public static Vector3 operator *( Vector3 V, Rot rot )
{
Rot InverseInRot = rot.Inverse();
Rot VectorRot = new Rot( V.x, V.y, V.z, 0 );
Rot IntRot = VectorRot * rot;
Rot ResultRot = InverseInRot * IntRot;
return new Vector3( ResultRot.x, ResultRot.y, ResultRot.z );
}
public static void ApplyRotToGLMatrix4d( ref GLMatrix4d matrix, Rot rot )
{
double fRotAngle = 0;
Vector3 vAxis = new Vector3();
mvMath.Rot2AxisAngle( ref vAxis, ref fRotAngle, rot );
matrix.applyRotate( (float)( fRotAngle / Math.PI * 180 ), (float)vAxis.x, (float)vAxis.y, (float)vAxis.z );
}
public static Rot operator *( Rot R1, Rot R2 )
{
Rot result = new Rot();
result.s = R1.s * R2.s - R1.x * R2.x - R1.y * R2.y - R1.z * R2.z;
result.x = R1.s * R2.x + R1.x * R2.s + R1.y * R2.z -R1.z * R2.y;
result.y = R1.s * R2.y + R1.y * R2.s + R1.z * R2.x - R1.x * R2.z;
result.z = R1.s * R2.z + R1.z * R2.s + R1.x * R2.y - R1.y * R2.x;
//Test.Debug( "RotMULITPLY in=" << Q1 << " " << Q2 << " out=" << Qr <<endl;
return result;
}
public bool Clip(Vertices clipVertices, Vector2 position)
{
Rot rot = new Rot(0);
Transform t = new Transform(ref position, ref rot);
//Transform shape
Transform thistransform;
Body.GetTransform(out thistransform);
//Transform the shape
Vertices transformedshape = new Vertices(clipVertices.Count);
foreach (Vector2 v in clipVertices)
{
Vector2 newv = v;
newv = MathUtils.Mul(ref t, ref newv);
newv = MathUtils.MulT(ref thistransform, ref newv);
transformedshape.Add(newv);
}
PolyClipError error;
List<Vertices> result = YuPengClipper.Difference(Vertices, transformedshape, out error);
//Need to check if the entire shape was cut,
//so we can destroy/erase it
if (result.Count == 0)
return false;
//The shape was split up,
//so create a new DestructableBody for each piece
if (result.Count > 1)
{
//Create a new destructable body for each extra shape
for (int i = 1; i < result.Count; i++)
{
DestructableBody db = new DestructableBody(_world, result[i]);
db.Body.Position = Body.Position;
}
}
//Set Shape
Vertices newshape = result[0];
SetShape(newshape);
return true;
}
public static void Rot2AxisAngle( ref Vector3 Vr, ref double Thetar, Rot R )
{
//QuaternionNormalize( |X,Y,Z,W| );
Vr = new Vector3();
double cos_a = R.s;
Thetar = Math.Acos( cos_a ) * 2;
double sin_a = Math.Sqrt( 1.0 - cos_a * cos_a );
if ( Math.Abs( sin_a )> 0.0005 )
{
Vr.x = R.x / sin_a;
Vr.y = R.y / sin_a;
Vr.z = R.z / sin_a;
}
else
{
Vr.x = 1;
Vr.y = 0;
Vr.z = 0;
}
}
public void Rotate( Rot rot )
{
double fRotAngle = 0;
Vector3 vAxis = new Vector3();
mvMath.Rot2AxisAngle( ref vAxis, ref fRotAngle, rot );
Gl.glRotatef( (float)( fRotAngle / Math.PI * 180 ), (float)vAxis.x, (float)vAxis.y, (float)vAxis.z );
}
/// <summary>
/// Compute the closest points between two shapes. Supports any combination of: CircleShape and
/// PolygonShape. The simplex cache is input/output. On the first call set SimplexCache.count to
/// zero.
/// </summary>
/// <param name="output"></param>
/// <param name="cache"></param>
/// <param name="input"></param>
public void GetDistance(DistanceOutput output, SimplexCache cache, DistanceInput input)
{
GJK_CALLS++;
DistanceProxy proxyA = input.ProxyA;
DistanceProxy proxyB = input.ProxyB;
Transform transformA = input.TransformA;
Transform transformB = input.TransformB;
// Initialize the simplex.
simplex.ReadCache(cache, proxyA, transformA, proxyB, transformB);
// Get simplex vertices as an array.
SimplexVertex[] vertices = simplex.Vertices;
// These store the vertices of the last simplex so that we
// can check for duplicates and prevent cycling.
// (pooled above)
simplex.GetClosestPoint(closestPoint);
float distanceSqr1 = closestPoint.LengthSquared();
// Main iteration loop
int iter = 0;
while (iter < GJK_MAX_ITERS)
{
// Copy simplex so we can identify duplicates.
int saveCount = simplex.Count;
for (int i = 0; i < saveCount; i++)
{
saveA[i] = vertices[i].IndexA;
saveB[i] = vertices[i].IndexB;
}
switch (simplex.Count)
{
case 1:
break;
case 2:
simplex.Solve2();
break;
case 3:
simplex.Solve3();
break;
default:
Debug.Assert(false);
break;
}
// If we have 3 points, then the origin is in the corresponding triangle.
if (simplex.Count == 3)
{
break;
}
// Compute closest point.
simplex.GetClosestPoint(closestPoint);
float distanceSqr2 = closestPoint.LengthSquared();
// ensure progress
if (distanceSqr2 >= distanceSqr1)
{
// break;
}
distanceSqr1 = distanceSqr2;
// get search direction;
simplex.GetSearchDirection(d);
// Ensure the search direction is numerically fit.
if (d.LengthSquared() < Settings.EPSILON * Settings.EPSILON)
{
// The origin is probably contained by a line segment
// or triangle. Thus the shapes are overlapped.
// We can't return zero here even though there may be overlap.
// In case the simplex is a point, segment, or triangle it is difficult
// to determine if the origin is contained in the CSO or very close to it.
break;
}
/*
* SimplexVertex* vertex = vertices + simplex.m_count; vertex.indexA =
* proxyA.GetSupport(MulT(transformA.R, -d)); vertex.wA = Mul(transformA,
* proxyA.GetVertex(vertex.indexA)); Vec2 wBLocal; vertex.indexB =
* proxyB.GetSupport(MulT(transformB.R, d)); vertex.wB = Mul(transformB,
* proxyB.GetVertex(vertex.indexB)); vertex.w = vertex.wB - vertex.wA;
*/
// Compute a tentative new simplex vertex using support points.
SimplexVertex vertex = vertices[simplex.Count];
Rot.MulTransUnsafe(transformA.Q, d.NegateLocal(), temp);
vertex.IndexA = proxyA.GetSupport(temp);
Transform.MulToOutUnsafe(transformA, proxyA.GetVertex(vertex.IndexA), vertex.WA);
// Vec2 wBLocal;
Rot.MulTransUnsafe(transformB.Q, d.NegateLocal(), temp);
vertex.IndexB = proxyB.GetSupport(temp);
Transform.MulToOutUnsafe(transformB, proxyB.GetVertex(vertex.IndexB), vertex.WB);
vertex.W.Set(vertex.WB).SubLocal(vertex.WA);
// Iteration count is equated to the number of support point calls.
++iter;
++GJK_ITERS;
// Check for duplicate support points. This is the main termination criteria.
bool duplicate = false;
for (int i = 0; i < saveCount; ++i)
{
if (vertex.IndexA == saveA[i] && vertex.IndexB == saveB[i])
{
duplicate = true;
break;
}
}
// If we found a duplicate support point we must exit to avoid cycling.
if (duplicate)
{
break;
}
// New vertex is ok and needed.
++simplex.Count;
}
GJK_MAX_ITERS = MathUtils.Max(GJK_MAX_ITERS, iter);
// Prepare output.
simplex.GetWitnessPoints(output.PointA, output.PointB);
output.Distance = MathUtils.Distance(output.PointA, output.PointB);
output.Iterations = iter;
// Cache the simplex.
simplex.WriteCache(cache);
// Apply radii if requested.
if (input.UseRadii)
{
float rA = proxyA.Radius;
float rB = proxyB.Radius;
if (output.Distance > rA + rB && output.Distance > Settings.EPSILON)
{
// Shapes are still no overlapped.
// Move the witness points to the outer surface.
output.Distance -= (rA + rB);
normal.Set(output.PointB).SubLocal(output.PointA);
normal.Normalize();
temp.Set(normal).MulLocal(rA);
output.PointA.AddLocal(temp);
temp.Set(normal).MulLocal(rB);
output.PointB.SubLocal(temp);
}
else
{
// Shapes are overlapped when radii are considered.
// Move the witness points to the middle.
// Vec2 p = 0.5f * (output.pointA + output.pointB);
output.PointA.AddLocal(output.PointB).MulLocal(.5f);
output.PointB.Set(output.PointA);
output.Distance = 0.0f;
}
}
}
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;
}
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;
Vec2 cC = data.positions[m_indexC].c;
double aC = data.positions[m_indexC].a;
Vec2 cD = data.positions[m_indexD].c;
double aD = data.positions[m_indexD].a;
Rot qA = pool.popRot(), qB = pool.popRot(), qC = pool.popRot(), qD = pool.popRot();
qA.set(aA);
qB.set(aB);
qC.set(aC);
qD.set(aD);
double linearError = 0.0d;
double coordinateA, coordinateB;
Vec2 temp = pool.popVec2();
Vec2 JvAC = pool.popVec2();
Vec2 JvBD = pool.popVec2();
double JwA, JwB, JwC, JwD;
double mass = 0.0d;
if (m_typeA == JointType.REVOLUTE)
{
JvAC.setZero();
JwA = 1.0d;
JwC = 1.0d;
mass += m_iA + m_iC;
coordinateA = aA - aC - m_referenceAngleA;
}
else
{
Vec2 rC = pool.popVec2();
Vec2 rA = pool.popVec2();
Vec2 pC = pool.popVec2();
Vec2 pA = pool.popVec2();
Rot.mulToOutUnsafe(qC, m_localAxisC, JvAC);
Rot.mulToOutUnsafe(qC, temp.set(m_localAnchorC).subLocal(m_lcC), rC);
Rot.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_lcA), rA);
JwC = Vec2.cross(rC, JvAC);
JwA = Vec2.cross(rA, JvAC);
mass += m_mC + m_mA + m_iC * JwC * JwC + m_iA * JwA * JwA;
pC.set(m_localAnchorC).subLocal(m_lcC);
Rot.mulTransUnsafe(qC, temp.set(rA).addLocal(cA).subLocal(cC), pA);
coordinateA = Vec2.dot(pA.subLocal(pC), m_localAxisC);
pool.pushVec2(4);
}
if (m_typeB == JointType.REVOLUTE)
{
JvBD.setZero();
JwB = m_ratio;
JwD = m_ratio;
mass += m_ratio * m_ratio * (m_iB + m_iD);
coordinateB = aB - aD - m_referenceAngleB;
}
else
{
Vec2 u = pool.popVec2();
Vec2 rD = pool.popVec2();
Vec2 rB = pool.popVec2();
Vec2 pD = pool.popVec2();
Vec2 pB = pool.popVec2();
Rot.mulToOutUnsafe(qD, m_localAxisD, u);
Rot.mulToOutUnsafe(qD, temp.set(m_localAnchorD).subLocal(m_lcD), rD);
Rot.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_lcB), rB);
JvBD.set(u).mulLocal(m_ratio);
JwD = Vec2.cross(rD, u);
JwB = Vec2.cross(rB, u);
mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * JwD * JwD + m_iB * JwB * JwB;
pD.set(m_localAnchorD).subLocal(m_lcD);
Rot.mulTransUnsafe(qD, temp.set(rB).addLocal(cB).subLocal(cD), pB);
coordinateB = Vec2.dot(pB.subLocal(pD), m_localAxisD);
pool.pushVec2(5);
}
double C = (coordinateA + m_ratio * coordinateB) - m_constant;
double impulse = 0.0d;
if (mass > 0.0d)
{
impulse = -C / mass;
}
pool.pushVec2(3);
pool.pushRot(4);
cA.x += (m_mA * impulse) * JvAC.x;
cA.y += (m_mA * impulse) * JvAC.y;
aA += m_iA * impulse * JwA;
cB.x += (m_mB * impulse) * JvBD.x;
cB.y += (m_mB * impulse) * JvBD.y;
aB += m_iB * impulse * JwB;
cC.x -= (m_mC * impulse) * JvAC.x;
cC.y -= (m_mC * impulse) * JvAC.y;
aC -= m_iC * impulse * JwC;
cD.x -= (m_mD * impulse) * JvBD.x;
cD.y -= (m_mD * impulse) * JvBD.y;
aD -= m_iD * impulse * JwD;
// data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
// data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
// data.positions[m_indexC].c = cC;
data.positions[m_indexC].a = aC;
// data.positions[m_indexD].c = cD;
data.positions[m_indexD].a = aD;
// TODO_ERIN not implemented
return(linearError < Settings.linearSlop);
}
internal override bool SolvePositionConstraints(ref SolverData data)
{
if (Frequency > 0.0f)
{
// There is no position correction for soft distance constraints.
return true;
}
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 - Length;
C = MathUtils.Clamp(C, -Settings.MaxLinearCorrection, 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 Math.Abs(C) < 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;
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;
}
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;
}
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;
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)
{
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 angularError = 0.0f;
float positionError;
bool fixedRotation = (m_invIA + m_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 = -m_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 = -m_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 = -m_motorMass * C;
}
aA -= m_invIA * limitImpulse;
aB += m_invIB * limitImpulse;
}
// Solve point-to-point constraint.
{
qA.Set(aA);
qB.Set(aB);
FVector2 rA = MathUtils.Mul(qA, LocalAnchorA - m_localCenterA);
FVector2 rB = MathUtils.Mul(qB, LocalAnchorB - m_localCenterB);
FVector2 C = cB + rB - cA - rA;
positionError = C.Length();
float mA = m_invMassA, mB = m_invMassB;
float iA = m_invIA, iB = m_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;
FVector2 impulse = -K.Solve(C);
cA -= mA * impulse;
aA -= iA * MathUtils.Cross(rA, impulse);
cB += mB * impulse;
aB += iB * MathUtils.Cross(rB, impulse);
}
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return positionError <= Settings.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;
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;
}
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;
}
/// <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 bool FuzzyEquals(CG_Transform trans)
{
return(Pos.FuzzyEquals(trans.Pos) && Rot.FuzzyEquals(trans.Rot) && Scl.FuzzyEquals(trans.Scl));
}
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;
}
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);
}
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);
Rot qB = new Rot(aB);
// Compute the effective mass matrix.
_rA = MathUtils.Mul(qA, -_localCenterA);
_rB = MathUtils.Mul(qB, -_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;
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 - MathUtils.Mul(qA, _linearOffset);
_angularError = aB - aA - _angularOffset;
if (Settings.EnableWarmstarting)
{
// 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(_rA, P) + _angularImpulse);
vB += mB * P;
wB += iB * (MathUtils.Cross(_rB, 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;
}
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;
}
/// Inverse rotate a vector
public static Vector2 MulT(Rot q, Vector2 v)
{
return(new Vector2(q.c * v.x + q.s * v.y, -q.s * v.x + q.c * v.y));
}
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);
// 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(rA, uA);
float ruB = MathUtils.Cross(rB, 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(rA, PA);
cB += _invMassB * PB;
aB += _invIB * MathUtils.Cross(rB, 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)
{
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;
}
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 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 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;
_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.DtRatio;
// 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;
}
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;
}
public static Rot RotBetween( Vector3 v1, Vector3 v2 )
{
Rot rResult = new Rot();
Vector3 VectorNorm1 = new Vector3( v1 ).Normalize();
Vector3 VectorNorm2 = new Vector3( v2 ).Normalize();
Vector3 RotationAxis = Vector3.CrossProduct( VectorNorm1, VectorNorm2 );
//Test.Debug( "math: " << RotationAxis ); // Test.Debug
//Test.Debug( Math.Abs( RotationAxis.x ) << " " << Math.Abs( RotationAxis.y ) << " " << Math.Abs( RotationAxis.z ) ); // Test.Debug
if( Math.Abs( RotationAxis.x ) < 0.0005 && Math.Abs( RotationAxis.y ) < 0.0005 && Math.Abs( RotationAxis.z ) < 0.0005 )
{
Vector3 RandomVector = new Vector3( VectorNorm1 );
RandomVector.x += 0.5;
RandomVector.Normalize();
RotationAxis = Vector3.CrossProduct( VectorNorm1, RandomVector );
rResult = mvMath.AxisAngle2Rot( RotationAxis, Math.PI );
}
else
{
double DotProduct = Vector3.DotProduct( VectorNorm1, VectorNorm2 );
Diag.Debug( "DotProduct: " + DotProduct.ToString() ); // Test.Debug
double Vangle = Math.Acos( DotProduct );
Diag.Debug( "math: " + Vangle.ToString() ); // Test.Debug
rResult = AxisAngle2Rot( RotationAxis, Vangle );
}
return rResult;
}
//! Feedback line buffer for OpenGL feedback, used by mvgraphics.cpp
/*
class FeedbackLineBufferItem
{
public double type;
public Vector2[] vertices = new Vector2[2];
}
*/
public Vector3 GetMouseVector(Vector3 OurPos, Rot OurRot, int mousex, int mousey)
{
IRenderer renderer = RendererFactory.GetInstance();
Vector3 MouseVectorObserverAxes = new Vector3(
- renderer.InnerWindowWidth / 2 + mousex,
- renderer.ScreenDistanceScreenCoords,
renderer.InnerWindowHeight / 2 - mousey);
//Console.WriteLine("MouseVectorObserverAxes: " + MouseVectorObserverAxes);
MouseVectorObserverAxes.Normalize();
//Console.WriteLine("MouseVectorObserverAxes (normalized): " + MouseVectorObserverAxes);
Vector3 MouseVectorWorldAxes = MouseVectorObserverAxes * OurRot.Inverse();
//Console.WriteLine("MouseVectorWorldAxes: " + MouseVectorWorldAxes.ToString());
MouseVectorWorldAxes.Normalize();
return MouseVectorWorldAxes;
}
internal rotOpt(float SAH, Rot rot)
{
this.SAH = SAH;
this.rot = rot;
}
internal override void InitVelocityConstraints(ref SolverData data)
{
m_indexA = BodyA.IslandIndex;
m_indexB = BodyB.IslandIndex;
m_indexC = m_bodyC.IslandIndex;
m_indexD = m_bodyD.IslandIndex;
m_lcA = BodyA.Sweep.LocalCenter;
m_lcB = BodyB.Sweep.LocalCenter;
m_lcC = m_bodyC.Sweep.LocalCenter;
m_lcD = m_bodyD.Sweep.LocalCenter;
m_mA = BodyA.InvMass;
m_mB = BodyB.InvMass;
m_mC = m_bodyC.InvMass;
m_mD = m_bodyD.InvMass;
m_iA = BodyA.InvI;
m_iB = BodyB.InvI;
m_iC = m_bodyC.InvI;
m_iD = m_bodyD.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;
//FVector2 cC = data.positions[m_indexC].c;
float aC = data.positions[m_indexC].a;
FVector2 vC = data.velocities[m_indexC].v;
float wC = data.velocities[m_indexC].w;
//FVector2 cD = data.positions[m_indexD].c;
float aD = data.positions[m_indexD].a;
FVector2 vD = data.velocities[m_indexD].v;
float wD = data.velocities[m_indexD].w;
Rot qA = new Rot(aA), qB = new Rot(aB), qC = new Rot(aC), qD = new Rot(aD);
m_mass = 0.0f;
if (m_typeA == JointType.Revolute)
{
m_JvAC = FVector2.Zero;
m_JwA = 1.0f;
m_JwC = 1.0f;
m_mass += m_iA + m_iC;
}
else
{
FVector2 u = MathUtils.Mul(qC, m_localAxisC);
FVector2 rC = MathUtils.Mul(qC, m_localAnchorC - m_lcC);
FVector2 rA = MathUtils.Mul(qA, m_localAnchorA - m_lcA);
m_JvAC = u;
m_JwC = MathUtils.Cross(rC, u);
m_JwA = MathUtils.Cross(rA, u);
m_mass += m_mC + m_mA + m_iC * m_JwC * m_JwC + m_iA * m_JwA * m_JwA;
}
if (m_typeB == JointType.Revolute)
{
m_JvBD = FVector2.Zero;
m_JwB = _ratio;
m_JwD = _ratio;
m_mass += _ratio * _ratio * (m_iB + m_iD);
}
else
{
FVector2 u = MathUtils.Mul(qD, m_localAxisD);
FVector2 rD = MathUtils.Mul(qD, m_localAnchorD - m_lcD);
FVector2 rB = MathUtils.Mul(qB, m_localAnchorB - m_lcB);
m_JvBD = _ratio * u;
m_JwD = _ratio * MathUtils.Cross(rD, u);
m_JwB = _ratio * MathUtils.Cross(rB, u);
m_mass += _ratio * _ratio * (m_mD + m_mB) + m_iD * m_JwD * m_JwD + m_iB * m_JwB * m_JwB;
}
// Compute effective mass.
m_mass = m_mass > 0.0f ? 1.0f / m_mass : 0.0f;
if (Settings.EnableWarmstarting)
{
vA += (m_mA * m_impulse) * m_JvAC;
wA += m_iA * m_impulse * m_JwA;
vB += (m_mB * m_impulse) * m_JvBD;
wB += m_iB * m_impulse * m_JwB;
vC -= (m_mC * m_impulse) * m_JvAC;
wC -= m_iC * m_impulse * m_JwC;
vD -= (m_mD * m_impulse) * m_JvBD;
wD -= m_iD * m_impulse * m_JwD;
}
else
{
m_impulse = 0.0f;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
data.velocities[m_indexC].v = vC;
data.velocities[m_indexC].w = wC;
data.velocities[m_indexD].v = vD;
data.velocities[m_indexD].w = wD;
}
// Requires Using System.Runtime.InteropServices.ComTypes
// Get all running instance by querying ROT
public static IEnumerable <RunningObjectTableEntry> GetActiveEntries()
{
// get Running Object Table ...
GetRunningObjectTable(0, out var Rot);
if (Rot == null)
{
yield break;
}
// get enumerator for ROT entries
Rot.EnumRunning(out var monikerEnumerator);
if (monikerEnumerator == null)
{
yield break;
}
monikerEnumerator.Reset();
var pNumFetched = new IntPtr();
var monikers = new IMoniker[1];
// go through all entries and identifies app instances
while (monikerEnumerator.Next(1, monikers, pNumFetched) == 0)
{
var ret = default(RunningObjectTableEntry);
try
{
CreateBindCtx(0, out var bindCtx);
if (bindCtx == null)
{
continue;
}
Rot.GetObject(monikers[0], out var ComObject);
monikers[0].GetDisplayName(bindCtx, null, out var displayName);
monikers[0].GetClassID(out var ClassId);
ret = new RunningObjectTableEntry()
{
Object = ComObject,
DisplayName = displayName,
ClassID = ClassId,
};
}
catch (Exception ex)
{
ex.Ignore();
}
if (ret != null)
{
yield return(ret);
}
}
}
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);
// 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(rA, uA);
float ruB = MathUtils.Cross(rB, 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(rA, PA);
cB += _invMassB * PB;
aB += _invIB * MathUtils.Cross(rB, 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);
}
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;
double aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
double wA = data.velocities[m_indexA].w;
// Vec2 cB = data.positions[m_indexB].c;
double aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
double 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.
Rot.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_localCenterA), m_rA);
Rot.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_localCenterB), 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]
double mA = m_invMassA, mB = m_invMassB;
double iA = m_invIA, iB = m_invIB;
Mat33 K = pool.popMat33();
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 > 0.0d)
{
K.getInverse22(m_mass);
double invM = iA + iB;
double m = invM > 0.0d ? 1.0d / invM : 0.0d;
double C = aB - aA - m_referenceAngle;
// Frequency
double omega = 2.0d * MathUtils.PI * m_frequencyHz;
// Damping coefficient
double d = 2.0d * m * m_dampingRatio * omega;
// Spring stiffness
double k = m * omega * omega;
// magic formulas
double h = data.step.dt;
m_gamma = h * (d + h * k);
m_gamma = m_gamma != 0.0d ? 1.0d / m_gamma : 0.0d;
m_bias = C * h * k * m_gamma;
invM += m_gamma;
m_mass.ez.z = invM != 0.0d ? 1.0d / invM : 0.0d;
}
else
{
K.getSymInverse33(m_mass);
m_gamma = 0.0d;
m_bias = 0.0d;
}
if (data.step.warmStarting)
{
Vec2 P = pool.popVec2();
// Scale impulses to support a variable time step.
m_impulse.mulLocal(data.step.dtRatio);
P.set(m_impulse.x, m_impulse.y);
vA.x -= mA * P.x;
vA.y -= mA * P.y;
wA -= iA * (Vec2.cross(m_rA, P) + m_impulse.z);
vB.x += mB * P.x;
vB.y += mB * P.y;
wB += iB * (Vec2.cross(m_rB, P) + m_impulse.z);
pool.pushVec2(1);
}
else
{
m_impulse.setZero();
}
// 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);
pool.pushMat33(1);
}
internal override void InitVelocityConstraints(ref SolverData data)
{
_indexB = BodyA.IslandIndex;
_localCenterB = BodyA.Sweep.LocalCenter;
_invMassB = BodyA.InvMass;
_invIB = 0;
FVector2 cB = data.positions[_indexB].c;
float aB = data.positions[_indexB].a;
FVector2 vB = data.velocities[_indexB].v;
float wB = data.velocities[_indexB].w;
Rot qB = new Rot(aB);
float mass = BodyA.Mass;
// Frequency
float omega = 2.0f * FSSettings.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 > FSSettings.Epsilon);
_gamma = h * (d + h * k);
if (!Mathf.Approximately(_gamma, 0.0f))
_gamma = 1.0f / _gamma;
_beta = h * k * _gamma;
// Compute the effective mass matrix.
_rB = MathUtils.Mul(qB, LocalAnchorB - _localCenterB);
// 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]
var K = new Mat22();
K.ex.X = _invMassB + _invIB * _rB.Y * _rB.Y + _gamma;
K.ex.Y = -_invIB * _rB.X * _rB.Y;
K.ey.X = K.ex.Y;
K.ey.Y = _invMassB + _invIB * _rB.X * _rB.X + _gamma;
_mass = K.Inverse;
_C = cB + _rB - _targetA;
_C *= _beta;
// Cheat with some damping
wB *= 0.98f;
// if (Settings.EnableWarmstarting)
// {
_impulse *= data.step.dtRatio;
vB += _invMassB * _impulse;
wB += _invIB * MathUtils.Cross(_rB, _impulse);
// }
// else
// _impulse = FVector2.Zero;
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;
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)
{
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;
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 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 = FVector2.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;
FVector2 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;
}
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)
{
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);
// Get the pulley axes.
m_uA = cA + m_rA - GroundAnchorA;
m_uB = cB + m_rB - GroundAnchorB;
float lengthA = m_uA.Length();
float lengthB = m_uB.Length();
if (lengthA > 10.0f * Settings.LinearSlop)
{
m_uA *= 1.0f / lengthA;
}
else
{
m_uA = FVector2.Zero;
}
if (lengthB > 10.0f * Settings.LinearSlop)
{
m_uB *= 1.0f / lengthB;
}
else
{
m_uB = FVector2.Zero;
}
// Compute effective mass.
float ruA = MathUtils.Cross(m_rA, m_uA);
float ruB = MathUtils.Cross(m_rB, m_uB);
float mA = m_invMassA + m_invIA * ruA * ruA;
float mB = m_invMassB + m_invIB * ruB * ruB;
m_mass = mA + Ratio * Ratio * mB;
if (m_mass > 0.0f)
{
m_mass = 1.0f / m_mass;
}
if (Settings.EnableWarmstarting)
{
// Scale impulses to support variable time steps.
_impulse *= data.step.dtRatio;
// Warm starting.
FVector2 PA = -(_impulse + _limitImpulse1) * m_uA;
FVector2 PB = (-Ratio * _impulse - _limitImpulse2) * m_uB;
vA += m_invMassA * PA;
wA += m_invIA * MathUtils.Cross(m_rA, PA);
vB += m_invMassB * PB;
wB += m_invIB * MathUtils.Cross(m_rB, PB);
}
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)
{
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;
// Vec2 cA = data.positions[m_indexA].c;
float aA = data.Positions[IndexA].A;
Vec2 vA = data.Velocities[IndexA].V;
float wA = data.Velocities[IndexA].W;
// Vec2 cB = data.positions[m_indexB].c;
float aB = data.Positions[IndexB].A;
Vec2 vB = data.Velocities[IndexB].V;
float wB = data.Velocities[IndexB].W;
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 temp = Pool.PopVec2();
qA.Set(aA);
qB.Set(aB);
// Compute the effective masses.
Rot.MulToOutUnsafe(qA, temp.Set(LocalAnchorA).SubLocal(LocalCenterA), RA);
Rot.MulToOutUnsafe(qB, temp.Set(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;
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 (m_motorEnabled == false || fixedRotation)
{
MotorImpulse = 0.0f;
}
if (m_limitEnabled && fixedRotation == false)
{
float jointAngle = aB - aA - ReferenceAngle;
if (MathUtils.Abs(UpperAngle - LowerAngle) < 2.0f * Settings.ANGULAR_SLOP)
{
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 (data.Step.WarmStarting)
{
Vec2 P = Pool.PopVec2();
// Scale impulses to support a variable time step.
Impulse.X *= data.Step.DtRatio;
Impulse.Y *= data.Step.DtRatio;
MotorImpulse *= data.Step.DtRatio;
P.X = Impulse.X;
P.Y = Impulse.Y;
vA.X -= mA * P.X;
vA.Y -= mA * P.Y;
wA -= iA * (Vec2.Cross(RA, P) + MotorImpulse + Impulse.Z);
vB.X += mB * P.X;
vB.Y += mB * P.Y;
wB += iB * (Vec2.Cross(RB, P) + MotorImpulse + Impulse.Z);
Pool.PushVec2(1);
}
else
{
Impulse.SetZero();
MotorImpulse = 0.0f;
}
data.Velocities[IndexA].V.Set(vA);
data.Velocities[IndexA].W = wA;
data.Velocities[IndexB].V.Set(vB);
data.Velocities[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;
//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;
}
public override bool SolvePositionConstraints(SolverData data)
{
Rot qA = Pool.PopRot();
Rot qB = Pool.PopRot();
Vec2 cA = data.Positions[IndexA].C;
float aA = data.Positions[IndexA].A;
Vec2 cB = data.Positions[IndexB].C;
float aB = data.Positions[IndexB].A;
qA.Set(aA);
qB.Set(aB);
float angularError = 0.0f;
float positionError = 0.0f;
bool fixedRotation = (InvIA + InvIB == 0.0f);
// Solve angular limit constraint.
if (m_limitEnabled && 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.MAX_ANGULAR_CORRECTION, Settings.MAX_ANGULAR_CORRECTION);
limitImpulse = (-MotorMass) * C;
angularError = MathUtils.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.ANGULAR_SLOP, -Settings.MAX_ANGULAR_CORRECTION, 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.ANGULAR_SLOP, 0.0f, Settings.MAX_ANGULAR_CORRECTION);
limitImpulse = (-MotorMass) * C;
}
aA -= InvIA * limitImpulse;
aB += 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();
Rot.MulToOutUnsafe(qA, C.Set(LocalAnchorA).SubLocal(LocalCenterA), rA);
Rot.MulToOutUnsafe(qB, C.Set(LocalAnchorB).SubLocal(LocalCenterB), rB);
C.Set(cB).AddLocal(rB).SubLocal(cA).SubLocal(rA);
positionError = C.Length();
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.SolveToOut(C, 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[IndexA].C.Set(cA);
data.Positions[IndexA].A = aA;
data.Positions[IndexB].C.Set(cB);
data.Positions[IndexB].A = aB;
Pool.PushRot(2);
return(positionError <= Settings.LINEAR_SLOP && angularError <= Settings.ANGULAR_SLOP);
}
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.dtRatio;
// 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;
}
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;
}
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;
// Handle singularity.
float length = _u.Length();
if (length > Settings.LinearSlop)
{
_u *= 1.0f / length;
}
else
{
_u = Vector2.Zero;
}
float crAu = MathUtils.Cross(_rA, _u);
float crBu = MathUtils.Cross(_rB, _u);
float invMass = _invMassA + _invIA * crAu * crAu + _invMassB + _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 -= _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)
{
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 = (float)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 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);
// Compute the effective mass matrix.
_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;
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;
}
if (Settings.EnableWarmstarting)
{
// 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(_rA, P) + _angularImpulse);
vB += mB * P;
wB += iB * (MathUtils.Cross(_rB, 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;
}
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 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;
}
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);
}
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 d = (cB - cA) + rB - rA;
Vector2 ay = MathUtils.Mul(qA, _localYAxis);
float sAy = MathUtils.Cross(d + rA, ay);
float sBy = MathUtils.Cross(rB, ay);
float C = Vector2.Dot(d, ay);
float k = _invMassA + _invMassB + _invIA * _sAy * _sAy + _invIB * _sBy * _sBy;
float impulse;
if (k != 0.0f)
{
impulse = -C / k;
}
else
{
impulse = 0.0f;
}
Vector2 P = impulse * ay;
float LA = impulse * sAy;
float LB = impulse * sBy;
cA -= _invMassA * P;
aA -= _invIA * LA;
cB += _invMassB * P;
aB += _invIB * LB;
data.positions[_indexA].c = cA;
data.positions[_indexA].a = aA;
data.positions[_indexB].c = cB;
data.positions[_indexB].a = aB;
return Math.Abs(C) <= 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;
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;
// Handle singularity.
float length = _u.Length();
if (length > Settings.LinearSlop)
{
_u *= 1.0f / length;
}
else
{
_u = Vector2.Zero;
}
float crAu = MathUtils.Cross(_rA, _u);
float crBu = MathUtils.Cross(_rB, _u);
float invMass = _invMassA + _invIA * crAu * crAu + _invMassB + _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;
}
#pragma warning disable 162
// ReSharper disable once ConditionIsAlwaysTrueOrFalse
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;
}
#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 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;
}
/// <summary>Inverse rotate a vector</summary>
/// <param name="q">The rotation matrix</param>
/// <param name="v">The value</param>
public static Vector2 MulT(Rot q, Vector2 v)
{
return(new Vector2(q.c * v.X + q.s * v.Y, -q.s * v.X + q.c * v.Y));
}
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;
}
public static Vector2 MulT(ref Rot rot, Vector2 axis)
{
return(MulT(rot, axis));
}
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;
}
public override void initVelocityConstraints(SolverData data)
{
m_indexA = m_bodyA.m_islandIndex;
m_indexB = m_bodyB.m_islandIndex;
m_indexC = m_bodyC.m_islandIndex;
m_indexD = m_bodyD.m_islandIndex;
m_lcA.set(m_bodyA.m_sweep.localCenter);
m_lcB.set(m_bodyB.m_sweep.localCenter);
m_lcC.set(m_bodyC.m_sweep.localCenter);
m_lcD.set(m_bodyD.m_sweep.localCenter);
m_mA = m_bodyA.m_invMass;
m_mB = m_bodyB.m_invMass;
m_mC = m_bodyC.m_invMass;
m_mD = m_bodyD.m_invMass;
m_iA = m_bodyA.m_invI;
m_iB = m_bodyB.m_invI;
m_iC = m_bodyC.m_invI;
m_iD = m_bodyD.m_invI;
// Vec2 cA = data.positions[m_indexA].c;
double aA = data.positions[m_indexA].a;
Vec2 vA = data.velocities[m_indexA].v;
double wA = data.velocities[m_indexA].w;
// Vec2 cB = data.positions[m_indexB].c;
double aB = data.positions[m_indexB].a;
Vec2 vB = data.velocities[m_indexB].v;
double wB = data.velocities[m_indexB].w;
// Vec2 cC = data.positions[m_indexC].c;
double aC = data.positions[m_indexC].a;
Vec2 vC = data.velocities[m_indexC].v;
double wC = data.velocities[m_indexC].w;
// Vec2 cD = data.positions[m_indexD].c;
double aD = data.positions[m_indexD].a;
Vec2 vD = data.velocities[m_indexD].v;
double wD = data.velocities[m_indexD].w;
Rot qA = pool.popRot(), qB = pool.popRot(), qC = pool.popRot(), qD = pool.popRot();
qA.set(aA);
qB.set(aB);
qC.set(aC);
qD.set(aD);
m_mass = 0.0d;
Vec2 temp = pool.popVec2();
if (m_typeA == JointType.REVOLUTE)
{
m_JvAC.setZero();
m_JwA = 1.0d;
m_JwC = 1.0d;
m_mass += m_iA + m_iC;
}
else
{
Vec2 rC = pool.popVec2();
Vec2 rA = pool.popVec2();
Rot.mulToOutUnsafe(qC, m_localAxisC, m_JvAC);
Rot.mulToOutUnsafe(qC, temp.set(m_localAnchorC).subLocal(m_lcC), rC);
Rot.mulToOutUnsafe(qA, temp.set(m_localAnchorA).subLocal(m_lcA), rA);
m_JwC = Vec2.cross(rC, m_JvAC);
m_JwA = Vec2.cross(rA, m_JvAC);
m_mass += m_mC + m_mA + m_iC * m_JwC * m_JwC + m_iA * m_JwA * m_JwA;
pool.pushVec2(2);
}
if (m_typeB == JointType.REVOLUTE)
{
m_JvBD.setZero();
m_JwB = m_ratio;
m_JwD = m_ratio;
m_mass += m_ratio * m_ratio * (m_iB + m_iD);
}
else
{
Vec2 u = pool.popVec2();
Vec2 rD = pool.popVec2();
Vec2 rB = pool.popVec2();
Rot.mulToOutUnsafe(qD, m_localAxisD, u);
Rot.mulToOutUnsafe(qD, temp.set(m_localAnchorD).subLocal(m_lcD), rD);
Rot.mulToOutUnsafe(qB, temp.set(m_localAnchorB).subLocal(m_lcB), rB);
m_JvBD.set(u).mulLocal(m_ratio);
m_JwD = m_ratio * Vec2.cross(rD, u);
m_JwB = m_ratio * Vec2.cross(rB, u);
m_mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * m_JwD * m_JwD + m_iB * m_JwB * m_JwB;
pool.pushVec2(3);
}
// Compute effective mass.
m_mass = m_mass > 0.0d ? 1.0d / m_mass : 0.0d;
if (data.step.warmStarting)
{
vA.x += (m_mA * m_impulse) * m_JvAC.x;
vA.y += (m_mA * m_impulse) * m_JvAC.y;
wA += m_iA * m_impulse * m_JwA;
vB.x += (m_mB * m_impulse) * m_JvBD.x;
vB.y += (m_mB * m_impulse) * m_JvBD.y;
wB += m_iB * m_impulse * m_JwB;
vC.x -= (m_mC * m_impulse) * m_JvAC.x;
vC.y -= (m_mC * m_impulse) * m_JvAC.y;
wC -= m_iC * m_impulse * m_JwC;
vD.x -= (m_mD * m_impulse) * m_JvBD.x;
vD.y -= (m_mD * m_impulse) * m_JvBD.y;
wD -= m_iD * m_impulse * m_JwD;
}
else
{
m_impulse = 0.0d;
}
pool.pushVec2(1);
pool.pushRot(4);
// data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
// data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
// data.velocities[m_indexC].v = vC;
data.velocities[m_indexC].w = wC;
// data.velocities[m_indexD].v = vD;
data.velocities[m_indexD].w = wD;
}
