ruA;
float mB = _invMassB + _invIB * ruB * ruB;
_mass = mA + Ratio * Ratio * mB;
if (_mass > 0.0f)
{
_mass = 1.0f / _mass;
}
if (data.step.warmStarting)
{
// Scale impulses to support variable time steps.
_impulse *= data.step.dtRatio;
// Warm starting.
Vector2 PA = -(_impulse) * _uA;
Vector2 PB = (-Ratio * _impulse) * _uB;
vA += _invMassA * PA;
wA += _invIA * MathUtils.Cross(ref _rA, ref PA);
vB += _invMassB * PB;
wB += _invIB * MathUtils.Cross(ref _rB, ref PB);
}
else
{
_impulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
// Get the pulley axes.
Vector2 uA = cA + rA - WorldAnchorA;
Vector2 uB = cB + rB - WorldAnchorB;
float lengthA = uA.Length();
float lengthB = uB.Length();
if (lengthA > 10.0f * Settings.LinearSlop)
{
uA *= 1.0f / lengthA;
}
else
{
uA = Vector2.Zero;
}
if (lengthB > 10.0f * Settings.LinearSlop)
{
uB *= 1.0f / lengthB;
}
else
{
uB = Vector2.Zero;
}
// Compute effective mass.
float ruA = MathUtils.Cross(ref rA, ref uA);
float ruB = MathUtils.Cross(ref rB, ref uB);
float mA = _invMassA + _invIA * ruA * ruA;
float mB = _invMassB + _invIB * ruB * ruB;
float mass = mA + Ratio * Ratio * mB;
if (mass > 0.0f)
{
mass = 1.0f / mass;
}
float C = Constant - lengthA - Ratio * lengthB;
float linearError = Math.Abs(C);
float impulse = -mass * C;
Vector2 PA = -impulse * uA;
Vector2 PB = -Ratio * impulse * uB;
cA += _invMassA * PA;
aA += _invIA * MathUtils.Cross(ref rA, ref PA);
cB += _invMassB * PB;
aB += _invIB * MathUtils.Cross(ref rB, ref PB);
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(linearError < Settings.LinearSlop);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
// Compute the effective masses.
Vector2 rA = Complex.Multiply(LocalAnchorA - _localCenterA, ref qA);
Vector2 rB = Complex.Multiply(LocalAnchorB - _localCenterB, ref qB);
Vector2 d1 = cB + rB - cA - rA;
// Point to line constraint
{
_ay = Complex.Multiply(ref _localYAxis, ref qA);
_sAy = MathUtils.Cross(d1 + rA, _ay);
_sBy = MathUtils.Cross(ref rB, ref _ay);
_mass = mA + mB + iA * _sAy * _sAy + iB * _sBy * _sBy;
if (_mass > 0.0f)
{
_mass = 1.0f / _mass;
}
}
// Spring constraint
_springMass = 0.0f;
_bias = 0.0f;
_gamma = 0.0f;
if (Frequency > 0.0f)
{
_ax = Complex.Multiply(ref _localXAxis, ref qA);
_sAx = MathUtils.Cross(d1 + rA, _ax);
_sBx = MathUtils.Cross(ref rB, ref _ax);
float invMass = mA + mB + iA * _sAx * _sAx + iB * _sBx * _sBx;
if (invMass > 0.0f)
{
_springMass = 1.0f / invMass;
float C = Vector2.Dot(d1, _ax);
// Frequency
float omega = 2.0f * MathHelper.Pi * Frequency;
// Damping coefficient
float d = 2.0f * _springMass * DampingRatio * omega;
// Spring stiffness
float k = _springMass * omega * omega;
// magic formulas
float h = data.step.dt;
_gamma = h * (d + h * k);
if (_gamma > 0.0f)
{
_gamma = 1.0f / _gamma;
}
_bias = C * h * k * _gamma;
_springMass = invMass + _gamma;
if (_springMass > 0.0f)
{
_springMass = 1.0f / _springMass;
}
}
}
else
{
_springImpulse = 0.0f;
}
// Rotational motor
if (_enableMotor)
{
_motorMass = iA + iB;
if (_motorMass > 0.0f)
{
_motorMass = 1.0f / _motorMass;
}
}
else
{
_motorMass = 0.0f;
_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
_impulse *= data.step.dtRatio;
_springImpulse *= data.step.dtRatio;
_motorImpulse *= data.step.dtRatio;
Vector2 P = _impulse * _ay + _springImpulse * _ax;
float LA = _impulse * _sAy + _springImpulse * _sAx + _motorImpulse;
float LB = _impulse * _sBy + _springImpulse * _sBx + _motorImpulse;
vA -= _invMassA * P;
wA -= _invIA * LA;
vB += _invMassB * P;
wB += _invIB * LB;
}
else
{
_impulse = 0.0f;
_springImpulse = 0.0f;
_motorImpulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.Positions[_indexA].C;
float aA = data.Positions[_indexA].A;
Vector2 vA = data.Velocities[_indexA].V;
float wA = data.Velocities[_indexA].W;
Vector2 cB = data.Positions[_indexB].C;
float aB = data.Positions[_indexB].A;
Vector2 vB = data.Velocities[_indexB].V;
float wB = data.Velocities[_indexB].W;
Rot qA = new Rot(aA), qB = new Rot(aB);
_rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
_rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
// Get the pulley axes.
_uA = cA + _rA - WorldAnchorA;
_uB = cB + _rB - WorldAnchorB;
float lengthA = _uA.Length();
float lengthB = _uB.Length();
if (lengthA > 10.0f * Settings.LinearSlop)
{
_uA *= 1.0f / lengthA;
}
else
{
_uA = Vector2.Zero;
}
if (lengthB > 10.0f * Settings.LinearSlop)
{
_uB *= 1.0f / lengthB;
}
else
{
_uB = Vector2.Zero;
}
// Compute effective mass.
float ruA = MathUtils.Cross(_rA, _uA);
float ruB = MathUtils.Cross(_rB, _uB);
float mA = _invMassA + _invIA * ruA * ruA;
float mB = _invMassB + _invIB * ruB * ruB;
_mass = mA + Ratio * Ratio * mB;
if (_mass > 0.0f)
{
_mass = 1.0f / _mass;
}
if (Settings.EnableWarmstarting)
{
// Scale impulses to support variable time steps.
_impulse *= data.Step.DeltaTimeRatio;
// Warm starting.
Vector2 PA = -(_impulse) * _uA;
Vector2 PB = (-Ratio * _impulse) * _uB;
vA += _invMassA * PA;
wA += _invIA * MathUtils.Cross(_rA, PA);
vB += _invMassB * PB;
wB += _invIB * MathUtils.Cross(_rB, PB);
}
else
{
_impulse = 0.0f;
}
data.Velocities[_indexA].V = vA;
data.Velocities[_indexA].W = wA;
data.Velocities[_indexB].V = vB;
data.Velocities[_indexB].W = wB;
}
public override bool SolvePositionConstraints(SolverData data)
{
return(true);
}
public override void SolveVelocityConstraints(SolverData data)
{
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
float h = data.Step.Dt;
// Solve angular friction
{
float Cdot = wB - wA;
float impulse = (-AngularMass) * Cdot;
float oldImpulse = m_angularImpulse;
float maxImpulse = h * m_maxTorque;
m_angularImpulse = MathUtils.Clamp(m_angularImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_angularImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve linear friction
{
Vec2 Cdot = Pool.PopVec2();
Vec2 temp = Pool.PopVec2();
Vec2.CrossToOutUnsafe(wA, RA, temp);
Vec2.CrossToOutUnsafe(wB, RB, Cdot);
Cdot.AddLocal(vB).SubLocal(vA).SubLocal(temp);
Vec2 impulse = Pool.PopVec2();
Mat22.MulToOutUnsafe(LinearMass, Cdot, impulse);
impulse.NegateLocal();
Vec2 oldImpulse = Pool.PopVec2();
oldImpulse.Set(m_linearImpulse);
m_linearImpulse.AddLocal(impulse);
float maxImpulse = h * m_maxForce;
if (m_linearImpulse.LengthSquared() > maxImpulse * maxImpulse)
{
m_linearImpulse.Normalize();
m_linearImpulse.MulLocal(maxImpulse);
}
impulse.Set(m_linearImpulse).SubLocal(oldImpulse);
temp.Set(impulse).MulLocal(mA);
vA.SubLocal(temp);
wA -= iA * Vec2.Cross(RA, impulse);
temp.Set(impulse).MulLocal(mB);
vB.AddLocal(temp);
wB += iB * Vec2.Cross(RB, impulse);
}
data.Velocities[IndexA].V.Set(vA);
if (data.Velocities[IndexA].W != wA)
{
Debug.Assert(data.Velocities[IndexA].W != wA);
}
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushVec2(4);
}
/// <seealso cref="Joint.initVelocityConstraints(TimeStep)"></seealso>
public override void InitVelocityConstraints(SolverData data)
{
IndexA = BodyA.IslandIndex;
IndexB = BodyB.IslandIndex;
LocalCenterA.Set(BodyA.Sweep.LocalCenter);
LocalCenterB.Set(BodyB.Sweep.LocalCenter);
InvMassA = BodyA.InvMass;
InvMassB = BodyB.InvMass;
InvIA = BodyA.InvI;
InvIB = BodyB.InvI;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Vec2 temp = Pool.PopVec2();
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
qA.Set(aA);
qB.Set(aB);
// Compute the effective mass matrix.
Rot.MulToOutUnsafe(qA, temp.Set(m_localAnchorA).SubLocal(LocalCenterA), RA);
Rot.MulToOutUnsafe(qB, temp.Set(m_localAnchorB).SubLocal(LocalCenterB), RB);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = InvMassA, mB = InvMassB;
float iA = InvIA, iB = InvIB;
Mat22 K = Pool.PopMat22();
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;
K.InvertToOut(LinearMass);
AngularMass = iA + iB;
if (AngularMass > 0.0f)
{
AngularMass = 1.0f / AngularMass;
}
if (data.Step.WarmStarting)
{
// Scale impulses to support a variable time step.
m_linearImpulse.MulLocal(data.Step.DtRatio);
m_angularImpulse *= data.Step.DtRatio;
Vec2 P = Pool.PopVec2();
P.Set(m_linearImpulse);
temp.Set(P).MulLocal(mA);
vA.SubLocal(temp);
wA -= iA * (Vec2.Cross(RA, P) + m_angularImpulse);
temp.Set(P).MulLocal(mB);
vB.AddLocal(temp);
wB += iB * (Vec2.Cross(RB, P) + m_angularImpulse);
Pool.PushVec2(1);
}
else
{
m_linearImpulse.SetZero();
m_angularImpulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
if (data.Velocities[IndexA].W != wA)
{
Debug.Assert(data.Velocities[IndexA].W != wA);
}
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[IndexB].W = wB;
Pool.PushRot(2);
Pool.PushVec2(1);
Pool.PushMat22(1);
}
public override void initVelocityConstraints(SolverData data)
{
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA.set(m_bodyA.m_sweep.localCenter);
m_localCenterB.set(m_bodyB.m_sweep.localCenter);
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_invI;
// Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
// Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 temp = pool.popVec2();
qA.set(aA);
qB.set(aB);
// Compute the effective masses.
temp.set(m_localAnchorA);
temp.subLocal(m_localCenterA);
Rot.mulToOutUnsafe(qA, temp, ref m_rA);
temp.set(m_localAnchorB);
temp.subLocal(m_localCenterB);
Rot.mulToOutUnsafe(qB, temp, ref m_rB);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
bool fixedRotation = (iA + iB == 0.0f);
m_mass.ex.x = mA + mB + m_rA.y*m_rA.y*iA + m_rB.y*m_rB.y*iB;
m_mass.ey.x = -m_rA.y*m_rA.x*iA - m_rB.y*m_rB.x*iB;
m_mass.ez.x = -m_rA.y*iA - m_rB.y*iB;
m_mass.ex.y = m_mass.ey.x;
m_mass.ey.y = mA + mB + m_rA.x*m_rA.x*iA + m_rB.x*m_rB.x*iB;
m_mass.ez.y = m_rA.x*iA + m_rB.x*iB;
m_mass.ex.z = m_mass.ez.x;
m_mass.ey.z = m_mass.ez.y;
m_mass.ez.z = iA + iB;
m_motorMass = iA + iB;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f/m_motorMass;
}
if (m_enableMotor == false || fixedRotation)
{
m_motorImpulse = 0.0f;
}
if (m_enableLimit && fixedRotation == false)
{
float jointAngle = aB - aA - m_referenceAngle;
if (MathUtils.abs(m_upperAngle - m_lowerAngle) < 2.0f*Settings.angularSlop)
{
m_limitState = LimitState.EQUAL;
}
else if (jointAngle <= m_lowerAngle)
{
if (m_limitState != LimitState.AT_LOWER)
{
m_impulse.z = 0.0f;
}
m_limitState = LimitState.AT_LOWER;
}
else if (jointAngle >= m_upperAngle)
{
if (m_limitState != LimitState.AT_UPPER)
{
m_impulse.z = 0.0f;
}
m_limitState = LimitState.AT_UPPER;
}
else
{
m_limitState = LimitState.INACTIVE;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = LimitState.INACTIVE;
}
if (data.step.warmStarting)
{
Vec2 P = pool.popVec2();
// Scale impulses to support a variable time step.
m_impulse.x *= data.step.dtRatio;
m_impulse.y *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
P.x = m_impulse.x;
P.y = m_impulse.y;
vA.x -= mA*P.x;
vA.y -= mA*P.y;
wA -= iA*(Vec2.cross(m_rA, P) + m_motorImpulse + m_impulse.z);
vB.x += mB*P.x;
vB.y += mB*P.y;
wB += iB*(Vec2.cross(m_rB, P) + m_motorImpulse + m_impulse.z);
pool.pushVec2(1);
}
else
{
m_impulse.setZero();
m_motorImpulse = 0.0f;
}
// data.velocities[m_indexA].v.set(vA);
data.velocities[m_indexA].w = wA;
// data.velocities[m_indexB].v.set(vB);
data.velocities[m_indexB].w = wB;
pool.pushVec2(1);
pool.pushRot(2);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
m_indexA = BodyA.IslandIndex;
m_indexB = BodyB.IslandIndex;
m_localCenterA = BodyA.Sweep.LocalCenter;
m_localCenterB = BodyB.Sweep.LocalCenter;
m_invMassA = BodyA.InvMass;
m_invMassB = BodyB.InvMass;
m_invIA = BodyA.InvI;
m_invIB = BodyB.InvI;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Vector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Vector2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Rot qA = new Rot(aA), qB = new Rot(aB);
// Compute the effective masses.
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_localCenterB);
Vector2 d1 = cB + rB - cA - rA;
// Point to line constraint
{
m_ay = MathUtils.Mul(qA, m_localYAxisA);
m_sAy = MathUtils.Cross(d1 + rA, m_ay);
m_sBy = MathUtils.Cross(rB, m_ay);
m_mass = mA + mB + iA * m_sAy * m_sAy + iB * m_sBy * m_sBy;
if (m_mass > 0.0f)
{
m_mass = 1.0f / m_mass;
}
}
// Spring constraint
m_springMass = 0.0f;
m_bias = 0.0f;
m_gamma = 0.0f;
if (SpringFrequencyHz > 0.0f)
{
m_ax = MathUtils.Mul(qA, m_localXAxisA);
m_sAx = MathUtils.Cross(d1 + rA, m_ax);
m_sBx = MathUtils.Cross(rB, m_ax);
float invMass = mA + mB + iA * m_sAx * m_sAx + iB * m_sBx * m_sBx;
if (invMass > 0.0f)
{
m_springMass = 1.0f / invMass;
float C = Vector2.Dot(d1, m_ax);
// Frequency
float omega = 2.0f * Settings.Pi * SpringFrequencyHz;
// Damping coefficient
float d = 2.0f * m_springMass * SpringDampingRatio * omega;
// Spring stiffness
float k = m_springMass * omega * omega;
// magic formulas
float h = data.step.dt;
m_gamma = h * (d + h * k);
if (m_gamma > 0.0f)
{
m_gamma = 1.0f / m_gamma;
}
m_bias = C * h * k * m_gamma;
m_springMass = invMass + m_gamma;
if (m_springMass > 0.0f)
{
m_springMass = 1.0f / m_springMass;
}
}
}
else
{
m_springImpulse = 0.0f;
}
// Rotational motor
if (m_enableMotor)
{
m_motorMass = iA + iB;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
}
else
{
m_motorMass = 0.0f;
m_motorImpulse = 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Account for variable time step.
m_impulse *= data.step.dtRatio;
m_springImpulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
Vector2 P = m_impulse * m_ay + m_springImpulse * m_ax;
float LA = m_impulse * m_sAy + m_springImpulse * m_sAx + m_motorImpulse;
float LB = m_impulse * m_sBy + m_springImpulse * m_sBx + m_motorImpulse;
vA -= m_invMassA * P;
wA -= m_invIA * LA;
vB += m_invMassB * P;
wB += m_invIB * LB;
}
else
{
m_impulse = 0.0f;
m_springImpulse = 0.0f;
m_motorImpulse = 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 void solveVelocityConstraints(SolverData data)
{
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
bool fixedRotation = (iA + iB == 0.0f);
// Solve motor constraint.
if (m_enableMotor && m_limitState != LimitState.EQUAL && fixedRotation == false)
{
float Cdot = wB - wA - m_motorSpeed;
float impulse = -m_motorMass*Cdot;
float oldImpulse = m_motorImpulse;
float maxImpulse = data.step.dt*m_maxMotorTorque;
m_motorImpulse = MathUtils.clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
wA -= iA*impulse;
wB += iB*impulse;
}
Vec2 temp = pool.popVec2();
// Solve limit constraint.
if (m_enableLimit && m_limitState != LimitState.INACTIVE && fixedRotation == false)
{
Vec2 Cdot1 = pool.popVec2();
Vec3 Cdot = pool.popVec3();
// Solve point-to-point constraint
Vec2.crossToOutUnsafe(wA, m_rA, ref temp);
Vec2.crossToOutUnsafe(wB, m_rB, ref Cdot1);
Cdot1.addLocal(vB);
Cdot1.subLocal(vA);
Cdot1.subLocal(temp);
float Cdot2 = wB - wA;
Cdot.set(Cdot1.x, Cdot1.y, Cdot2);
Vec3 impulse = pool.popVec3();
m_mass.solve33ToOut(Cdot, ref impulse);
impulse.negateLocal();
if (m_limitState == LimitState.EQUAL)
{
m_impulse.addLocal(impulse);
}
else if (m_limitState == LimitState.AT_LOWER)
{
float newImpulse = m_impulse.z + impulse.z;
if (newImpulse < 0.0f)
{
Vec2 rhs = pool.popVec2();
rhs.set(m_mass.ez.x, m_mass.ez.y);
rhs.mulLocal(m_impulse.z);
rhs.subLocal(Cdot1);
m_mass.solve22ToOut(rhs, ref temp);
impulse.x = temp.x;
impulse.y = temp.y;
impulse.z = -m_impulse.z;
m_impulse.x += temp.x;
m_impulse.y += temp.y;
m_impulse.z = 0.0f;
pool.pushVec2(1);
}
else
{
m_impulse.addLocal(impulse);
}
}
else if (m_limitState == LimitState.AT_UPPER)
{
float newImpulse = m_impulse.z + impulse.z;
if (newImpulse > 0.0f)
{
Vec2 rhs = pool.popVec2();
rhs.set(m_mass.ez.x, m_mass.ez.y);
rhs.mulLocal(m_impulse.z);
rhs.subLocal(Cdot1);
m_mass.solve22ToOut(rhs, ref temp);
impulse.x = temp.x;
impulse.y = temp.y;
impulse.z = -m_impulse.z;
m_impulse.x += temp.x;
m_impulse.y += temp.y;
m_impulse.z = 0.0f;
pool.pushVec2(1);
}
else
{
m_impulse.addLocal(impulse);
}
}
Vec2 P = pool.popVec2();
P.set(impulse.x, impulse.y);
vA.x -= mA*P.x;
vA.y -= mA*P.y;
wA -= iA*(Vec2.cross(m_rA, P) + impulse.z);
vB.x += mB*P.x;
vB.y += mB*P.y;
wB += iB*(Vec2.cross(m_rB, P) + impulse.z);
pool.pushVec2(2);
pool.pushVec3(2);
}
else
{
// Solve point-to-point constraint
Vec2 Cdot = pool.popVec2();
Vec2 impulse = pool.popVec2();
Vec2.crossToOutUnsafe(wA, m_rA, ref temp);
Vec2.crossToOutUnsafe(wB, m_rB, ref Cdot);
Cdot.addLocal(vB);
Cdot.subLocal(vA);
Cdot.subLocal(temp);
Cdot.negateLocal();
m_mass.solve22ToOut(Cdot, ref impulse); // just leave negated
m_impulse.x += impulse.x;
m_impulse.y += impulse.y;
vA.x -= mA*impulse.x;
vA.y -= mA*impulse.y;
wA -= iA*Vec2.cross(m_rA, impulse);
vB.x += mB*impulse.x;
vB.y += mB*impulse.y;
wB += iB*Vec2.cross(m_rB, impulse);
pool.pushVec2(2);
}
// data.velocities[m_indexA].v.set(vA);
data.velocities[m_indexA].w = wA;
// data.velocities[m_indexB].v.set(vB);
data.velocities[m_indexB].w = wB;
pool.pushVec2(1);
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Vector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vector2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
// Solve spring constraint
{
float Cdot = Vector2.Dot(m_ax, vB - vA) + m_sBx * wB - m_sAx * wA;
float impulse = -m_springMass * (Cdot + m_bias + m_gamma * m_springImpulse);
m_springImpulse += impulse;
Vector2 P = impulse * m_ax;
float LA = impulse * m_sAx;
float LB = impulse * m_sBx;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
// Solve rotational motor constraint
{
float Cdot = wB - wA - m_motorSpeed;
float impulse = -m_motorMass * Cdot;
float oldImpulse = m_motorImpulse;
float maxImpulse = data.step.dt * m_maxMotorTorque;
m_motorImpulse = MathUtils.Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve point to line constraint
{
float Cdot = Vector2.Dot(m_ay, vB - vA) + m_sBy * wB - m_sAy * wA;
float impulse = -m_mass * Cdot;
m_impulse += impulse;
Vector2 P = impulse * m_ay;
float LA = impulse * m_sAy;
float LB = impulse * m_sBy;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = _bodyA.IslandIndex;
_indexB = _bodyB.IslandIndex;
_indexC = _bodyC.IslandIndex;
_indexD = _bodyD.IslandIndex;
_lcA = _bodyA.Sweep.LocalCenter;
_lcB = _bodyB.Sweep.LocalCenter;
_lcC = _bodyC.Sweep.LocalCenter;
_lcD = _bodyD.Sweep.LocalCenter;
_mA = _bodyA.InvMass;
_mB = _bodyB.InvMass;
_mC = _bodyC.InvMass;
_mD = _bodyD.InvMass;
_iA = _bodyA.InvI;
_iB = _bodyB.InvI;
_iC = _bodyC.InvI;
_iD = _bodyD.InvI;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
float aC = data.positions[_indexC].a;
Vector2 vC = data.velocities[_indexC].v;
float wC = data.velocities[_indexC].w;
float aD = data.positions[_indexD].a;
Vector2 vD = data.velocities[_indexD].v;
float wD = data.velocities[_indexD].w;
Rot qA = new Rot(aA), qB = new Rot(aB), qC = new Rot(aC), qD = new Rot(aD);
_mass = 0.0f;
if (_typeA == JointType.Revolute)
{
_JvAC = Vector2.Zero;
_JwA = 1.0f;
_JwC = 1.0f;
_mass += _iA + _iC;
}
else
{
Vector2 u = MathUtils.Mul(qC, _localAxisC);
Vector2 rC = MathUtils.Mul(qC, _localAnchorC - _lcC);
Vector2 rA = MathUtils.Mul(qA, _localAnchorA - _lcA);
_JvAC = u;
_JwC = MathUtils.Cross(rC, u);
_JwA = MathUtils.Cross(rA, u);
_mass += _mC + _mA + _iC * _JwC * _JwC + _iA * _JwA * _JwA;
}
if (_typeB == JointType.Revolute)
{
_JvBD = Vector2.Zero;
_JwB = _ratio;
_JwD = _ratio;
_mass += _ratio * _ratio * (_iB + _iD);
}
else
{
Vector2 u = MathUtils.Mul(qD, _localAxisD);
Vector2 rD = MathUtils.Mul(qD, _localAnchorD - _lcD);
Vector2 rB = MathUtils.Mul(qB, _localAnchorB - _lcB);
_JvBD = _ratio * u;
_JwD = _ratio * MathUtils.Cross(rD, u);
_JwB = _ratio * MathUtils.Cross(rB, u);
_mass += _ratio * _ratio * (_mD + _mB) + _iD * _JwD * _JwD + _iB * _JwB * _JwB;
}
// Compute effective mass.
_mass = _mass > 0.0f ? 1.0f / _mass : 0.0f;
if (Settings.EnableWarmstarting)
{
vA += (_mA * _impulse) * _JvAC;
wA += _iA * _impulse * _JwA;
vB += (_mB * _impulse) * _JvBD;
wB += _iB * _impulse * _JwB;
vC -= (_mC * _impulse) * _JvAC;
wC -= _iC * _impulse * _JwC;
vD -= (_mD * _impulse) * _JvBD;
wD -= _iD * _impulse * _JwD;
}
else
{
_impulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
data.velocities[_indexC].v = vC;
data.velocities[_indexC].w = wC;
data.velocities[_indexD].v = vD;
data.velocities[_indexD].w = wD;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = _bodyA.IslandIndex;
_indexB = _bodyB.IslandIndex;
_indexC = _bodyC.IslandIndex;
_indexD = _bodyD.IslandIndex;
_lcA = _bodyA._sweep.LocalCenter;
_lcB = _bodyB._sweep.LocalCenter;
_lcC = _bodyC._sweep.LocalCenter;
_lcD = _bodyD._sweep.LocalCenter;
_mA = _bodyA._invMass;
_mB = _bodyB._invMass;
_mC = _bodyC._invMass;
_mD = _bodyD._invMass;
_iA = _bodyA._invI;
_iB = _bodyB._invI;
_iC = _bodyC._invI;
_iD = _bodyD._invI;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
float aC = data.positions[_indexC].a;
Vector2 vC = data.velocities[_indexC].v;
float wC = data.velocities[_indexC].w;
float aD = data.positions[_indexD].a;
Vector2 vD = data.velocities[_indexD].v;
float wD = data.velocities[_indexD].w;
Rot qA = new Rot(aA), qB = new Rot(aB), qC = new Rot(aC), qD = new Rot(aD);
_mass = 0.0f;
if (_typeA == JointType.Revolute)
{
_JvAC = Vector2.Zero;
_JwA = 1.0f;
_JwC = 1.0f;
_mass += _iA + _iC;
}
else
{
Vector2 u = MathUtils.Mul(qC, _localAxisC);
Vector2 rC = MathUtils.Mul(qC, _localAnchorC - _lcC);
Vector2 rA = MathUtils.Mul(qA, _localAnchorA - _lcA);
_JvAC = u;
_JwC = MathUtils.Cross(rC, u);
_JwA = MathUtils.Cross(rA, u);
_mass += _mC + _mA + _iC * _JwC * _JwC + _iA * _JwA * _JwA;
}
if (_typeB == JointType.Revolute)
{
_JvBD = Vector2.Zero;
_JwB = _ratio;
_JwD = _ratio;
_mass += _ratio * _ratio * (_iB + _iD);
}
else
{
Vector2 u = MathUtils.Mul(qD, _localAxisD);
Vector2 rD = MathUtils.Mul(qD, _localAnchorD - _lcD);
Vector2 rB = MathUtils.Mul(qB, _localAnchorB - _lcB);
_JvBD = _ratio * u;
_JwD = _ratio * MathUtils.Cross(rD, u);
_JwB = _ratio * MathUtils.Cross(rB, u);
_mass += _ratio * _ratio * (_mD + _mB) + _iD * _JwD * _JwD + _iB * _JwB * _JwB;
}
// Compute effective mass.
_mass = _mass > 0.0f ? 1.0f / _mass : 0.0f;
if (Settings.EnableWarmstarting)
{
vA += (_mA * _impulse) * _JvAC;
wA += _iA * _impulse * _JwA;
vB += (_mB * _impulse) * _JvBD;
wB += _iB * _impulse * _JwB;
vC -= (_mC * _impulse) * _JvAC;
wC -= _iC * _impulse * _JwC;
vD -= (_mD * _impulse) * _JvBD;
wD -= _iD * _impulse * _JwD;
}
else
{
_impulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
data.velocities[_indexC].v = vC;
data.velocities[_indexC].w = wC;
data.velocities[_indexD].v = vD;
data.velocities[_indexD].w = wD;
}
public override bool solvePositionConstraints(SolverData data)
{
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 rA = pool.popVec2();
Vec2 rB = pool.popVec2();
Vec2 uA = pool.popVec2();
Vec2 uB = pool.popVec2();
Vec2 temp = pool.popVec2();
Vec2 PA = pool.popVec2();
Vec2 PB = pool.popVec2();
Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
qA.set_Renamed(aA);
qB.set_Renamed(aB);
Rot.mulToOutUnsafe(qA, temp.set_Renamed(m_localAnchorA).subLocal(m_localCenterA), rA);
Rot.mulToOutUnsafe(qB, temp.set_Renamed(m_localAnchorB).subLocal(m_localCenterB), rB);
uA.set_Renamed(cA).addLocal(rA).subLocal(m_groundAnchorA);
uB.set_Renamed(cB).addLocal(rB).subLocal(m_groundAnchorB);
float lengthA = uA.length();
float lengthB = uB.length();
if (lengthA > 10.0f * Settings.linearSlop)
{
uA.mulLocal(1.0f / lengthA);
}
else
{
uA.setZero();
}
if (lengthB > 10.0f * Settings.linearSlop)
{
uB.mulLocal(1.0f / lengthB);
}
else
{
uB.setZero();
}
// Compute effective mass.
float ruA = Vec2.cross(rA, uA);
float ruB = Vec2.cross(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 = MathUtils.abs(C);
float impulse = (-mass) * C;
PA.set_Renamed(uA).mulLocal(-impulse);
PB.set_Renamed(uB).mulLocal((-m_ratio) * impulse);
cA.x += m_invMassA * PA.x;
cA.y += m_invMassA * PA.y;
aA += m_invIA * Vec2.cross(rA, PA);
cB.x += m_invMassB * PB.x;
cB.y += m_invMassB * PB.y;
aB += m_invIB * Vec2.cross(rB, PB);
data.positions[m_indexA].c.set_Renamed(cA);
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c.set_Renamed(cB);
data.positions[m_indexB].a = aB;
pool.pushRot(2);
pool.pushVec2(7);
return linearError < Settings.linearSlop;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 cC = data.positions[_indexC].c;
float aC = data.positions[_indexC].a;
Vector2 cD = data.positions[_indexD].c;
float aD = data.positions[_indexD].a;
Rot qA = new Rot(aA), qB = new Rot(aB), qC = new Rot(aC), qD = new Rot(aD);
const float linearError = 0.0f;
float coordinateA, coordinateB;
Vector2 JvAC, JvBD;
float JwA, JwB, JwC, JwD;
float mass = 0.0f;
if (_typeA == JointType.Revolute)
{
JvAC = Vector2.Zero;
JwA = 1.0f;
JwC = 1.0f;
mass += _iA + _iC;
coordinateA = aA - aC - _referenceAngleA;
}
else
{
Vector2 u = MathUtils.Mul(qC, _localAxisC);
Vector2 rC = MathUtils.Mul(qC, _localAnchorC - _lcC);
Vector2 rA = MathUtils.Mul(qA, _localAnchorA - _lcA);
JvAC = u;
JwC = MathUtils.Cross(rC, u);
JwA = MathUtils.Cross(rA, u);
mass += _mC + _mA + _iC * JwC * JwC + _iA * JwA * JwA;
Vector2 pC = _localAnchorC - _lcC;
Vector2 pA = MathUtils.MulT(qC, rA + (cA - cC));
coordinateA = Vector2.Dot(pA - pC, _localAxisC);
}
if (_typeB == JointType.Revolute)
{
JvBD = Vector2.Zero;
JwB = _ratio;
JwD = _ratio;
mass += _ratio * _ratio * (_iB + _iD);
coordinateB = aB - aD - _referenceAngleB;
}
else
{
Vector2 u = MathUtils.Mul(qD, _localAxisD);
Vector2 rD = MathUtils.Mul(qD, _localAnchorD - _lcD);
Vector2 rB = MathUtils.Mul(qB, _localAnchorB - _lcB);
JvBD = _ratio * u;
JwD = _ratio * MathUtils.Cross(rD, u);
JwB = _ratio * MathUtils.Cross(rB, u);
mass += _ratio * _ratio * (_mD + _mB) + _iD * JwD * JwD + _iB * JwB * JwB;
Vector2 pD = _localAnchorD - _lcD;
Vector2 pB = MathUtils.MulT(qD, rB + (cB - cD));
coordinateB = Vector2.Dot(pB - pD, _localAxisD);
}
float C = (coordinateA + _ratio * coordinateB) - _constant;
float impulse = 0.0f;
if (mass > 0.0f)
{
impulse = -C / mass;
}
cA += _mA * impulse * JvAC;
aA += _iA * impulse * JwA;
cB += _mB * impulse * JvBD;
aB += _iB * impulse * JwB;
cC -= _mC * impulse * JvAC;
aC -= _iC * impulse * JwC;
cD -= _mD * impulse * JvBD;
aD -= _iD * impulse * JwD;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
data.positions[_indexC].c = cC;
data.positions[_indexC].a = aC;
data.positions[_indexD].c = cD;
data.positions[_indexD].a = aD;
// TODO_ERIN not implemented
return(linearError < Settings.LinearSlop);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
Vector2 u = cB + rB - cA - rA;
float length = u.Length(); u.Normalize();
float C = length - MaxLength;
C = MathUtils.Clamp(C, 0.0f, Settings.MaxLinearCorrection);
float impulse = -_mass * C;
Vector2 P = impulse * u;
cA -= _invMassA * P;
aA -= _invIA * MathUtils.Cross(rA, P);
cB += _invMassB * P;
aB += _invIB * MathUtils.Cross(rB, P);
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return length - MaxLength < Settings.LinearSlop;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
m_indexA = BodyA.IslandIndex;
m_indexB = BodyB.IslandIndex;
m_localCenterA = BodyA.Sweep.LocalCenter;
m_localCenterB = BodyB.Sweep.LocalCenter;
m_invMassA = BodyA.InvMass;
m_invMassB = BodyB.InvMass;
m_invIA = BodyA.InvI;
m_invIB = BodyB.InvI;
Vector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Vector2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Rot qA = new Rot(aA), qB = new Rot(aB);
m_rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
m_rB = MathUtils.Mul(qB, LocalAnchorB - m_localCenterB);
_u = cB + m_rB - cA - m_rA;
// Handle singularity.
float length = _u.Length();
if (length > Settings.LinearSlop)
{
_u *= 1.0f / length;
}
else
{
_u = Vector2.Zero;
}
float crAu = MathUtils.Cross(m_rA, _u);
float crBu = MathUtils.Cross(m_rB, _u);
float invMass = m_invMassA + m_invIA * crAu * crAu + m_invMassB + m_invIB * crBu * crBu;
// Compute the effective mass matrix.
_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (Frequency > 0.0f)
{
float C = length - Length;
// Frequency
float omega = 2.0f * Settings.Pi * Frequency;
// Damping coefficient
float d = 2.0f * _mass * DampingRatio * omega;
// Spring stiffness
float k = _mass * omega * omega;
// magic formulas
float h = data.step.dt;
_gamma = h * (d + h * k);
_gamma = _gamma != 0.0f ? 1.0f / _gamma : 0.0f;
_bias = C * h * k * _gamma;
invMass += _gamma;
_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
}
else
{
_gamma = 0.0f;
_bias = 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Scale the impulse to support a variable time step.
_impulse *= data.step.dtRatio;
Vector2 P = _impulse * _u;
vA -= m_invMassA * P;
wA -= m_invIA * MathUtils.Cross(m_rA, P);
vB += m_invMassB * P;
wB += m_invIB * MathUtils.Cross(m_rB, P);
}
else
{
_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 void initVelocityConstraints(SolverData data)
{
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA.set_Renamed(m_bodyA.m_sweep.localCenter);
m_localCenterB.set_Renamed(m_bodyB.m_sweep.localCenter);
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_invI;
Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 d = pool.popVec2();
Vec2 temp = pool.popVec2();
Vec2 rA = pool.popVec2();
Vec2 rB = pool.popVec2();
qA.set_Renamed(aA);
qB.set_Renamed(aB);
// Compute the effective masses.
Rot.mulToOutUnsafe(qA, d.set_Renamed(m_localAnchorA).subLocal(m_localCenterA), rA);
Rot.mulToOutUnsafe(qB, d.set_Renamed(m_localAnchorB).subLocal(m_localCenterB), rB);
d.set_Renamed(cB).subLocal(cA).addLocal(rB).subLocal(rA);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute motor Jacobian and effective mass.
{
Rot.mulToOutUnsafe(qA, m_localXAxisA, m_axis);
temp.set_Renamed(d).addLocal(rA);
m_a1 = Vec2.cross(temp, m_axis);
m_a2 = Vec2.cross(rB, m_axis);
m_motorMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
}
// Prismatic constraint.
{
Rot.mulToOutUnsafe(qA, m_localYAxisA, m_perp);
temp.set_Renamed(d).addLocal(rA);
m_s1 = Vec2.cross(temp, m_perp);
m_s2 = Vec2.cross(rB, m_perp);
float k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
float k12 = iA * m_s1 + iB * m_s2;
float k13 = iA * m_s1 * m_a1 + iB * m_s2 * m_a2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
// For bodies with fixed rotation.
k22 = 1.0f;
}
float k23 = iA * m_a1 + iB * m_a2;
float k33 = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
m_K.ex.set_Renamed(k11, k12, k13);
m_K.ey.set_Renamed(k12, k22, k23);
m_K.ez.set_Renamed(k13, k23, k33);
}
// Compute motor and limit terms.
if (m_enableLimit)
{
float jointTranslation = Vec2.dot(m_axis, d);
if (MathUtils.abs(m_upperTranslation - m_lowerTranslation) < 2.0f * Settings.linearSlop)
{
m_limitState = LimitState.EQUAL;
}
else if (jointTranslation <= m_lowerTranslation)
{
if (m_limitState != LimitState.AT_LOWER)
{
m_limitState = LimitState.AT_LOWER;
m_impulse.z = 0.0f;
}
}
else if (jointTranslation >= m_upperTranslation)
{
if (m_limitState != LimitState.AT_UPPER)
{
m_limitState = LimitState.AT_UPPER;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = LimitState.INACTIVE;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = LimitState.INACTIVE;
m_impulse.z = 0.0f;
}
if (m_enableMotor == false)
{
m_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
m_impulse.mulLocal(data.step.dtRatio);
m_motorImpulse *= data.step.dtRatio;
Vec2 P = pool.popVec2();
temp.set_Renamed(m_axis).mulLocal(m_motorImpulse + m_impulse.z);
P.set_Renamed(m_perp).mulLocal(m_impulse.x).addLocal(temp);
float LA = m_impulse.x * m_s1 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a1;
float LB = m_impulse.x * m_s2 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a2;
vA.x -= mA * P.x;
vA.y -= mA * P.y;
wA -= iA * LA;
vB.x += mB * P.x;
vB.y += mB * P.y;
wB += iB * LB;
pool.pushVec2(1);
}
else
{
m_impulse.setZero();
m_motorImpulse = 0.0f;
}
data.velocities[m_indexA].v.set_Renamed(vA);
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v.set_Renamed(vB);
data.velocities[m_indexB].w = wB;
pool.pushRot(2);
pool.pushVec2(4);
}
public override bool SolvePositionConstraints(SolverData data)
{
return ConstrainEdges(data.Step);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
float positionError, angularError;
Mat33 K = new Mat33();
K.ex.X = mA + mB + rA.Y * rA.Y * iA + rB.Y * rB.Y * iB;
K.ey.X = -rA.Y * rA.X * iA - rB.Y * rB.X * iB;
K.ez.X = -rA.Y * iA - rB.Y * iB;
K.ex.Y = K.ey.X;
K.ey.Y = mA + mB + rA.X * rA.X * iA + rB.X * rB.X * iB;
K.ez.Y = rA.X * iA + rB.X * iB;
K.ex.Z = K.ez.X;
K.ey.Z = K.ez.Y;
K.ez.Z = iA + iB;
if (FrequencyHz > 0.0f)
{
Vector2 C1 = cB + rB - cA - rA;
positionError = C1.Length();
angularError = 0.0f;
Vector2 P = -K.Solve22(C1);
cA -= mA * P;
aA -= iA * MathUtils.Cross(rA, P);
cB += mB * P;
aB += iB * MathUtils.Cross(rB, P);
}
else
{
Vector2 C1 = cB + rB - cA - rA;
float C2 = aB - aA - ReferenceAngle;
positionError = C1.Length();
angularError = Math.Abs(C2);
Vector3 C = new Vector3(C1.X, C1.Y, C2);
Vector3 impulse = -K.Solve33(C);
Vector2 P = new Vector2(impulse.X, impulse.Y);
cA -= mA * P;
aA -= iA * (MathUtils.Cross(rA, P) + impulse.Z);
cB += mB * P;
aB += iB * (MathUtils.Cross(rB, P) + impulse.Z);
}
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return positionError <= Settings.LinearSlop && angularError <= Settings.AngularSlop;
}
/// <summary> /// Solves the position constraints. /// </summary> /// <param name="data"></param> /// <returns>returns true if the position errors are within tolerance.</returns> internal abstract bool SolvePositionConstraints(ref SolverData data);
internal override bool SolvePositionConstraints(ref SolverData data)
{
//no position solving for this joint
return(true);
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Vector2 vA = data.Velocities[_indexA].V;
float wA = data.Velocities[_indexA].W;
Vector2 vB = data.Velocities[_indexB].V;
float wB = data.Velocities[_indexB].W;
// Solve spring constraint
{
float Cdot = Vector2.Dot(_ax, vB - vA) + _sBx * wB - _sAx * wA;
float impulse = -_springMass * (Cdot + _bias + _gamma * _springImpulse);
_springImpulse += impulse;
Vector2 P = impulse * _ax;
float LA = impulse * _sAx;
float LB = impulse * _sBx;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
// Solve rotational motor constraint
{
float Cdot = wB - wA - _motorSpeed;
float impulse = -_motorMass * Cdot;
float oldImpulse = _motorImpulse;
float maxImpulse = data.Step.dt * _maxMotorTorque;
_motorImpulse = MathUtils.Clamp(_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = _motorImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve point to line constraint
{
float Cdot = Vector2.Dot(_ay, vB - vA) + _sBy * wB - _sAy * wA;
float impulse = -_mass * Cdot;
_impulse += impulse;
Vector2 P = impulse * _ay;
float LA = impulse * _sAy;
float LB = impulse * _sBy;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
data.Velocities[_indexA].V = vA;
data.Velocities[_indexA].W = wA;
data.Velocities[_indexB].V = vB;
data.Velocities[_indexB].W = wB;
}
public override void SolveVelocityConstraints(SolverData data)
{
float crossMassSum = 0.0f;
float dotMassSum = 0.0f;
Vec2[] d = Pool.GetVec2Array(Bodies.Length);
for (int i = 0; i < Bodies.Length; ++i)
{
int prev = (i == 0) ? Bodies.Length - 1 : i - 1;
int next = (i == Bodies.Length - 1) ? 0 : i + 1;
d[i].Set(Bodies[next].WorldCenter);
d[i].SubLocal(Bodies[prev].WorldCenter);
dotMassSum += (d[i].LengthSquared()) / Bodies[i].Mass;
crossMassSum += Vec2.Cross(Bodies[i].LinearVelocity, d[i]);
}
float lambda = (-2.0f) * crossMassSum / dotMassSum;
// System.out.println(crossMassSum + " " +dotMassSum);
// lambda = MathUtils.clamp(lambda, -Settings.maxLinearCorrection,
// Settings.maxLinearCorrection);
m_impulse += lambda;
// System.out.println(m_impulse);
for (int i = 0; i < Bodies.Length; ++i)
{
Bodies[i].LinearVelocity.X += Bodies[i].InvMass * d[i].Y * .5f * lambda;
Bodies[i].LinearVelocity.Y += Bodies[i].InvMass * (-d[i].X) * .5f * lambda;
}
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Rot qA = new Rot(aA), qB = new Rot(aB);
// Compute the effective masses.
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
Vector2 d = (cB - cA) + rB - rA;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
// Compute motor Jacobian and effective mass.
{
_axis = MathUtils.Mul(qA, LocalXAxis);
_a1 = MathUtils.Cross(d + rA, _axis);
_a2 = MathUtils.Cross(rB, _axis);
_motorMass = mA + mB + iA * _a1 * _a1 + iB * _a2 * _a2;
if (_motorMass > 0.0f)
{
_motorMass = 1.0f / _motorMass;
}
}
// Prismatic constraint.
{
_perp = MathUtils.Mul(qA, _localYAxisA);
_s1 = MathUtils.Cross(d + rA, _perp);
_s2 = MathUtils.Cross(rB, _perp);
float k11 = mA + mB + iA * _s1 * _s1 + iB * _s2 * _s2;
float k12 = iA * _s1 + iB * _s2;
float k13 = iA * _s1 * _a1 + iB * _s2 * _a2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
// For bodies with fixed rotation.
k22 = 1.0f;
}
float k23 = iA * _a1 + iB * _a2;
float k33 = mA + mB + iA * _a1 * _a1 + iB * _a2 * _a2;
_K.ex = new Vector3(k11, k12, k13);
_K.ey = new Vector3(k12, k22, k23);
_K.ez = new Vector3(k13, k23, k33);
}
// Compute motor and limit terms.
if (_enableLimit)
{
float jointTranslation = Vector2.Dot(_axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
{
_limitState = LimitState.Equal;
}
else if (jointTranslation <= _lowerTranslation)
{
if (_limitState != LimitState.AtLower)
{
_limitState = LimitState.AtLower;
_impulse.Z = 0.0f;
}
}
else if (jointTranslation >= _upperTranslation)
{
if (_limitState != LimitState.AtUpper)
{
_limitState = LimitState.AtUpper;
_impulse.Z = 0.0f;
}
}
else
{
_limitState = LimitState.Inactive;
_impulse.Z = 0.0f;
}
}
else
{
_limitState = LimitState.Inactive;
_impulse.Z = 0.0f;
}
if (_enableMotor == false)
{
MotorImpulse = 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Account for variable time step.
_impulse *= data.step.dtRatio;
MotorImpulse *= data.step.dtRatio;
Vector2 P = _impulse.X * _perp + (MotorImpulse + _impulse.Z) * _axis;
float LA = _impulse.X * _s1 + _impulse.Y + (MotorImpulse + _impulse.Z) * _a1;
float LB = _impulse.X * _s2 + _impulse.Y + (MotorImpulse + _impulse.Z) * _a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
_impulse = Vector3.Zero;
MotorImpulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal abstract void SolveVelocityConstraints(ref SolverData data);
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
// Solve linear motor constraint.
if (_enableMotor && _limitState != LimitState.Equal)
{
float Cdot = Vector2.Dot(_axis, vB - vA) + _a2 * wB - _a1 * wA;
float impulse = _motorMass * (_motorSpeed - Cdot);
float oldImpulse = MotorImpulse;
float maxImpulse = data.step.dt * _maxMotorForce;
MotorImpulse = MathUtils.Clamp(MotorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = MotorImpulse - oldImpulse;
Vector2 P = impulse * _axis;
float LA = impulse * _a1;
float LB = impulse * _a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
Vector2 Cdot1 = new Vector2();
Cdot1.X = Vector2.Dot(_perp, vB - vA) + _s2 * wB - _s1 * wA;
Cdot1.Y = wB - wA;
if (_enableLimit && _limitState != LimitState.Inactive)
{
// Solve prismatic and limit constraint in block form.
float Cdot2;
Cdot2 = Vector2.Dot(_axis, vB - vA) + _a2 * wB - _a1 * wA;
Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
Vector3 f1 = _impulse;
Vector3 df = _K.Solve33(-Cdot);
_impulse += df;
if (_limitState == LimitState.AtLower)
{
_impulse.Z = Math.Max(_impulse.Z, 0.0f);
}
else if (_limitState == LimitState.AtUpper)
{
_impulse.Z = Math.Min(_impulse.Z, 0.0f);
}
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
Vector2 b = -Cdot1 - (_impulse.Z - f1.Z) * new Vector2(_K.ez.X, _K.ez.Y);
Vector2 f2r = _K.Solve22(b) + new Vector2(f1.X, f1.Y);
_impulse.X = f2r.X;
_impulse.Y = f2r.Y;
df = _impulse - f1;
Vector2 P = df.X * _perp + df.Z * _axis;
float LA = df.X * _s1 + df.Y + df.Z * _a1;
float LB = df.X * _s2 + df.Y + df.Z * _a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
Vector2 df = _K.Solve22(-Cdot1);
_impulse.X += df.X;
_impulse.Y += df.Y;
Vector2 P = df.X * _perp;
float LA = df.X * _s1 + df.Y;
float LB = df.X * _s2 + df.Y;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
public override bool solvePositionConstraints(SolverData data)
{
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
qA.set(aA);
qB.set(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 != LimitState.INACTIVE && fixedRotation == false)
{
float angle = aB - aA - m_referenceAngle;
float limitImpulse = 0.0f;
if (m_limitState == LimitState.EQUAL)
{
// Prevent large angular corrections
float C =
MathUtils.clamp(angle - m_lowerAngle, -Settings.maxAngularCorrection,
Settings.maxAngularCorrection);
limitImpulse = -m_motorMass*C;
angularError = MathUtils.abs(C);
}
else if (m_limitState == LimitState.AT_LOWER)
{
float C = angle - m_lowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.clamp(C + Settings.angularSlop, -Settings.maxAngularCorrection, 0.0f);
limitImpulse = -m_motorMass*C;
}
else if (m_limitState == LimitState.AT_UPPER)
{
float C = angle - m_upperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.clamp(C - Settings.angularSlop, 0.0f, Settings.maxAngularCorrection);
limitImpulse = -m_motorMass*C;
}
aA -= m_invIA*limitImpulse;
aB += m_invIB*limitImpulse;
}
// Solve point-to-point constraint.
{
qA.set(aA);
qB.set(aB);
Vec2 rA = pool.popVec2();
Vec2 rB = pool.popVec2();
Vec2 C = pool.popVec2();
Vec2 impulse = pool.popVec2();
C.set(m_localAnchorA);
C.subLocal(m_localCenterA);
Rot.mulToOutUnsafe(qA, C, ref rA);
C.set(m_localAnchorB);
C.subLocal(m_localCenterB);
Rot.mulToOutUnsafe(qB, C, ref rB);
C.set(cB);
C.addLocal(rB);
C.subLocal(cA);
C.subLocal(rA);
positionError = C.length();
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Mat22 K = pool.popMat22();
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;
K.solveToOut(C, ref impulse);
impulse.negateLocal();
cA.x -= mA*impulse.x;
cA.y -= mA*impulse.y;
aA -= iA*Vec2.cross(rA, impulse);
cB.x += mB*impulse.x;
cB.y += mB*impulse.y;
aB += iB*Vec2.cross(rB, impulse);
pool.pushVec2(4);
pool.pushMat22(1);
}
// data.positions[m_indexA].c.set(cA);
data.positions[m_indexA].a = aA;
// data.positions[m_indexB].c.set(cB);
data.positions[m_indexB].a = aB;
pool.pushRot(2);
return positionError <= Settings.linearSlop && angularError <= Settings.angularSlop;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
// Compute fresh Jacobians
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
Vector2 d = cB + rB - cA - rA;
Vector2 axis = MathUtils.Mul(qA, LocalXAxis);
float a1 = MathUtils.Cross(d + rA, axis);
float a2 = MathUtils.Cross(rB, axis);
Vector2 perp = MathUtils.Mul(qA, _localYAxisA);
float s1 = MathUtils.Cross(d + rA, perp);
float s2 = MathUtils.Cross(rB, perp);
Vector3 impulse;
Vector2 C1 = new Vector2();
C1.X = Vector2.Dot(perp, d);
C1.Y = aB - aA - ReferenceAngle;
float linearError = Math.Abs(C1.X);
float angularError = Math.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (_enableLimit)
{
float translation = Vector2.Dot(axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
{
// Prevent large angular corrections
C2 = MathUtils.Clamp(translation, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
linearError = Math.Max(linearError, Math.Abs(translation));
active = true;
}
else if (translation <= _lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - _lowerTranslation + Settings.LinearSlop, -Settings.MaxLinearCorrection, 0.0f);
linearError = Math.Max(linearError, _lowerTranslation - translation);
active = true;
}
else if (translation >= _upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - _upperTranslation - Settings.LinearSlop, 0.0f, Settings.MaxLinearCorrection);
linearError = Math.Max(linearError, translation - _upperTranslation);
active = true;
}
}
if (active)
{
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float k12 = iA * s1 + iB * s2;
float k13 = iA * s1 * a1 + iB * s2 * a2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
// For fixed rotation
k22 = 1.0f;
}
float k23 = iA * a1 + iB * a2;
float k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
Mat33 K = new Mat33();
K.ex = new Vector3(k11, k12, k13);
K.ey = new Vector3(k12, k22, k23);
K.ez = new Vector3(k13, k23, k33);
Vector3 C = new Vector3();
C.X = C1.X;
C.Y = C1.Y;
C.Z = C2;
impulse = K.Solve33(-C);
}
else
{
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float k12 = iA * s1 + iB * s2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
k22 = 1.0f;
}
Mat22 K = new Mat22();
K.ex = new Vector2(k11, k12);
K.ey = new Vector2(k12, k22);
Vector2 impulse1 = K.Solve(-C1);
impulse = new Vector3();
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
Vector2 P = impulse.X * perp + impulse.Z * axis;
float LA = impulse.X * s1 + impulse.Y + impulse.Z * a1;
float LB = impulse.X * s2 + impulse.Y + impulse.Z * a2;
cA -= mA * P;
aA -= iA * LA;
cB += mB * P;
aB += iB * LB;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(linearError <= Settings.LinearSlop && angularError <= Settings.AngularSlop);
}
public override void initVelocityConstraints(SolverData data)
{
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA.set(m_bodyA.m_sweep.localCenter);
m_localCenterB.set(m_bodyB.m_sweep.localCenter);
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_invI;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 temp = pool.popVec2();
qA.set(aA);
qB.set(aB);
// Compute the effective masses.
temp.set(m_localAnchorA);
temp.subLocal(m_localCenterA);
Rot.mulToOutUnsafe(qA, temp , ref rA);
temp.set(m_localAnchorB);
temp.subLocal(m_localCenterB);
Rot.mulToOutUnsafe(qB, temp, ref rB);
d.set(cB);
d.addLocal(rB);
d.subLocal(cA);
d.subLocal(rA);
// Point to line constraint
{
Rot.mulToOut(qA, m_localYAxisA, ref m_ay);
temp.set(d);
temp.addLocal(rA);
m_sAy = Vec2.cross(temp, m_ay);
m_sBy = Vec2.cross(rB, m_ay);
m_mass = mA + mB + iA*m_sAy*m_sAy + iB*m_sBy*m_sBy;
if (m_mass > 0.0f)
{
m_mass = 1.0f/m_mass;
}
}
// Spring constraint
m_springMass = 0.0f;
m_bias = 0.0f;
m_gamma = 0.0f;
if (m_frequencyHz > 0.0f)
{
Rot.mulToOut(qA, m_localXAxisA, ref m_ax);
temp.set(d);
temp.addLocal(rA);
m_sAx = Vec2.cross(temp, m_ax);
m_sBx = Vec2.cross(rB, m_ax);
float invMass = mA + mB + iA*m_sAx*m_sAx + iB*m_sBx*m_sBx;
if (invMass > 0.0f)
{
m_springMass = 1.0f/invMass;
float C = Vec2.dot(d, m_ax);
// Frequency
float omega = 2.0f*MathUtils.PI*m_frequencyHz;
// Damping coefficient
float da = 2.0f*m_springMass*m_dampingRatio*omega;
// Spring stiffness
float k = m_springMass*omega*omega;
// magic formulas
float h = data.step.dt;
m_gamma = h*(da + h*k);
if (m_gamma > 0.0f)
{
m_gamma = 1.0f/m_gamma;
}
m_bias = C*h*k*m_gamma;
m_springMass = invMass + m_gamma;
if (m_springMass > 0.0f)
{
m_springMass = 1.0f/m_springMass;
}
}
}
else
{
m_springImpulse = 0.0f;
}
// Rotational motor
if (m_enableMotor)
{
m_motorMass = iA + iB;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f/m_motorMass;
}
}
else
{
m_motorMass = 0.0f;
m_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
Vec2 P = pool.popVec2();
// Account for variable time step.
m_impulse *= data.step.dtRatio;
m_springImpulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
P.x = m_impulse*m_ay.x + m_springImpulse*m_ax.x;
P.y = m_impulse*m_ay.y + m_springImpulse*m_ax.y;
float LA = m_impulse*m_sAy + m_springImpulse*m_sAx + m_motorImpulse;
float LB = m_impulse*m_sBy + m_springImpulse*m_sBx + m_motorImpulse;
vA.x -= m_invMassA*P.x;
vA.y -= m_invMassA*P.y;
wA -= m_invIA*LA;
vB.x += m_invMassB*P.x;
vB.y += m_invMassB*P.y;
wB += m_invIB*LB;
pool.pushVec2(1);
}
else
{
m_impulse = 0.0f;
m_springImpulse = 0.0f;
m_motorImpulse = 0.0f;
}
pool.pushRot(2);
pool.pushVec2(1);
// data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
// data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Complex qA = Complex.FromAngle(aA);
Complex qB = Complex.FromAngle(aB);
// Compute the effective mass matrix.
_rA = -Complex.Multiply(ref _localCenterA, ref qA);
_rB = -Complex.Multiply(ref _localCenterB, ref qB);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Mat22 K = new Mat22();
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;
_linearMass = K.Inverse;
_angularMass = iA + iB;
if (_angularMass > 0.0f)
{
_angularMass = 1.0f / _angularMass;
}
_linearError = cB + _rB - cA - _rA - Complex.Multiply(ref _linearOffset, ref qA);
_angularError = aB - aA - _angularOffset;
if (data.step.warmStarting)
{
// Scale impulses to support a variable time step.
_linearImpulse *= data.step.dtRatio;
_angularImpulse *= data.step.dtRatio;
Vector2 P = new Vector2(_linearImpulse.X, _linearImpulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(ref _rA, ref P) + _angularImpulse);
vB += mB * P;
wB += iB * (MathUtils.Cross(ref _rB, ref P) + _angularImpulse);
}
else
{
_linearImpulse = Vector2.Zero;
_angularImpulse = 0.0f;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
public override void solveVelocityConstraints(SolverData data)
{
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Vec2 temp = pool.popVec2();
Vec2 P = pool.popVec2();
// Solve spring constraint
{
temp.set(vB);
temp.subLocal(vA);
float Cdot = Vec2.dot(m_ax, temp) + m_sBx*wB - m_sAx*wA;
float impulse = -m_springMass*(Cdot + m_bias + m_gamma*m_springImpulse);
m_springImpulse += impulse;
P.x = impulse*m_ax.x;
P.y = impulse*m_ax.y;
float LA = impulse*m_sAx;
float LB = impulse*m_sBx;
vA.x -= mA*P.x;
vA.y -= mA*P.y;
wA -= iA*LA;
vB.x += mB*P.x;
vB.y += mB*P.y;
wB += iB*LB;
}
// Solve rotational motor constraint
{
float Cdot = wB - wA - m_motorSpeed;
float impulse = -m_motorMass*Cdot;
float oldImpulse = m_motorImpulse;
float maxImpulse = data.step.dt*m_maxMotorTorque;
m_motorImpulse = MathUtils.clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
wA -= iA*impulse;
wB += iB*impulse;
}
// Solve point to line constraint
{
temp.set(vB);
temp.subLocal(vA);
float Cdot = Vec2.dot(m_ay, temp) + m_sBy*wB - m_sAy*wA;
float impulse = -m_mass*Cdot;
m_impulse += impulse;
P.x = impulse*m_ay.x;
P.y = impulse*m_ay.y;
float LA = impulse*m_sAy;
float LB = impulse*m_sBy;
vA.x -= mA*P.x;
vA.y -= mA*P.y;
wA -= iA*LA;
vB.x += mB*P.x;
vB.y += mB*P.y;
wB += iB*LB;
}
pool.pushVec2(2);
// data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
// data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
return(true);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Vector2 cC = data.positions[_indexC].c;
float aC = data.positions[_indexC].a;
Vector2 cD = data.positions[_indexD].c;
float aD = data.positions[_indexD].a;
Rot qA = new Rot(aA), qB = new Rot(aB), qC = new Rot(aC), qD = new Rot(aD);
const float linearError = 0.0f;
float coordinateA, coordinateB;
Vector2 JvAC, JvBD;
float JwA, JwB, JwC, JwD;
float mass = 0.0f;
if (_typeA == JointType.Revolute)
{
JvAC = Vector2.Zero;
JwA = 1.0f;
JwC = 1.0f;
mass += _iA + _iC;
coordinateA = aA - aC - _referenceAngleA;
}
else
{
Vector2 u = MathUtils.Mul(qC, _localAxisC);
Vector2 rC = MathUtils.Mul(qC, _localAnchorC - _lcC);
Vector2 rA = MathUtils.Mul(qA, _localAnchorA - _lcA);
JvAC = u;
JwC = MathUtils.Cross(rC, u);
JwA = MathUtils.Cross(rA, u);
mass += _mC + _mA + _iC * JwC * JwC + _iA * JwA * JwA;
Vector2 pC = _localAnchorC - _lcC;
Vector2 pA = MathUtils.MulT(qC, rA + (cA - cC));
coordinateA = Vector2.Dot(pA - pC, _localAxisC);
}
if (_typeB == JointType.Revolute)
{
JvBD = Vector2.Zero;
JwB = _ratio;
JwD = _ratio;
mass += _ratio * _ratio * (_iB + _iD);
coordinateB = aB - aD - _referenceAngleB;
}
else
{
Vector2 u = MathUtils.Mul(qD, _localAxisD);
Vector2 rD = MathUtils.Mul(qD, _localAnchorD - _lcD);
Vector2 rB = MathUtils.Mul(qB, _localAnchorB - _lcB);
JvBD = _ratio * u;
JwD = _ratio * MathUtils.Cross(rD, u);
JwB = _ratio * MathUtils.Cross(rB, u);
mass += _ratio * _ratio * (_mD + _mB) + _iD * JwD * JwD + _iB * JwB * JwB;
Vector2 pD = _localAnchorD - _lcD;
Vector2 pB = MathUtils.MulT(qD, rB + (cB - cD));
coordinateB = Vector2.Dot(pB - pD, _localAxisD);
}
float C = (coordinateA + _ratio * coordinateB) - _constant;
float impulse = 0.0f;
if (mass > 0.0f)
{
impulse = -C / mass;
}
cA += _mA * impulse * JvAC;
aA += _iA * impulse * JwA;
cB += _mB * impulse * JvBD;
aB += _iB * impulse * JwB;
cC -= _mC * impulse * JvAC;
aC -= _iC * impulse * JwC;
cD -= _mD * impulse * JvBD;
aD -= _iD * impulse * JwD;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
data.positions[_indexC].c = cC;
data.positions[_indexC].a = aC;
data.positions[_indexD].c = cD;
data.positions[_indexD].a = aD;
// TODO_ERIN not implemented
return linearError < Settings.LinearSlop;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
float aA = data.Positions[_indexA].A;
Vector2 vA = data.Velocities[_indexA].V;
float wA = data.Velocities[_indexA].W;
float aB = data.Positions[_indexB].A;
Vector2 vB = data.Velocities[_indexB].V;
float wB = data.Velocities[_indexB].W;
Rot qA = new Rot(aA), qB = new Rot(aB);
_rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
_rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
bool fixedRotation = (iA + iB == 0.0f);
_mass.ex.X = mA + mB + _rA.Y * _rA.Y * iA + _rB.Y * _rB.Y * iB;
_mass.ey.X = -_rA.Y * _rA.X * iA - _rB.Y * _rB.X * iB;
_mass.ez.X = -_rA.Y * iA - _rB.Y * iB;
_mass.ex.Y = _mass.ey.X;
_mass.ey.Y = mA + mB + _rA.X * _rA.X * iA + _rB.X * _rB.X * iB;
_mass.ez.Y = _rA.X * iA + _rB.X * iB;
_mass.ex.Z = _mass.ez.X;
_mass.ey.Z = _mass.ez.Y;
_mass.ez.Z = iA + iB;
_motorMass = iA + iB;
if (_motorMass > 0.0f)
{
_motorMass = 1.0f / _motorMass;
}
if (_enableMotor == false || fixedRotation)
{
_motorImpulse = 0.0f;
}
if (_enableLimit && fixedRotation == false)
{
float jointAngle = aB - aA - ReferenceAngle;
if (Math.Abs(_upperAngle - _lowerAngle) < 2.0f * Settings.AngularSlop)
{
_limitState = LimitState.Equal;
}
else if (jointAngle <= _lowerAngle)
{
if (_limitState != LimitState.AtLower)
{
_impulse.Z = 0.0f;
}
_limitState = LimitState.AtLower;
}
else if (jointAngle >= _upperAngle)
{
if (_limitState != LimitState.AtUpper)
{
_impulse.Z = 0.0f;
}
_limitState = LimitState.AtUpper;
}
else
{
_limitState = LimitState.Inactive;
_impulse.Z = 0.0f;
}
}
else
{
_limitState = LimitState.Inactive;
}
if (Settings.EnableWarmstarting)
{
// Scale impulses to support a variable time step.
_impulse *= data.Step.dtRatio;
_motorImpulse *= data.Step.dtRatio;
Vector2 P = new Vector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(_rA, P) + MotorImpulse + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(_rB, P) + MotorImpulse + _impulse.Z);
}
else
{
_impulse = Vector3.Zero;
_motorImpulse = 0.0f;
}
data.Velocities[_indexA].V = vA;
data.Velocities[_indexA].W = wA;
data.Velocities[_indexB].V = vB;
data.Velocities[_indexB].W = wB;
}
public override void initVelocityConstraints(SolverData data)
{
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_localCenterA.set_Renamed(m_bodyA.m_sweep.localCenter);
m_localCenterB.set_Renamed(m_bodyB.m_sweep.localCenter);
m_invMassA = m_bodyA.m_invMass;
m_invMassB = m_bodyB.m_invMass;
m_invIA = m_bodyA.m_invI;
m_invIB = m_bodyB.m_invI;
Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 temp = pool.popVec2();
qA.set_Renamed(aA);
qB.set_Renamed(aB);
// Compute the effective masses.
Rot.mulToOutUnsafe(qA, temp.set_Renamed(m_localAnchorA).subLocal(m_localCenterA), m_rA);
Rot.mulToOutUnsafe(qB, temp.set_Renamed(m_localAnchorB).subLocal(m_localCenterB), m_rB);
m_uA.set_Renamed(cA).addLocal(m_rA).subLocal(m_groundAnchorA);
m_uB.set_Renamed(cB).addLocal(m_rB).subLocal(m_groundAnchorB);
float lengthA = m_uA.length();
float lengthB = m_uB.length();
if (lengthA > 10f * Settings.linearSlop)
{
m_uA.mulLocal(1.0f / lengthA);
}
else
{
m_uA.setZero();
}
if (lengthB > 10f * Settings.linearSlop)
{
m_uB.mulLocal(1.0f / lengthB);
}
else
{
m_uB.setZero();
}
// Compute effective mass.
float ruA = Vec2.cross(m_rA, m_uA);
float ruB = Vec2.cross(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.
Vec2 PA = pool.popVec2();
Vec2 PB = pool.popVec2();
PA.set_Renamed(m_uA).mulLocal(-m_impulse);
PB.set_Renamed(m_uB).mulLocal((-m_ratio) * m_impulse);
vA.x += m_invMassA * PA.x;
vA.y += m_invMassA * PA.y;
wA += m_invIA * Vec2.cross(m_rA, PA);
vB.x += m_invMassB * PB.x;
vB.y += m_invMassB * PB.y;
wB += m_invIB * Vec2.cross(m_rB, PB);
pool.pushVec2(2);
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v.set_Renamed(vA);
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v.set_Renamed(vB);
data.velocities[m_indexB].w = wB;
pool.pushVec2(1);
pool.pushRot(2);
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.Velocities[_indexA].V;
float wA = data.Velocities[_indexA].W;
Vector2 vB = data.Velocities[_indexB].V;
float wB = data.Velocities[_indexB].W;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
bool fixedRotation = (iA + iB == 0.0f);
// Solve motor constraint.
if (_enableMotor && _limitState != LimitState.Equal && fixedRotation == false)
{
float Cdot = wB - wA - _motorSpeed;
float impulse = _motorMass * (-Cdot);
float oldImpulse = _motorImpulse;
float maxImpulse = data.Step.dt * _maxMotorTorque;
_motorImpulse = MathUtils.Clamp(_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = _motorImpulse - oldImpulse;
wA -= iA * impulse;
wB += iB * impulse;
}
// Solve limit constraint.
if (_enableLimit && _limitState != LimitState.Inactive && fixedRotation == false)
{
Vector2 Cdot1 = vB + MathUtils.Cross(wB, _rB) - vA - MathUtils.Cross(wA, _rA);
float Cdot2 = wB - wA;
Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
Vector3 impulse = -_mass.Solve33(Cdot);
if (_limitState == LimitState.Equal)
{
_impulse += impulse;
}
else if (_limitState == LimitState.AtLower)
{
float newImpulse = _impulse.Z + impulse.Z;
if (newImpulse < 0.0f)
{
Vector2 rhs = -Cdot1 + _impulse.Z * new Vector2(_mass.ez.X, _mass.ez.Y);
Vector2 reduced = _mass.Solve22(rhs);
impulse.X = reduced.X;
impulse.Y = reduced.Y;
impulse.Z = -_impulse.Z;
_impulse.X += reduced.X;
_impulse.Y += reduced.Y;
_impulse.Z = 0.0f;
}
else
{
_impulse += impulse;
}
}
else if (_limitState == LimitState.AtUpper)
{
float newImpulse = _impulse.Z + impulse.Z;
if (newImpulse > 0.0f)
{
Vector2 rhs = -Cdot1 + _impulse.Z * new Vector2(_mass.ez.X, _mass.ez.Y);
Vector2 reduced = _mass.Solve22(rhs);
impulse.X = reduced.X;
impulse.Y = reduced.Y;
impulse.Z = -_impulse.Z;
_impulse.X += reduced.X;
_impulse.Y += reduced.Y;
_impulse.Z = 0.0f;
}
else
{
_impulse += impulse;
}
}
Vector2 P = new Vector2(impulse.X, impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(_rA, P) + impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(_rB, P) + impulse.Z);
}
else
{
// Solve point-to-point constraint
Vector2 Cdot = vB + MathUtils.Cross(wB, _rB) - vA - MathUtils.Cross(wA, _rA);
Vector2 impulse = _mass.Solve22(-Cdot);
_impulse.X += impulse.X;
_impulse.Y += impulse.Y;
vA -= mA * impulse;
wA -= iA * MathUtils.Cross(_rA, impulse);
vB += mB * impulse;
wB += iB * MathUtils.Cross(_rB, impulse);
}
data.Velocities[_indexA].V = vA;
data.Velocities[_indexA].W = wA;
data.Velocities[_indexB].V = vB;
data.Velocities[_indexB].W = wB;
}
public override void solveVelocityConstraints(SolverData data)
{
Vec2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
Vec2 vB = data.velocities[m_indexB].v;
float wB = data.velocities[m_indexB].w;
Vec2 vpA = pool.popVec2();
Vec2 vpB = pool.popVec2();
Vec2 PA = pool.popVec2();
Vec2 PB = pool.popVec2();
Vec2.crossToOutUnsafe(wA, m_rA, vpA);
vpA.addLocal(vA);
Vec2.crossToOutUnsafe(wB, m_rB, vpB);
vpB.addLocal(vB);
float Cdot = -Vec2.dot(m_uA, vpA) - m_ratio * Vec2.dot(m_uB, vpB);
float impulse = (-m_mass) * Cdot;
m_impulse += impulse;
PA.set_Renamed(m_uA).mulLocal(-impulse);
PB.set_Renamed(m_uB).mulLocal((-m_ratio) * impulse);
vA.x += m_invMassA * PA.x;
vA.y += m_invMassA * PA.y;
wA += m_invIA * Vec2.cross(m_rA, PA);
vB.x += m_invMassB * PB.x;
vB.y += m_invMassB * PB.y;
wB += m_invIB * Vec2.cross(m_rB, PB);
data.velocities[m_indexA].v.set_Renamed(vA);
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v.set_Renamed(vB);
data.velocities[m_indexB].w = wB;
pool.pushVec2(4);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.Positions[_indexA].C;
float aA = data.Positions[_indexA].A;
Vector2 cB = data.Positions[_indexB].C;
float aB = data.Positions[_indexB].A;
Rot qA = new Rot(aA), qB = new Rot(aB);
float angularError = 0.0f;
float positionError;
bool fixedRotation = (_invIA + _invIB == 0.0f);
// Solve angular limit constraint.
if (_enableLimit && _limitState != LimitState.Inactive && fixedRotation == false)
{
float angle = aB - aA - ReferenceAngle;
float limitImpulse = 0.0f;
if (_limitState == LimitState.Equal)
{
// Prevent large angular corrections
float C = MathUtils.Clamp(angle - _lowerAngle, -Settings.MaxAngularCorrection, Settings.MaxAngularCorrection);
limitImpulse = -_motorMass * C;
angularError = Math.Abs(C);
}
else if (_limitState == LimitState.AtLower)
{
float C = angle - _lowerAngle;
angularError = -C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C + Settings.AngularSlop, -Settings.MaxAngularCorrection, 0.0f);
limitImpulse = -_motorMass * C;
}
else if (_limitState == LimitState.AtUpper)
{
float C = angle - _upperAngle;
angularError = C;
// Prevent large angular corrections and allow some slop.
C = MathUtils.Clamp(C - Settings.AngularSlop, 0.0f, Settings.MaxAngularCorrection);
limitImpulse = -_motorMass * C;
}
aA -= _invIA * limitImpulse;
aB += _invIB * limitImpulse;
}
// Solve point-to-point constraint.
{
qA.Set(aA);
qB.Set(aB);
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
Vector2 C = cB + rB - cA - rA;
positionError = C.Length();
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Mat22 K = new Mat22();
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;
Vector2 impulse = -K.Solve(C);
cA -= mA * impulse;
aA -= iA * MathUtils.Cross(rA, impulse);
cB += mB * impulse;
aB += iB * MathUtils.Cross(rB, impulse);
}
data.Positions[_indexA].C = cA;
data.Positions[_indexA].A = aA;
data.Positions[_indexB].C = cB;
data.Positions[_indexB].A = aB;
return(positionError <= Settings.LinearSlop && angularError <= Settings.AngularSlop);
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
// Cdot = dot(u, v + cross(w, r))
Vector2 vpA = vA + MathUtils.Cross(wA, _rA);
Vector2 vpB = vB + MathUtils.Cross(wB, _rB);
float C = _length - MaxLength;
float Cdot = Vector2.Dot(_u, vpB - vpA);
// Predictive constraint.
if (C < 0.0f)
{
Cdot += data.step.inv_dt * C;
}
float impulse = -_mass * Cdot;
float oldImpulse = _impulse;
_impulse = Math.Min(0.0f, _impulse + impulse);
impulse = _impulse - oldImpulse;
Vector2 P = impulse * _u;
vA -= _invMassA * P;
wA -= _invIA * MathUtils.Cross(_rA, P);
vB += _invMassB * P;
wB += _invIB * MathUtils.Cross(_rB, P);
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal abstract void SolveVelocityConstraints(ref SolverData data);
internal override void InitVelocityConstraints(ref SolverData data)
{
Body b1 = BodyA;
Body b2 = BodyB;
Transform xf1, xf2;
b1.GetTransform(out xf1);
b2.GetTransform(out xf2);
// Compute the effective mass matrix.
Vector2 r1 = MathUtils.Mul(ref xf1.q, LocalAnchorA - b1.LocalCenter);
Vector2 r2 = MathUtils.Mul(ref xf2.q, LocalAnchorB - b2.LocalCenter);
_u = b2.Sweep.C + r2 - b1.Sweep.C - r1;
// Handle singularity.
float length = _u.Length();
if (length < MaxLength && length > MinLength)
{
return;
}
if (length > Settings.LinearSlop)
{
_u *= 1.0f / length;
}
else
{
_u = Vector2.Zero;
}
float cr1u = MathUtils.Cross(r1, _u);
float cr2u = MathUtils.Cross(r2, _u);
float invMass = b1.InvMass + b1.InvI * cr1u * cr1u + b2.InvMass + b2.InvI * cr2u * cr2u;
Debug.Assert(invMass > Settings.Epsilon);
_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
if (Frequency > 0.0f)
{
float C = length - MaxLength;
// Frequency
float omega = 2.0f * Settings.Pi * Frequency;
// Damping coefficient
float d = 2.0f * _mass * DampingRatio * omega;
// Spring stiffness
float k = _mass * omega * omega;
// magic formulas
_gamma = data.step.dt * (d + data.step.dt * k);
_gamma = _gamma != 0.0f ? 1.0f / _gamma : 0.0f;
_bias = C * data.step.dt * k * _gamma;
_mass = invMass + _gamma;
_mass = _mass != 0.0f ? 1.0f / _mass : 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Scale the impulse to support a variable time step.
_impulse *= data.step.dtRatio;
Vector2 P = _impulse * _u;
b1.LinearVelocityInternal -= b1.InvMass * P;
b1.AngularVelocityInternal -= b1.InvI * MathUtils.Cross(r1, P);
b2.LinearVelocityInternal += b2.InvMass * P;
b2.AngularVelocityInternal += b2.InvI * MathUtils.Cross(r2, P);
}
else
{
_impulse = 0.0f;
}
}
/// <summary> /// Solves the position constraints. /// </summary> /// <param name="data"></param> /// <returns>returns true if the position errors are within tolerance.</returns> internal abstract bool SolvePositionConstraints(ref SolverData data);
internal override void SolveVelocityConstraints(ref SolverData data)
{
Body b1 = BodyA;
Body b2 = BodyB;
Transform xf1, xf2;
b1.GetTransform(out xf1);
b2.GetTransform(out xf2);
Vector2 r1 = MathUtils.Mul(ref xf1.q, LocalAnchorA - b1.LocalCenter);
Vector2 r2 = MathUtils.Mul(ref xf2.q, LocalAnchorB - b2.LocalCenter);
Vector2 d = b2.Sweep.C + r2 - b1.Sweep.C - r1;
float length = d.Length();
if (length < MaxLength && length > MinLength)
{
return;
}
// Cdot = dot(u, v + cross(w, r))
Vector2 v1 = b1.LinearVelocityInternal + MathUtils.Cross(b1.AngularVelocityInternal, r1);
Vector2 v2 = b2.LinearVelocityInternal + MathUtils.Cross(b2.AngularVelocityInternal, r2);
float Cdot = Vector2.Dot(_u, v2 - v1);
float impulse = -_mass * (Cdot + _bias + _gamma * _impulse);
_impulse += impulse;
Vector2 P = impulse * _u;
b1.LinearVelocityInternal -= b1.InvMass * P;
b1.AngularVelocityInternal -= b1.InvI * MathUtils.Cross(r1, P);
b2.LinearVelocityInternal += b2.InvMass * P;
b2.AngularVelocityInternal += b2.InvI * MathUtils.Cross(r2, P);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = KinematicBodyB ? 0.0f : BodyB._invMass;
_invIA = BodyA._invI;
_invIB = KinematicBodyB ? 0.0f : BodyB._invI;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Rot qA = new Rot(aA), qB = new Rot(aB);
_rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
_rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Mat33 K = new Mat33();
K.ex.X = mA + mB + _rA.Y * _rA.Y * iA + _rB.Y * _rB.Y * iB;
K.ey.X = -_rA.Y * _rA.X * iA - _rB.Y * _rB.X * iB;
K.ez.X = -_rA.Y * iA - _rB.Y * iB;
K.ex.Y = K.ey.X;
K.ey.Y = mA + mB + _rA.X * _rA.X * iA + _rB.X * _rB.X * iB;
K.ez.Y = _rA.X * iA + _rB.X * iB;
K.ex.Z = K.ez.X;
K.ey.Z = K.ez.Y;
K.ez.Z = iA + iB;
if (FrequencyHz > 0.0f)
{
K.GetInverse22(ref _mass);
float invM = iA + iB;
float m = invM > 0.0f ? 1.0f / invM : 0.0f;
float C = aB - aA - ReferenceAngle;
// Frequency
float omega = 2.0f * Settings.Pi * FrequencyHz;
// Damping coefficient
float d = 2.0f * m * DampingRatio * omega;
// Spring stiffness
float k = m * omega * omega;
// magic formulas
float h = data.step.dt;
_gamma = h * (d + h * k);
_gamma = _gamma != 0.0f ? 1.0f / _gamma : 0.0f;
_bias = C * h * k * _gamma;
invM += _gamma;
_mass.ez.Z = invM != 0.0f ? 1.0f / invM : 0.0f;
}
else
{
K.GetSymInverse33(ref _mass);
_gamma = 0.0f;
_bias = 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Scale impulses to support a variable time step.
_impulse *= data.step.dtRatio;
Vector2 P = new Vector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(_rA, P) + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(_rB, P) + _impulse.Z);
}
else
{
_impulse = Vector3.Zero;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
public override bool solvePositionConstraints(SolverData data)
{
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 rA = pool.popVec2();
Vec2 rB = pool.popVec2();
Vec2 d = pool.popVec2();
Vec2 axis = pool.popVec2();
Vec2 perp = pool.popVec2();
Vec2 temp = pool.popVec2();
Vec2 C1 = pool.popVec2();
Vec3 impulse = pool.popVec3();
Vec2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
Vec2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
qA.set_Renamed(aA);
qB.set_Renamed(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
Rot.mulToOutUnsafe(qA, temp.set_Renamed(m_localAnchorA).subLocal(m_localCenterA), rA);
Rot.mulToOutUnsafe(qB, temp.set_Renamed(m_localAnchorB).subLocal(m_localCenterB), rB);
d.set_Renamed(cB).addLocal(rB).subLocal(cA).subLocal(rA);
Rot.mulToOutUnsafe(qA, m_localXAxisA, axis);
float a1 = Vec2.cross(temp.set_Renamed(d).addLocal(rA), axis);
float a2 = Vec2.cross(rB, axis);
Rot.mulToOutUnsafe(qA, m_localYAxisA, perp);
float s1 = Vec2.cross(temp.set_Renamed(d).addLocal(rA), perp);
float s2 = Vec2.cross(rB, perp);
C1.x = Vec2.dot(perp, d);
C1.y = aB - aA - m_referenceAngle;
float linearError = MathUtils.abs(C1.x);
float angularError = MathUtils.abs(C1.y);
bool active = false;
float C2 = 0.0f;
if (m_enableLimit)
{
float translation = Vec2.dot(axis, d);
if (MathUtils.abs(m_upperTranslation - m_lowerTranslation) < 2.0f * Settings.linearSlop)
{
// Prevent large angular corrections
C2 = MathUtils.clamp(translation, -Settings.maxLinearCorrection, Settings.maxLinearCorrection);
linearError = MathUtils.max(linearError, MathUtils.abs(translation));
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.clamp(translation - m_lowerTranslation + Settings.linearSlop, -Settings.maxLinearCorrection, 0.0f);
linearError = MathUtils.max(linearError, m_lowerTranslation - translation);
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.clamp(translation - m_upperTranslation - Settings.linearSlop, 0.0f, Settings.maxLinearCorrection);
linearError = MathUtils.max(linearError, translation - m_upperTranslation);
active = true;
}
}
if (active)
{
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float k12 = iA * s1 + iB * s2;
float k13 = iA * s1 * a1 + iB * s2 * a2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
// For fixed rotation
k22 = 1.0f;
}
float k23 = iA * a1 + iB * a2;
float k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
Mat33 K = pool.popMat33();
K.ex.set_Renamed(k11, k12, k13);
K.ey.set_Renamed(k12, k22, k23);
K.ez.set_Renamed(k13, k23, k33);
Vec3 C = pool.popVec3();
C.x = C1.x;
C.y = C1.y;
C.z = C2;
K.solve33ToOut(C.negateLocal(), impulse);
pool.pushVec3(1);
pool.pushMat33(1);
}
else
{
float k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float k12 = iA * s1 + iB * s2;
float k22 = iA + iB;
if (k22 == 0.0f)
{
k22 = 1.0f;
}
Mat22 K = pool.popMat22();
K.ex.set_Renamed(k11, k12);
K.ey.set_Renamed(k12, k22);
// temp is impulse1
K.solveToOut(C1.negateLocal(), temp);
C1.negateLocal();
impulse.x = temp.x;
impulse.y = temp.y;
impulse.z = 0.0f;
pool.pushMat22(1);
}
float Px = impulse.x * perp.x + impulse.z * axis.x;
float Py = impulse.x * perp.y + impulse.z * axis.y;
float LA = impulse.x * s1 + impulse.y + impulse.z * a1;
float LB = impulse.x * s2 + impulse.y + impulse.z * a2;
cA.x -= mA * Px;
cA.y -= mA * Py;
aA -= iA * LA;
cB.x += mB * Px;
cB.y += mB * Py;
aB += iB * LB;
data.positions[m_indexA].c.set_Renamed(cA);
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c.set_Renamed(cB);
data.positions[m_indexB].a = aB;
pool.pushVec2(7);
pool.pushVec3(1);
pool.pushRot(2);
return linearError <= Settings.linearSlop && angularError <= Settings.angularSlop;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
Vector2 cA = data.positions[_indexA].c;
float aA = data.positions[_indexA].a;
Vector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Vector2 rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
Vector2 rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
float positionError, angularError;
Mat33 K = new Mat33();
K.ex.X = mA + mB + rA.Y * rA.Y * iA + rB.Y * rB.Y * iB;
K.ey.X = -rA.Y * rA.X * iA - rB.Y * rB.X * iB;
K.ez.X = -rA.Y * iA - rB.Y * iB;
K.ex.Y = K.ey.X;
K.ey.Y = mA + mB + rA.X * rA.X * iA + rB.X * rB.X * iB;
K.ez.Y = rA.X * iA + rB.X * iB;
K.ex.Z = K.ez.X;
K.ey.Z = K.ez.Y;
K.ez.Z = iA + iB;
if (FrequencyHz > 0.0f)
{
Vector2 C1 = cB + rB - cA - rA;
positionError = C1.Length();
angularError = 0.0f;
Vector2 P = -K.Solve22(C1);
cA -= mA * P;
aA -= iA * MathUtils.Cross(rA, P);
cB += mB * P;
aB += iB * MathUtils.Cross(rB, P);
}
else
{
Vector2 C1 = cB + rB - cA - rA;
float C2 = aB - aA - ReferenceAngle;
positionError = C1.Length();
angularError = Math.Abs(C2);
Vector3 C = new Vector3(C1.X, C1.Y, C2);
Vector3 impulse = -K.Solve33(C);
Vector2 P = new Vector2(impulse.X, impulse.Y);
cA -= mA * P;
aA -= iA * (MathUtils.Cross(rA, P) + impulse.Z);
cB += mB * P;
aB += iB * (MathUtils.Cross(rB, P) + impulse.Z);
}
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return(positionError <= Settings.LinearSlop && angularError <= Settings.AngularSlop);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_indexB = BodyB.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_localCenterB = BodyB._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invMassB = BodyB._invMass;
_invIA = BodyA._invI;
_invIB = BodyB._invI;
float aA = data.positions[_indexA].a;
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
float aB = data.positions[_indexB].a;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Rot qA = new Rot(aA), qB = new Rot(aB);
_rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
_rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
Mat33 K = new Mat33();
K.ex.X = mA + mB + _rA.Y * _rA.Y * iA + _rB.Y * _rB.Y * iB;
K.ey.X = -_rA.Y * _rA.X * iA - _rB.Y * _rB.X * iB;
K.ez.X = -_rA.Y * iA - _rB.Y * iB;
K.ex.Y = K.ey.X;
K.ey.Y = mA + mB + _rA.X * _rA.X * iA + _rB.X * _rB.X * iB;
K.ez.Y = _rA.X * iA + _rB.X * iB;
K.ex.Z = K.ez.X;
K.ey.Z = K.ez.Y;
K.ez.Z = iA + iB;
if (FrequencyHz > 0.0f)
{
K.GetInverse22(ref _mass);
float invM = iA + iB;
float m = invM > 0.0f ? 1.0f / invM : 0.0f;
float C = aB - aA - ReferenceAngle;
// Frequency
float omega = 2.0f * Settings.Pi * FrequencyHz;
// Damping coefficient
float d = 2.0f * m * DampingRatio * omega;
// Spring stiffness
float k = m * omega * omega;
// magic formulas
float h = data.step.dt;
_gamma = h * (d + h * k);
_gamma = _gamma != 0.0f ? 1.0f / _gamma : 0.0f;
_bias = C * h * k * _gamma;
invM += _gamma;
_mass.ez.Z = invM != 0.0f ? 1.0f / invM : 0.0f;
}
else
{
K.GetSymInverse33(ref _mass);
_gamma = 0.0f;
_bias = 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Scale impulses to support a variable time step.
_impulse *= data.step.dtRatio;
Vector2 P = new Vector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(_rA, P) + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(_rB, P) + _impulse.Z);
}
else
{
_impulse = Vector3.Zero;
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexA = BodyA.IslandIndex;
_localCenterA = BodyA._sweep.LocalCenter;
_invMassA = BodyA._invMass;
_invIA = BodyA._invI;
Vector2 cA = data.Positions[_indexA].C;
float aA = data.Positions[_indexA].A;
Vector2 vA = data.Velocities[_indexA].V;
float wA = data.Velocities[_indexA].W;
Rot qA = new Rot(aA);
float mass = BodyA.Mass;
// Frequency
float omega = 2.0f * Settings.Pi * Frequency;
// Damping coefficient
float d = 2.0f * mass * DampingRatio * omega;
// Spring stiffness
float k = mass * (omega * omega);
// magic formulas
// gamma has units of inverse mass.
// beta has units of inverse time.
float h = data.Step.dt;
Debug.Assert(d + h * k > Settings.Epsilon);
_gamma = h * (d + h * k);
if (_gamma != 0.0f)
{
_gamma = 1.0f / _gamma;
}
_beta = h * k * _gamma;
// Compute the effective mass matrix.
_rA = MathUtils.Mul(qA, LocalAnchorA - _localCenterA);
// K = [(1/m1 + 1/m2) * eye(2) - skew(r1) * invI1 * skew(r1) - skew(r2) * invI2 * skew(r2)]
// = [1/m1+1/m2 0 ] + invI1 * [r1.Y*r1.Y -r1.X*r1.Y] + invI2 * [r1.Y*r1.Y -r1.X*r1.Y]
// [ 0 1/m1+1/m2] [-r1.X*r1.Y r1.X*r1.X] [-r1.X*r1.Y r1.X*r1.X]
Mat22 K = new Mat22();
K.ex.X = _invMassA + _invIA * _rA.Y * _rA.Y + _gamma;
K.ex.Y = -_invIA * _rA.X * _rA.Y;
K.ey.X = K.ex.Y;
K.ey.Y = _invMassA + _invIA * _rA.X * _rA.X + _gamma;
_mass = K.Inverse;
_C = cA + _rA - _worldAnchor;
_C *= _beta;
// Cheat with some damping
wA *= 0.98f;
if (Settings.EnableWarmstarting)
{
_impulse *= data.Step.dtRatio;
vA += _invMassA * _impulse;
wA += _invIA * MathUtils.Cross(_rA, _impulse);
}
else
{
_impulse = Vector2.Zero;
}
data.Velocities[_indexA].V = vA;
data.Velocities[_indexA].W = wA;
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
Vector2 vA = data.velocities[_indexA].v;
float wA = data.velocities[_indexA].w;
Vector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
float mA = _invMassA, mB = _invMassB;
float iA = _invIA, iB = _invIB;
if (FrequencyHz > 0.0f)
{
float Cdot2 = wB - wA;
float impulse2 = -_mass.ez.Z * (Cdot2 + _bias + _gamma * _impulse.Z);
_impulse.Z += impulse2;
wA -= iA * impulse2;
wB += iB * impulse2;
Vector2 Cdot1 = vB + MathUtils.Cross(wB, _rB) - vA - MathUtils.Cross(wA, _rA);
Vector2 impulse1 = -MathUtils.Mul22(_mass, Cdot1);
_impulse.X += impulse1.X;
_impulse.Y += impulse1.Y;
Vector2 P = impulse1;
vA -= mA * P;
wA -= iA * MathUtils.Cross(_rA, P);
vB += mB * P;
wB += iB * MathUtils.Cross(_rB, P);
}
else
{
Vector2 Cdot1 = vB + MathUtils.Cross(wB, _rB) - vA - MathUtils.Cross(wA, _rA);
float Cdot2 = wB - wA;
Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
Vector3 impulse = -MathUtils.Mul(_mass, Cdot);
_impulse += impulse;
Vector2 P = new Vector2(impulse.X, impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(_rA, P) + impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(_rB, P) + impulse.Z);
}
data.velocities[_indexA].v = vA;
data.velocities[_indexA].w = wA;
data.velocities[_indexB].v = vB;
data.velocities[_indexB].w = wB;
}
public override bool solvePositionConstraints(SolverData data)
{
Vec2 cA = data.positions[m_indexA].c;
double aA = data.positions[m_indexA].a;
Vec2 cB = data.positions[m_indexB].c;
double aB = data.positions[m_indexB].a;
Rot qA = pool.popRot();
Rot qB = pool.popRot();
Vec2 temp = pool.popVec2();
Vec2 rA = pool.popVec2();
Vec2 rB = pool.popVec2();
qA.set(aA);
qB.set(aB);
double mA = m_invMassA, mB = m_invMassB;
double iA = m_invIA, iB = m_invIB;
Rot.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), rA);
Rot.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), rB);
double positionError, angularError;
Mat33 K = pool.popMat33();
Vec2 C1 = pool.popVec2();
Vec2 P = pool.popVec2();
K.ex.x = mA + mB + rA.y * rA.y * iA + rB.y * rB.y * iB;
K.ey.x = -rA.y * rA.x * iA - rB.y * rB.x * iB;
K.ez.x = -rA.y * iA - rB.y * iB;
K.ex.y = K.ey.x;
K.ey.y = mA + mB + rA.x * rA.x * iA + rB.x * rB.x * iB;
K.ez.y = rA.x * iA + rB.x * iB;
K.ex.z = K.ez.x;
K.ey.z = K.ez.y;
K.ez.z = iA + iB;
if (m_frequencyHz > 0.0d)
{
C1.set(cB).addLocal(rB).subLocal(cA).subLocal(rA);
positionError = C1.length();
angularError = 0.0d;
K.solve22ToOut(C1, P);
P.negateLocal();
cA.x -= mA * P.x;
cA.y -= mA * P.y;
aA -= iA * Vec2.cross(rA, P);
cB.x += mB * P.x;
cB.y += mB * P.y;
aB += iB * Vec2.cross(rB, P);
}
else
{
C1.set(cB).addLocal(rB).subLocal(cA).subLocal(rA);
double C2 = aB - aA - m_referenceAngle;
positionError = C1.length();
angularError = MathUtils.abs(C2);
Vec3 C = pool.popVec3();
Vec3 impulse = pool.popVec3();
C.set(C1.x, C1.y, C2);
K.solve33ToOut(C, impulse);
impulse.negateLocal();
P.set(impulse.x, impulse.y);
cA.x -= mA * P.x;
cA.y -= mA * P.y;
aA -= iA * (Vec2.cross(rA, P) + impulse.z);
cB.x += mB * P.x;
cB.y += mB * P.y;
aB += iB * (Vec2.cross(rB, P) + impulse.z);
pool.pushVec3(2);
}
// data.positions[m_indexA].c.set(cA);
data.positions[m_indexA].a = aA;
// data.positions[m_indexB].c.set(cB);
data.positions[m_indexB].a = aB;
pool.pushVec2(5);
pool.pushRot(2);
pool.pushMat33(1);
return(positionError <= Settings.linearSlop && angularError <= Settings.angularSlop);
}
