/// Get the inverse of this matrix as a 2-by-2.
/// Returns the zero matrix if singular.
public void GetInverse22(out Mat33 M) {
float a = ex.X, b = ey.X, c = ex.Y, d = ey.Y;
float det = a * d - b * c;
if (det != 0.0f) {
det = 1.0f / det;
}
M.ex.X = det * d; M.ey.X = -det * b; M.ex.Z = 0.0f;
M.ex.Y = -det * c; M.ey.Y = det * a; M.ey.Z = 0.0f;
M.ez.X = 0.0f; M.ez.Y = 0.0f; M.ez.Z = 0.0f;
}
/// Get the symmetric inverse of this matrix as a 3-by-3.
/// Returns the zero matrix if singular.
public void GetSymInverse33(out Mat33 M) {
float det = Utilities.Dot(ex, Utilities.Cross(ey, ez));
if (det != 0.0f) {
det = 1.0f / det;
}
float a11 = ex.X, a12 = ey.X, a13 = ez.X;
float a22 = ey.Y, a23 = ez.Y;
float a33 = ez.Z;
M.ex.X = det * (a22 * a33 - a23 * a23);
M.ex.Y = det * (a13 * a23 - a12 * a33);
M.ex.Z = det * (a12 * a23 - a13 * a22);
M.ey.X = M.ex.Y;
M.ey.Y = det * (a11 * a33 - a13 * a13);
M.ey.Z = det * (a13 * a12 - a11 * a23);
M.ez.X = M.ex.Z;
M.ez.Y = M.ey.Z;
M.ez.Z = det * (a11 * a22 - a12 * a12);
}
/// Multiply a matrix times a vector.
public static Vec2 Mul22(Mat33 A, Vec2 v)
{
return new Vec2(A.ex.X * v.X + A.ey.X * v.Y, A.ex.Y * v.X + A.ey.Y * v.Y);
}
/// Multiply a matrix times a vector.
public static Vec3 Mul(Mat33 A, Vec3 v)
{
return v.X * A.ex + v.Y * A.ey + v.Z * A.ez;
}
internal 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 = new Rot(aA);
Rot qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 d = cB + rB - cA - rA;
Vec2 axis = Utilities.Mul(qA, m_localXAxisA);
float a1 = Utilities.Cross(d + rA, axis);
float a2 = Utilities.Cross(rB, axis);
Vec2 perp = Utilities.Mul(qA, m_localYAxisA);
float s1 = Utilities.Cross(d + rA, perp);
float s2 = Utilities.Cross(rB, perp);
Vec3 impulse;
Vec2 C1;
C1.X = Utilities.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 (m_enableLimit)
{
float translation = Utilities.Dot(axis, d);
if (Math.Abs(m_upperTranslation - m_lowerTranslation) < 2.0f *Settings._linearSlop)
{
// Prevent large angular corrections
C2 = Utilities.Clamp(translation, -Settings._maxLinearCorrection, Settings._maxLinearCorrection);
linearError = Math.Max(linearError, Math.Abs(translation));
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = Utilities.Clamp(translation - m_lowerTranslation + Settings._linearSlop, -Settings._maxLinearCorrection, 0.0f);
linearError = Math.Max(linearError, m_lowerTranslation - translation);
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = Utilities.Clamp(translation - m_upperTranslation - Settings._linearSlop, 0.0f, Settings._maxLinearCorrection);
linearError = Math.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 = new Mat33();
K.ex.Set(k11, k12, k13);
K.ey.Set(k12, k22, k23);
K.ez.Set(k13, k23, k33);
Vec3 C = new Vec3();
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.Set(k11, k12);
K.ey.Set(k12, k22);
Vec2 impulse1 = K.Solve(-C1);
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
Vec2 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 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 = new Rot(aA);
Rot qB = new Rot(aB);
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
Vec2 rA = Utilities.Mul(qA, m_localAnchorA - m_localCenterA);
Vec2 rB = Utilities.Mul(qB, m_localAnchorB - m_localCenterB);
Vec2 d = cB + rB - cA - rA;
Vec2 axis = Utilities.Mul(qA, m_localXAxisA);
float a1 = Utilities.Cross(d + rA, axis);
float a2 = Utilities.Cross(rB, axis);
Vec2 perp = Utilities.Mul(qA, m_localYAxisA);
float s1 = Utilities.Cross(d + rA, perp);
float s2 = Utilities.Cross(rB, perp);
Vec3 impulse;
Vec2 C1;
C1.X = Utilities.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 (m_enableLimit)
{
float translation = Utilities.Dot(axis, d);
if (Math.Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * Settings._linearSlop)
{
// Prevent large angular corrections
C2 = Utilities.Clamp(translation, -Settings._maxLinearCorrection, Settings._maxLinearCorrection);
linearError = Math.Max(linearError, Math.Abs(translation));
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = Utilities.Clamp(translation - m_lowerTranslation + Settings._linearSlop, -Settings._maxLinearCorrection, 0.0f);
linearError = Math.Max(linearError, m_lowerTranslation - translation);
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = Utilities.Clamp(translation - m_upperTranslation - Settings._linearSlop, 0.0f, Settings._maxLinearCorrection);
linearError = Math.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 = new Mat33();
K.ex.Set(k11, k12, k13);
K.ey.Set(k12, k22, k23);
K.ez.Set(k13, k23, k33);
Vec3 C = new Vec3();
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.Set(k11, k12);
K.ey.Set(k12, k22);
Vec2 impulse1 = K.Solve(-C1);
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
Vec2 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);
}