/// <summary>
/// Solve A * x = b, where b is a column vector. This is more efficient
/// than computing the inverse in one-shot cases.
/// </summary>
/// <param name="b">The b.</param>
/// <returns></returns>
public FVector3 Solve33(FVector3 b)
{
float det = FVector3.Dot(ex, FVector3.Cross(ey, ez));
if (det != 0.0f)
{
det = 1.0f / det;
}
return(new FVector3(det * FVector3.Dot(b, FVector3.Cross(ey, ez)),
det * FVector3.Dot(ex, FVector3.Cross(b, ez)),
det * FVector3.Dot(ex, FVector3.Cross(ey, b))));
}
/// <summary>
/// Initialize the bodies and local anchor.
/// This requires defining an
/// anchor point where the bodies are joined. The definition
/// uses local anchor points so that the initial configuration
/// can violate the constraint slightly. You also need to
/// specify the initial relative angle for joint limits. This
/// helps when saving and loading a game.
/// The local anchor points are measured from the body's origin
/// rather than the center of mass because:
/// 1. you might not know where the center of mass will be.
/// 2. if you add/remove shapes from a body and recompute the mass,
/// the joints will be broken.
/// </summary>
/// <param name="bodyA">The first body.</param>
/// <param name="bodyB">The second body.</param>
/// <param name="localAnchorA">The first body anchor.</param>
/// <param name="localAnchorB">The second anchor.</param>
public FSRevoluteJoint(FSBody bodyA, FSBody bodyB, FVector2 localAnchorA, FVector2 localAnchorB)
: base(bodyA, bodyB)
{
JointType = JointType.Revolute;
// Changed to local coordinates.
LocalAnchorA = localAnchorA;
LocalAnchorB = localAnchorB;
ReferenceAngle = BodyB.Rotation - BodyA.Rotation;
_impulse = FVector3.Zero;
_limitState = LimitState.Inactive;
}
/// <summary>
/// Initialize the bodies and world anchor.
/// </summary>
/// <param name="bodyA">The first body.</param>
/// <param name="bodyB">The second body.</param>
/// <param name="worldAnchor">The world coordinate anchor.</param>
public RevoluteJoint(Body bodyA, Body bodyB, FVector2 worldAnchor)
: base(bodyA, bodyB)
{
JointType = JointType.Revolute;
// Changed to local coordinates.
LocalAnchorA = bodyA.GetLocalPoint(worldAnchor);
LocalAnchorB = bodyB.GetLocalPoint(worldAnchor);
ReferenceAngle = BodyB.Rotation - BodyA.Rotation;
_impulse = FVector3.Zero;
_limitState = LimitState.Inactive;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
FVector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
FVector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_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 (m_frequencyHz > 0.0f)
{
FVector2 C1 = cB + rB - cA - rA;
positionError = C1.Length();
angularError = 0.0f;
FVector2 P = -K.Solve22(C1);
cA -= mA * P;
aA -= iA * MathUtils.Cross(rA, P);
cB += mB * P;
aB += iB * MathUtils.Cross(rB, P);
}
else
{
FVector2 C1 = cB + rB - cA - rA;
float C2 = aB - aA - ReferenceAngle;
positionError = C1.Length();
angularError = Math.Abs(C2);
FVector3 C = new FVector3(C1.X, C1.Y, C2);
FVector3 impulse = -K.Solve33(C);
FVector2 P = new FVector2(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[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return(positionError <= Settings.LinearSlop && angularError <= Settings.AngularSlop);
}
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;
//FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
//FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
FVector2 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);
// 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 (_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;
FVector2 P = new FVector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(m_rA, P) + MotorImpulse + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(m_rB, P) + MotorImpulse + _impulse.Z);
}
else
{
_impulse = FVector3.Zero;
_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;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
FVector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
FVector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_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 (m_frequencyHz > 0.0f)
{
FVector2 C1 = cB + rB - cA - rA;
positionError = C1.Length();
angularError = 0.0f;
FVector2 P = -K.Solve22(C1);
cA -= mA * P;
aA -= iA * MathUtils.Cross(rA, P);
cB += mB * P;
aB += iB * MathUtils.Cross(rB, P);
}
else
{
FVector2 C1 = cB + rB - cA - rA;
float C2 = aB - aA - ReferenceAngle;
positionError = C1.Length();
angularError = Math.Abs(C2);
FVector3 C = new FVector3(C1.X, C1.Y, C2);
FVector3 impulse = -K.Solve33(C);
FVector2 P = new FVector2(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[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return positionError <= FSSettings.LinearSlop && angularError <= FSSettings.AngularSlop;
}
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;
//FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
//FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
FVector2 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);
// 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;
Mat33 K = new Mat33();
K.ex.X = mA + mB + m_rA.Y * m_rA.Y * iA + m_rB.Y * m_rB.Y * iB;
K.ey.X = -m_rA.Y * m_rA.X * iA - m_rB.Y * m_rB.X * iB;
K.ez.X = -m_rA.Y * iA - m_rB.Y * iB;
K.ex.Y = K.ey.X;
K.ey.Y = mA + mB + m_rA.X * m_rA.X * iA + m_rB.X * m_rB.X * iB;
K.ez.Y = m_rA.X * iA + m_rB.X * iB;
K.ex.Z = K.ez.X;
K.ey.Z = K.ez.Y;
K.ez.Z = iA + iB;
if (m_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 * m_frequencyHz;
// Damping coefficient
float d = 2.0f * m * m_dampingRatio * omega;
// Spring stiffness
float k = m * omega * omega;
// magic formulas
float h = data.step.dt;
m_gamma = h * (d + h * k);
m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
m_bias = C * h * k * m_gamma;
invM += m_gamma;
_mass.ez.Z = invM != 0.0f ? 1.0f / invM : 0.0f;
}
else
{
K.GetSymInverse33(ref _mass);
m_gamma = 0.0f;
m_bias = 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Scale impulses to support a variable time step.
_impulse *= data.step.dtRatio;
FVector2 P = new FVector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(m_rA, P) + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(m_rB, P) + _impulse.Z);
}
else
{
_impulse = FVector3.Zero;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
/// <summary>
/// Set this matrix to all zeros.
/// </summary>
public void SetZero()
{
ex = FVector3.Zero;
ey = FVector3.Zero;
ez = FVector3.Zero;
}
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;
//FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
//FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
FVector2 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);
// 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;
Mat33 K = new Mat33();
K.ex.X = mA + mB + m_rA.Y * m_rA.Y * iA + m_rB.Y * m_rB.Y * iB;
K.ey.X = -m_rA.Y * m_rA.X * iA - m_rB.Y * m_rB.X * iB;
K.ez.X = -m_rA.Y * iA - m_rB.Y * iB;
K.ex.Y = K.ey.X;
K.ey.Y = mA + mB + m_rA.X * m_rA.X * iA + m_rB.X * m_rB.X * iB;
K.ez.Y = m_rA.X * iA + m_rB.X * iB;
K.ex.Z = K.ez.X;
K.ey.Z = K.ez.Y;
K.ez.Z = iA + iB;
if (m_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 * FSSettings.Pi * m_frequencyHz;
// Damping coefficient
float d = 2.0f * m * m_dampingRatio * omega;
// Spring stiffness
float k = m * omega * omega;
// magic formulas
float h = data.step.dt;
m_gamma = h * (d + h * k);
m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
m_bias = C * h * k * m_gamma;
invM += m_gamma;
_mass.ez.Z = invM != 0.0f ? 1.0f / invM : 0.0f;
}
else
{
K.GetSymInverse33(ref _mass);
m_gamma = 0.0f;
m_bias = 0.0f;
}
if (FSSettings.EnableWarmstarting)
{
// Scale impulses to support a variable time step.
_impulse *= data.step.dtRatio;
FVector2 P = new FVector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(m_rA, P) + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(m_rB, P) + _impulse.Z);
}
else
{
_impulse = FVector3.Zero;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
/// Multiply a matrix times a vector.
public static FVector3 Mul(Mat33 A, FVector3 v)
{
return(v.X * A.ex + v.Y * A.ey + v.Z * A.ez);
}
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;
FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
FVector2 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.
FVector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
FVector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_localCenterB);
FVector2 d = (cB - cA) + rB - rA;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute motor Jacobian and effective mass.
{
m_axis = MathUtils.Mul(qA, LocalXAxisA);
m_a1 = MathUtils.Cross(d + rA, m_axis);
m_a2 = MathUtils.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.
{
m_perp = MathUtils.Mul(qA, _localYAxisA);
m_s1 = MathUtils.Cross(d + rA, m_perp);
m_s2 = MathUtils.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 = new FVector3(k11, k12, k13);
m_K.ey = new FVector3(k12, k22, k23);
m_K.ez = new FVector3(k13, k23, k33);
}
// Compute motor and limit terms.
if (_enableLimit)
{
float jointTranslation = FVector2.Dot(m_axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * FSSettings.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;
}
if (_enableMotor == false)
{
_motorImpulse = 0.0f;
}
if (FSSettings.EnableWarmstarting)
{
// Account for variable time step.
_impulse *= data.step.dtRatio;
_motorImpulse *= data.step.dtRatio;
FVector2 P = _impulse.X * m_perp + (_motorImpulse + _impulse.Z) * m_axis;
float LA = _impulse.X * m_s1 + _impulse.Y + (_motorImpulse + _impulse.Z) * m_a1;
float LB = _impulse.X * m_s2 + _impulse.Y + (_motorImpulse + _impulse.Z) * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
_impulse = FVector3.Zero;
_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;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
FVector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
FVector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_localCenterB);
FVector2 d = cB + rB - cA - rA;
FVector2 axis = MathUtils.Mul(qA, LocalXAxisA);
float a1 = MathUtils.Cross(d + rA, axis);
float a2 = MathUtils.Cross(rB, axis);
FVector2 perp = MathUtils.Mul(qA, _localYAxisA);
float s1 = MathUtils.Cross(d + rA, perp);
float s2 = MathUtils.Cross(rB, perp);
FVector3 impulse;
FVector2 C1 = new FVector2();
C1.X = FVector2.Dot(perp, d);
C1.Y = aB - aA - m_referenceAngle;
float linearError = Math.Abs(C1.X);
float angularError = Math.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (_enableLimit)
{
float translation = FVector2.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 FVector3(k11, k12, k13);
K.ey = new FVector3(k12, k22, k23);
K.ez = new FVector3(k13, k23, k33);
FVector3 C = new FVector3();
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 FVector2(k11, k12);
K.ey = new FVector2(k12, k22);
FVector2 impulse1 = K.Solve(-C1);
impulse = new FVector3();
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
FVector2 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[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return linearError <= Settings.LinearSlop && angularError <= Settings.AngularSlop;
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
FVector2 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;
// Solve linear motor constraint.
if (_enableMotor && _limitState != LimitState.Equal)
{
float Cdot = FVector2.Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
float impulse = m_motorMass * (_motorSpeed - Cdot);
float oldImpulse = _motorImpulse;
float maxImpulse = data.step.dt * _maxMotorForce;
_motorImpulse = MathUtils.Clamp(_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = _motorImpulse - oldImpulse;
FVector2 P = impulse * m_axis;
float LA = impulse * m_a1;
float LB = impulse * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
FVector2 Cdot1 = new FVector2();
Cdot1.X = FVector2.Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
Cdot1.Y = wB - wA;
if (_enableLimit && _limitState != LimitState.Inactive)
{
// Solve prismatic and limit constraint in block form.
float Cdot2;
Cdot2 = FVector2.Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
FVector3 Cdot = new FVector3(Cdot1.X, Cdot1.Y, Cdot2);
FVector3 f1 = _impulse;
FVector3 df = m_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)
FVector2 b = -Cdot1 - (_impulse.Z - f1.Z) * new FVector2(m_K.ez.X, m_K.ez.Y);
FVector2 f2r = m_K.Solve22(b) + new FVector2(f1.X, f1.Y);
_impulse.X = f2r.X;
_impulse.Y = f2r.Y;
df = _impulse - f1;
FVector2 P = df.X * m_perp + df.Z * m_axis;
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 -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
FVector2 df = m_K.Solve22(-Cdot1);
_impulse.X += df.X;
_impulse.Y += df.Y;
FVector2 P = df.X * m_perp;
float LA = df.X * m_s1 + df.Y;
float LB = df.X * m_s2 + df.Y;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
//FVector2 Cdot10 = Cdot1;
Cdot1.X = FVector2.Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
Cdot1.Y = wB - wA;
if (Math.Abs(Cdot1.X) > 0.01f || Math.Abs(Cdot1.Y) > 0.01f)
{
//FVector2 test = MathUtils.Mul22(m_K, df);
Cdot1.X += 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;
}
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;
FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
FVector2 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.
FVector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
FVector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_localCenterB);
FVector2 d = (cB - cA) + rB - rA;
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute motor Jacobian and effective mass.
{
m_axis = MathUtils.Mul(qA, LocalXAxisA);
m_a1 = MathUtils.Cross(d + rA, m_axis);
m_a2 = MathUtils.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.
{
m_perp = MathUtils.Mul(qA, _localYAxisA);
m_s1 = MathUtils.Cross(d + rA, m_perp);
m_s2 = MathUtils.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 = new FVector3(k11, k12, k13);
m_K.ey = new FVector3(k12, k22, k23);
m_K.ez = new FVector3(k13, k23, k33);
}
// Compute motor and limit terms.
if (_enableLimit)
{
float jointTranslation = FVector2.Dot(m_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;
}
if (_enableMotor == false)
{
_motorImpulse = 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Account for variable time step.
_impulse *= data.step.dtRatio;
_motorImpulse *= data.step.dtRatio;
FVector2 P = _impulse.X * m_perp + (_motorImpulse + _impulse.Z) * m_axis;
float LA = _impulse.X * m_s1 + _impulse.Y + (_motorImpulse + _impulse.Z) * m_a1;
float LB = _impulse.X * m_s2 + _impulse.Y + (_motorImpulse + _impulse.Z) * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
_impulse = FVector3.Zero;
_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;
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
Rot qA = new Rot(aA), qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
FVector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
FVector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_localCenterB);
FVector2 d = cB + rB - cA - rA;
FVector2 axis = MathUtils.Mul(qA, LocalXAxisA);
float a1 = MathUtils.Cross(d + rA, axis);
float a2 = MathUtils.Cross(rB, axis);
FVector2 perp = MathUtils.Mul(qA, _localYAxisA);
float s1 = MathUtils.Cross(d + rA, perp);
float s2 = MathUtils.Cross(rB, perp);
FVector3 impulse;
FVector2 C1 = new FVector2();
C1.X = FVector2.Dot(perp, d);
C1.Y = aB - aA - m_referenceAngle;
float linearError = Math.Abs(C1.X);
float angularError = Math.Abs(C1.Y);
bool active = false;
float C2 = 0.0f;
if (_enableLimit)
{
float translation = FVector2.Dot(axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * FSSettings.LinearSlop)
{
// Prevent large angular corrections
C2 = MathUtils.Clamp(translation, -FSSettings.MaxLinearCorrection, FSSettings.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 + FSSettings.LinearSlop,
-FSSettings.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 - FSSettings.LinearSlop, 0.0f,
FSSettings.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 FVector3(k11, k12, k13);
K.ey = new FVector3(k12, k22, k23);
K.ez = new FVector3(k13, k23, k33);
FVector3 C = new FVector3();
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 FVector2(k11, k12);
K.ey = new FVector2(k12, k22);
FVector2 impulse1 = K.Solve(-C1);
impulse = new FVector3();
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
FVector2 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[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return(linearError <= FSSettings.LinearSlop && angularError <= FSSettings.AngularSlop);
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
FVector2 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;
// Solve linear motor constraint.
if (_enableMotor && _limitState != LimitState.Equal)
{
float Cdot = FVector2.Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
float impulse = m_motorMass * (_motorSpeed - Cdot);
float oldImpulse = _motorImpulse;
float maxImpulse = data.step.dt * _maxMotorForce;
_motorImpulse = MathUtils.Clamp(_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = _motorImpulse - oldImpulse;
FVector2 P = impulse * m_axis;
float LA = impulse * m_a1;
float LB = impulse * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
FVector2 Cdot1 = new FVector2();
Cdot1.X = FVector2.Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
Cdot1.Y = wB - wA;
if (_enableLimit && _limitState != LimitState.Inactive)
{
// Solve prismatic and limit constraint in block form.
float Cdot2;
Cdot2 = FVector2.Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
FVector3 Cdot = new FVector3(Cdot1.X, Cdot1.Y, Cdot2);
FVector3 f1 = _impulse;
FVector3 df = m_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)
FVector2 b = -Cdot1 - (_impulse.Z - f1.Z) * new FVector2(m_K.ez.X, m_K.ez.Y);
FVector2 f2r = m_K.Solve22(b) + new FVector2(f1.X, f1.Y);
_impulse.X = f2r.X;
_impulse.Y = f2r.Y;
df = _impulse - f1;
FVector2 P = df.X * m_perp + df.Z * m_axis;
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 -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
FVector2 df = m_K.Solve22(-Cdot1);
_impulse.X += df.X;
_impulse.Y += df.Y;
FVector2 P = df.X * m_perp;
float LA = df.X * m_s1 + df.Y;
float LB = df.X * m_s2 + df.Y;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
//FVector2 Cdot10 = Cdot1;
Cdot1.X = FVector2.Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
Cdot1.Y = wB - wA;
if (Math.Abs(Cdot1.X) > 0.01f || Math.Abs(Cdot1.Y) > 0.01f)
{
//FVector2 test = MathUtils.Mul22(m_K, df);
Cdot1.X += 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;
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
//GABS: NOT A BOTTLENECK
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
FVector2 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 (_enableMotor && _limitState != LimitState.Equal && fixedRotation == false)
{
float Cdot = wB - wA - _motorSpeed;
float impulse = m_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)
{
FVector2 Cdot1 = vB + MathUtils.Cross(wB, m_rB) - vA - MathUtils.Cross(wA, m_rA);
float Cdot2 = wB - wA;
FVector3 Cdot = new FVector3(Cdot1.X, Cdot1.Y, Cdot2);
FVector3 impulse = -m_mass.Solve33(Cdot);
if (_limitState == LimitState.Equal)
{
_impulse += impulse;
}
else if (_limitState == LimitState.AtLower)
{
float newImpulse = _impulse.Z + impulse.Z;
if (newImpulse < 0.0f)
{
FVector2 rhs = -Cdot1 + _impulse.Z * new FVector2(m_mass.ez.X, m_mass.ez.Y);
FVector2 reduced = m_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)
{
FVector2 rhs = -Cdot1 + _impulse.Z * new FVector2(m_mass.ez.X, m_mass.ez.Y);
FVector2 reduced = m_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;
}
}
FVector2 P = new FVector2(impulse.X, impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(m_rA, P) + impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(m_rB, P) + impulse.Z);
}
else
{
// Solve point-to-point constraint
FVector2 Cdot = vB + MathUtils.Cross(wB, m_rB) - vA - MathUtils.Cross(wA, m_rA);
FVector2 impulse = m_mass.Solve22(-Cdot);
_impulse.X += impulse.X;
_impulse.Y += impulse.Y;
vA -= mA * impulse;
wA -= iA * MathUtils.Cross(m_rA, impulse);
vB += mB * impulse;
wB += iB * MathUtils.Cross(m_rB, impulse);
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
/// Perform the cross product on two vectors.
public static FVector3 Cross(FVector3 a, FVector3 b)
{
return(new FVector3(a.Y * b.Z - a.Z * b.Y, a.Z * b.X - a.X * b.Z, a.X * b.Y - a.Y * b.X));
}
/// <summary>
/// Initialize the bodies and local anchor.
/// This requires defining an
/// anchor point where the bodies are joined. The definition
/// uses local anchor points so that the initial configuration
/// can violate the constraint slightly. You also need to
/// specify the initial relative angle for joint limits. This
/// helps when saving and loading a game.
/// The local anchor points are measured from the body's origin
/// rather than the center of mass because:
/// 1. you might not know where the center of mass will be.
/// 2. if you add/remove shapes from a body and recompute the mass,
/// the joints will be broken.
/// </summary>
/// <param name="bodyA">The first body.</param>
/// <param name="bodyB">The second body.</param>
/// <param name="localAnchorA">The first body anchor.</param>
/// <param name="localAnchorB">The second anchor.</param>
public RevoluteJoint(Body bodyA, Body bodyB, FVector2 localAnchorA, FVector2 localAnchorB)
: base(bodyA, bodyB)
{
JointType = JointType.Revolute;
// Changed to local coordinates.
LocalAnchorA = localAnchorA;
LocalAnchorB = localAnchorB;
ReferenceAngle = BodyB.Rotation - BodyA.Rotation;
_impulse = FVector3.Zero;
_limitState = LimitState.Inactive;
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
FVector2 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;
if (m_frequencyHz > 0.0f)
{
float Cdot2 = wB - wA;
float impulse2 = -_mass.ez.Z * (Cdot2 + m_bias + m_gamma * _impulse.Z);
_impulse.Z += impulse2;
wA -= iA * impulse2;
wB += iB * impulse2;
FVector2 Cdot1 = vB + MathUtils.Cross(wB, m_rB) - vA - MathUtils.Cross(wA, m_rA);
FVector2 impulse1 = -MathUtils.Mul22(_mass, Cdot1);
_impulse.X += impulse1.X;
_impulse.Y += impulse1.Y;
FVector2 P = impulse1;
vA -= mA * P;
wA -= iA * MathUtils.Cross(m_rA, P);
vB += mB * P;
wB += iB * MathUtils.Cross(m_rB, P);
}
else
{
FVector2 Cdot1 = vB + MathUtils.Cross(wB, m_rB) - vA - MathUtils.Cross(wA, m_rA);
float Cdot2 = wB - wA;
FVector3 Cdot = new FVector3(Cdot1.X, Cdot1.Y, Cdot2);
FVector3 impulse = -MathUtils.Mul(_mass, Cdot);
_impulse += impulse;
FVector2 P = new FVector2(impulse.X, impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(m_rA, P) + impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(m_rB, P) + impulse.Z);
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
/// Perform the dot product on two vectors.
public static float Dot(FVector3 a, FVector3 b)
{
return(a.X * b.X + a.Y * b.Y + a.Z * b.Z);
}
/// <summary>
/// Initialize the bodies and world anchor.
/// </summary>
/// <param name="bodyA">The first body.</param>
/// <param name="bodyB">The second body.</param>
/// <param name="worldAnchor">The world coordinate anchor.</param>
public FSRevoluteJoint(FSBody bodyA, FSBody bodyB, FVector2 worldAnchor)
: base(bodyA, bodyB)
{
JointType = JointType.Revolute;
// Changed to local coordinates.
LocalAnchorA = bodyA.GetLocalPoint(worldAnchor);
LocalAnchorB = bodyB.GetLocalPoint(worldAnchor);
ReferenceAngle = BodyB.Rotation - BodyA.Rotation;
_impulse = FVector3.Zero;
_limitState = LimitState.Inactive;
}
/// <summary>
/// Construct this matrix using columns.
/// </summary>
/// <param name="c1">The c1.</param>
/// <param name="c2">The c2.</param>
/// <param name="c3">The c3.</param>
public Mat33(FVector3 c1, FVector3 c2, FVector3 c3)
{
ex = c1;
ey = c2;
ez = c3;
}
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;
//FVector2 cA = data.positions[m_indexA].c;
float aA = data.positions[m_indexA].a;
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
//FVector2 cB = data.positions[m_indexB].c;
float aB = data.positions[m_indexB].a;
FVector2 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);
// 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 (_enableMotor == false || fixedRotation)
{
_motorImpulse = 0.0f;
}
if (_enableLimit && fixedRotation == false)
{
float jointAngle = aB - aA - ReferenceAngle;
if (Math.Abs(_upperAngle - _lowerAngle) < 2.0f * FSSettings.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 (FSSettings.EnableWarmstarting)
{
// Scale impulses to support a variable time step.
_impulse *= data.step.dtRatio;
_motorImpulse *= data.step.dtRatio;
FVector2 P = new FVector2(_impulse.X, _impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(m_rA, P) + MotorImpulse + _impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(m_rB, P) + MotorImpulse + _impulse.Z);
}
else
{
_impulse = FVector3.Zero;
_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;
}
/// <summary>
/// Plot a line start/end point
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="z"></param>
/// <param name="color"></param>
protected void Plot(float x, float y, float z, FVector3 color)
{
lines.Add(new FVector3(x, y, z));
lines.Add(color);
}
internal override void SolveVelocityConstraints(ref SolverData data)
{
FVector2 vA = data.velocities[m_indexA].v;
float wA = data.velocities[m_indexA].w;
FVector2 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 (_enableMotor && _limitState != LimitState.Equal && fixedRotation == false)
{
float Cdot = wB - wA - _motorSpeed;
float impulse = m_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)
{
FVector2 Cdot1 = vB + MathUtils.Cross(wB, m_rB) - vA - MathUtils.Cross(wA, m_rA);
float Cdot2 = wB - wA;
FVector3 Cdot = new FVector3(Cdot1.X, Cdot1.Y, Cdot2);
FVector3 impulse = -m_mass.Solve33(Cdot);
if (_limitState == LimitState.Equal)
{
_impulse += impulse;
}
else if (_limitState == LimitState.AtLower)
{
float newImpulse = _impulse.Z + impulse.Z;
if (newImpulse < 0.0f)
{
FVector2 rhs = -Cdot1 + _impulse.Z * new FVector2(m_mass.ez.X, m_mass.ez.Y);
FVector2 reduced = m_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)
{
FVector2 rhs = -Cdot1 + _impulse.Z * new FVector2(m_mass.ez.X, m_mass.ez.Y);
FVector2 reduced = m_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;
}
}
FVector2 P = new FVector2(impulse.X, impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(m_rA, P) + impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(m_rB, P) + impulse.Z);
}
else
{
// Solve point-to-point constraint
FVector2 Cdot = vB + MathUtils.Cross(wB, m_rB) - vA - MathUtils.Cross(wA, m_rA);
FVector2 impulse = m_mass.Solve22(-Cdot);
_impulse.X += impulse.X;
_impulse.Y += impulse.Y;
vA -= mA * impulse;
wA -= iA * MathUtils.Cross(m_rA, impulse);
vB += mB * impulse;
wB += iB * MathUtils.Cross(m_rB, impulse);
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}