public ContactConstraint()
{
for (int i = 0; i < Settings.MaxManifoldPoints; i++)
{
Points[i] = new ContactConstraintPoint();
}
}
public void StoreImpulses()
{
for (int i = 0; i < _constraintCount; ++i)
{
ContactConstraint c = Constraints[i];
Manifold m = c.Manifold;
for (int j = 0; j < c.PointCount; ++j)
{
ManifoldPoint pj = m.Points[j];
ContactConstraintPoint cp = c.Points[j];
pj.NormalImpulse = cp.NormalImpulse;
pj.TangentImpulse = cp.TangentImpulse;
m.Points[j] = pj;
}
c.Manifold = m;
_contacts[i].Manifold = m;
}
}
public void WarmStart()
{
// Warm start.
for (int i = 0; i < _constraintCount; ++i)
{
ContactConstraint c = Constraints[i];
float tangentx = c.Normal.Y;
float tangenty = -c.Normal.X;
for (int j = 0; j < c.PointCount; ++j)
{
ContactConstraintPoint ccp = c.Points[j];
float px = ccp.NormalImpulse * c.Normal.X + ccp.TangentImpulse * tangentx;
float py = ccp.NormalImpulse * c.Normal.Y + ccp.TangentImpulse * tangenty;
c.BodyA.AngularVelocityInternal -= c.BodyA.InvI * (ccp.rA.X * py - ccp.rA.Y * px);
c.BodyA.LinearVelocityInternal.X -= c.BodyA.InvMass * px;
c.BodyA.LinearVelocityInternal.Y -= c.BodyA.InvMass * py;
c.BodyB.AngularVelocityInternal += c.BodyB.InvI * (ccp.rB.X * py - ccp.rB.Y * px);
c.BodyB.LinearVelocityInternal.X += c.BodyB.InvMass * px;
c.BodyB.LinearVelocityInternal.Y += c.BodyB.InvMass * py;
}
}
}
public void Reset(Contact[] contacts, int contactCount, float impulseRatio, bool warmstarting)
{
_contacts = contacts;
_constraintCount = contactCount;
// grow the array
if (Constraints == null || Constraints.Length < _constraintCount)
{
Constraints = new ContactConstraint[_constraintCount * 2];
for (int i = 0; i < Constraints.Length; i++)
{
Constraints[i] = new ContactConstraint();
}
}
// Initialize position independent portions of the constraints.
for (int i = 0; i < _constraintCount; ++i)
{
Contact contact = contacts[i];
Fixture fixtureA = contact.FixtureA;
Fixture fixtureB = contact.FixtureB;
Shape shapeA = fixtureA.Shape;
Shape shapeB = fixtureB.Shape;
float radiusA = shapeA.Radius;
float radiusB = shapeB.Radius;
Body bodyA = fixtureA.Body;
Body bodyB = fixtureB.Body;
Manifold manifold = contact.Manifold;
Debug.Assert(manifold.PointCount > 0);
ContactConstraint cc = Constraints[i];
cc.Friction = Settings.MixFriction(fixtureA.Friction, fixtureB.Friction);
cc.Restitution = Settings.MixRestitution(fixtureA.Restitution, fixtureB.Restitution);
cc.BodyA = bodyA;
cc.BodyB = bodyB;
cc.Manifold = manifold;
cc.Normal = Vector2.Zero;
cc.PointCount = manifold.PointCount;
cc.LocalNormal = manifold.LocalNormal;
cc.LocalPoint = manifold.LocalPoint;
cc.RadiusA = radiusA;
cc.RadiusB = radiusB;
cc.Type = manifold.Type;
for (int j = 0; j < cc.PointCount; ++j)
{
ManifoldPoint cp = manifold.Points[j];
ContactConstraintPoint ccp = cc.Points[j];
if (warmstarting)
{
ccp.NormalImpulse = impulseRatio * cp.NormalImpulse;
ccp.TangentImpulse = impulseRatio * cp.TangentImpulse;
}
else
{
ccp.NormalImpulse = 0.0f;
ccp.TangentImpulse = 0.0f;
}
ccp.LocalPoint = cp.LocalPoint;
ccp.rA = Vector2.Zero;
ccp.rB = Vector2.Zero;
ccp.NormalMass = 0.0f;
ccp.TangentMass = 0.0f;
ccp.VelocityBias = 0.0f;
}
cc.K.SetZero();
cc.NormalMass.SetZero();
}
}
public void SolveVelocityConstraints()
{
for (int i = 0; i < _constraintCount; ++i)
{
ContactConstraint c = Constraints[i];
float wA = c.BodyA.AngularVelocityInternal;
float wB = c.BodyB.AngularVelocityInternal;
float tangentx = c.Normal.Y;
float tangenty = -c.Normal.X;
float friction = c.Friction;
Debug.Assert(c.PointCount == 1 || c.PointCount == 2);
// Solve tangent constraints
for (int j = 0; j < c.PointCount; ++j)
{
ContactConstraintPoint ccp = c.Points[j];
float lambda = ccp.TangentMass *
-((c.BodyB.LinearVelocityInternal.X + (-wB * ccp.rB.Y) -
c.BodyA.LinearVelocityInternal.X - (-wA * ccp.rA.Y)) * tangentx +
(c.BodyB.LinearVelocityInternal.Y + (wB * ccp.rB.X) -
c.BodyA.LinearVelocityInternal.Y - (wA * ccp.rA.X)) * tangenty);
// MathUtils.Clamp the accumulated force
float maxFriction = friction * ccp.NormalImpulse;
float newImpulse = Math.Max(-maxFriction, Math.Min(ccp.TangentImpulse + lambda, maxFriction));
lambda = newImpulse - ccp.TangentImpulse;
// Apply contact impulse
float px = lambda * tangentx;
float py = lambda * tangenty;
c.BodyA.LinearVelocityInternal.X -= c.BodyA.InvMass * px;
c.BodyA.LinearVelocityInternal.Y -= c.BodyA.InvMass * py;
wA -= c.BodyA.InvI * (ccp.rA.X * py - ccp.rA.Y * px);
c.BodyB.LinearVelocityInternal.X += c.BodyB.InvMass * px;
c.BodyB.LinearVelocityInternal.Y += c.BodyB.InvMass * py;
wB += c.BodyB.InvI * (ccp.rB.X * py - ccp.rB.Y * px);
ccp.TangentImpulse = newImpulse;
}
// Solve normal constraints
if (c.PointCount == 1)
{
ContactConstraintPoint ccp = c.Points[0];
// Relative velocity at contact
// Compute normal impulse
float lambda = -ccp.NormalMass *
((c.BodyB.LinearVelocityInternal.X + (-wB * ccp.rB.Y) -
c.BodyA.LinearVelocityInternal.X - (-wA * ccp.rA.Y)) * c.Normal.X +
(c.BodyB.LinearVelocityInternal.Y + (wB * ccp.rB.X) -
c.BodyA.LinearVelocityInternal.Y -
(wA * ccp.rA.X)) * c.Normal.Y - ccp.VelocityBias);
// Clamp the accumulated impulse
float newImpulse = Math.Max(ccp.NormalImpulse + lambda, 0.0f);
lambda = newImpulse - ccp.NormalImpulse;
// Apply contact impulse
float px = lambda * c.Normal.X;
float py = lambda * c.Normal.Y;
c.BodyA.LinearVelocityInternal.X -= c.BodyA.InvMass * px;
c.BodyA.LinearVelocityInternal.Y -= c.BodyA.InvMass * py;
wA -= c.BodyA.InvI * (ccp.rA.X * py - ccp.rA.Y * px);
c.BodyB.LinearVelocityInternal.X += c.BodyB.InvMass * px;
c.BodyB.LinearVelocityInternal.Y += c.BodyB.InvMass * py;
wB += c.BodyB.InvI * (ccp.rB.X * py - ccp.rB.Y * px);
ccp.NormalImpulse = newImpulse;
}
else
{
// Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
// Build the mini LCP for this contact patch
//
// vn = A * x + b, vn >= 0, , vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
//
// A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
// b = vn_0 - velocityBias
//
// The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i
// implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases
// vn1 = 0 and vn2 = 0, x1 = 0 and x2 = 0, x1 = 0 and vn2 = 0, x2 = 0 and vn1 = 0 need to be tested. The first valid
// solution that satisfies the problem is chosen.
//
// In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires
// that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i).
//
// Substitute:
//
// x = x' - a
//
// Plug into above equation:
//
// vn = A * x + b
// = A * (x' - a) + b
// = A * x' + b - A * a
// = A * x' + b'
// b' = b - A * a;
ContactConstraintPoint cp1 = c.Points[0];
ContactConstraintPoint cp2 = c.Points[1];
float ax = cp1.NormalImpulse;
float ay = cp2.NormalImpulse;
Debug.Assert(ax >= 0.0f && ay >= 0.0f);
// Relative velocity at contact
// Compute normal velocity
float vn1 = (c.BodyB.LinearVelocityInternal.X + (-wB * cp1.rB.Y) - c.BodyA.LinearVelocityInternal.X -
(-wA * cp1.rA.Y)) * c.Normal.X +
(c.BodyB.LinearVelocityInternal.Y + (wB * cp1.rB.X) - c.BodyA.LinearVelocityInternal.Y -
(wA * cp1.rA.X)) * c.Normal.Y;
float vn2 = (c.BodyB.LinearVelocityInternal.X + (-wB * cp2.rB.Y) - c.BodyA.LinearVelocityInternal.X -
(-wA * cp2.rA.Y)) * c.Normal.X +
(c.BodyB.LinearVelocityInternal.Y + (wB * cp2.rB.X) - c.BodyA.LinearVelocityInternal.Y -
(wA * cp2.rA.X)) * c.Normal.Y;
float bx = vn1 - cp1.VelocityBias - (c.K.Col1.X * ax + c.K.Col2.X * ay);
float by = vn2 - cp2.VelocityBias - (c.K.Col1.Y * ax + c.K.Col2.Y * ay);
float xx = -(c.NormalMass.Col1.X * bx + c.NormalMass.Col2.X * by);
float xy = -(c.NormalMass.Col1.Y * bx + c.NormalMass.Col2.Y * by);
while (true)
{
//
// Case 1: vn = 0
//
// 0 = A * x' + b'
//
// Solve for x':
//
// x' = - inv(A) * b'
//
if (xx >= 0.0f && xy >= 0.0f)
{
// Resubstitute for the incremental impulse
float dx = xx - ax;
float dy = xy - ay;
// Apply incremental impulse
float p1x = dx * c.Normal.X;
float p1y = dx * c.Normal.Y;
float p2x = dy * c.Normal.X;
float p2y = dy * c.Normal.Y;
float p12x = p1x + p2x;
float p12y = p1y + p2y;
c.BodyA.LinearVelocityInternal.X -= c.BodyA.InvMass * p12x;
c.BodyA.LinearVelocityInternal.Y -= c.BodyA.InvMass * p12y;
wA -= c.BodyA.InvI * ((cp1.rA.X * p1y - cp1.rA.Y * p1x) + (cp2.rA.X * p2y - cp2.rA.Y * p2x));
c.BodyB.LinearVelocityInternal.X += c.BodyB.InvMass * p12x;
c.BodyB.LinearVelocityInternal.Y += c.BodyB.InvMass * p12y;
wB += c.BodyB.InvI * ((cp1.rB.X * p1y - cp1.rB.Y * p1x) + (cp2.rB.X * p2y - cp2.rB.Y * p2x));
// Accumulate
cp1.NormalImpulse = xx;
cp2.NormalImpulse = xy;
#if B2_DEBUG_SOLVER
float k_errorTol = 1e-3f;
// Postconditions
dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
// Compute normal velocity
vn1 = Vector2.Dot(dv1, normal);
vn2 = Vector2.Dot(dv2, normal);
Debug.Assert(MathUtils.Abs(vn1 - cp1.velocityBias) < k_errorTol);
Debug.Assert(MathUtils.Abs(vn2 - cp2.velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 2: vn1 = 0 and x2 = 0
//
// 0 = a11 * x1' + a12 * 0 + b1'
// vn2 = a21 * x1' + a22 * 0 + b2'
//
xx = -cp1.NormalMass * bx;
xy = 0.0f;
vn1 = 0.0f;
vn2 = c.K.Col1.Y * xx + by;
if (xx >= 0.0f && vn2 >= 0.0f)
{
// Resubstitute for the incremental impulse
float dx = xx - ax;
float dy = xy - ay;
// Apply incremental impulse
float p1x = dx * c.Normal.X;
float p1y = dx * c.Normal.Y;
float p2x = dy * c.Normal.X;
float p2y = dy * c.Normal.Y;
float p12x = p1x + p2x;
float p12y = p1y + p2y;
c.BodyA.LinearVelocityInternal.X -= c.BodyA.InvMass * p12x;
c.BodyA.LinearVelocityInternal.Y -= c.BodyA.InvMass * p12y;
wA -= c.BodyA.InvI * ((cp1.rA.X * p1y - cp1.rA.Y * p1x) + (cp2.rA.X * p2y - cp2.rA.Y * p2x));
c.BodyB.LinearVelocityInternal.X += c.BodyB.InvMass * p12x;
c.BodyB.LinearVelocityInternal.Y += c.BodyB.InvMass * p12y;
wB += c.BodyB.InvI * ((cp1.rB.X * p1y - cp1.rB.Y * p1x) + (cp2.rB.X * p2y - cp2.rB.Y * p2x));
// Accumulate
cp1.NormalImpulse = xx;
cp2.NormalImpulse = xy;
#if B2_DEBUG_SOLVER
// Postconditions
dv1 = vB + MathUtils.Cross(wB, cp1.rB) - vA - MathUtils.Cross(wA, cp1.rA);
// Compute normal velocity
vn1 = Vector2.Dot(dv1, normal);
Debug.Assert(MathUtils.Abs(vn1 - cp1.velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 3: vn2 = 0 and x1 = 0
//
// vn1 = a11 * 0 + a12 * x2' + b1'
// 0 = a21 * 0 + a22 * x2' + b2'
//
xx = 0.0f;
xy = -cp2.NormalMass * by;
vn1 = c.K.Col2.X * xy + bx;
vn2 = 0.0f;
if (xy >= 0.0f && vn1 >= 0.0f)
{
// Resubstitute for the incremental impulse
float dx = xx - ax;
float dy = xy - ay;
// Apply incremental impulse
float p1x = dx * c.Normal.X;
float p1y = dx * c.Normal.Y;
float p2x = dy * c.Normal.X;
float p2y = dy * c.Normal.Y;
float p12x = p1x + p2x;
float p12y = p1y + p2y;
c.BodyA.LinearVelocityInternal.X -= c.BodyA.InvMass * p12x;
c.BodyA.LinearVelocityInternal.Y -= c.BodyA.InvMass * p12y;
wA -= c.BodyA.InvI * ((cp1.rA.X * p1y - cp1.rA.Y * p1x) + (cp2.rA.X * p2y - cp2.rA.Y * p2x));
c.BodyB.LinearVelocityInternal.X += c.BodyB.InvMass * p12x;
c.BodyB.LinearVelocityInternal.Y += c.BodyB.InvMass * p12y;
wB += c.BodyB.InvI * ((cp1.rB.X * p1y - cp1.rB.Y * p1x) + (cp2.rB.X * p2y - cp2.rB.Y * p2x));
// Accumulate
cp1.NormalImpulse = xx;
cp2.NormalImpulse = xy;
#if B2_DEBUG_SOLVER
// Postconditions
dv2 = vB + MathUtils.Cross(wB, cp2.rB) - vA - MathUtils.Cross(wA, cp2.rA);
// Compute normal velocity
vn2 = Vector2.Dot(dv2, normal);
Debug.Assert(MathUtils.Abs(vn2 - cp2.velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 4: x1 = 0 and x2 = 0
//
// vn1 = b1
// vn2 = b2;
xx = 0.0f;
xy = 0.0f;
vn1 = bx;
vn2 = by;
if (vn1 >= 0.0f && vn2 >= 0.0f)
{
// Resubstitute for the incremental impulse
float dx = xx - ax;
float dy = xy - ay;
// Apply incremental impulse
float p1x = dx * c.Normal.X;
float p1y = dx * c.Normal.Y;
float p2x = dy * c.Normal.X;
float p2y = dy * c.Normal.Y;
float p12x = p1x + p2x;
float p12y = p1y + p2y;
c.BodyA.LinearVelocityInternal.X -= c.BodyA.InvMass * p12x;
c.BodyA.LinearVelocityInternal.Y -= c.BodyA.InvMass * p12y;
wA -= c.BodyA.InvI * ((cp1.rA.X * p1y - cp1.rA.Y * p1x) + (cp2.rA.X * p2y - cp2.rA.Y * p2x));
c.BodyB.LinearVelocityInternal.X += c.BodyB.InvMass * p12x;
c.BodyB.LinearVelocityInternal.Y += c.BodyB.InvMass * p12y;
wB += c.BodyB.InvI * ((cp1.rB.X * p1y - cp1.rB.Y * p1x) + (cp2.rB.X * p2y - cp2.rB.Y * p2x));
// Accumulate
cp1.NormalImpulse = xx;
cp2.NormalImpulse = xy;
break;
}
// No solution, give up. This is hit sometimes, but it doesn't seem to matter.
break;
}
}
c.BodyA.AngularVelocityInternal = wA;
c.BodyB.AngularVelocityInternal = wB;
}
}
public void InitializeVelocityConstraints()
{
for (int i = 0; i < _constraintCount; ++i)
{
ContactConstraint cc = Constraints[i];
float radiusA = cc.RadiusA;
float radiusB = cc.RadiusB;
Body bodyA = cc.BodyA;
Body bodyB = cc.BodyB;
Manifold manifold = cc.Manifold;
Vector2 vA = bodyA.LinearVelocity;
Vector2 vB = bodyB.LinearVelocity;
float wA = bodyA.AngularVelocity;
float wB = bodyB.AngularVelocity;
Debug.Assert(manifold.PointCount > 0);
FixedArray2 <Vector2> points;
Collision.Collision.GetWorldManifold(ref manifold, ref bodyA.Xf, radiusA, ref bodyB.Xf, radiusB,
out cc.Normal, out points);
Vector2 tangent = new Vector2(cc.Normal.Y, -cc.Normal.X);
for (int j = 0; j < cc.PointCount; ++j)
{
ContactConstraintPoint ccp = cc.Points[j];
ccp.rA = points[j] - bodyA.Sweep.C;
ccp.rB = points[j] - bodyB.Sweep.C;
float rnA = ccp.rA.X * cc.Normal.Y - ccp.rA.Y * cc.Normal.X;
float rnB = ccp.rB.X * cc.Normal.Y - ccp.rB.Y * cc.Normal.X;
rnA *= rnA;
rnB *= rnB;
float kNormal = bodyA.InvMass + bodyB.InvMass + bodyA.InvI * rnA + bodyB.InvI * rnB;
Debug.Assert(kNormal > Settings.Epsilon);
ccp.NormalMass = 1.0f / kNormal;
float rtA = ccp.rA.X * tangent.Y - ccp.rA.Y * tangent.X;
float rtB = ccp.rB.X * tangent.Y - ccp.rB.Y * tangent.X;
rtA *= rtA;
rtB *= rtB;
float kTangent = bodyA.InvMass + bodyB.InvMass + bodyA.InvI * rtA + bodyB.InvI * rtB;
Debug.Assert(kTangent > Settings.Epsilon);
ccp.TangentMass = 1.0f / kTangent;
// Setup a velocity bias for restitution.
ccp.VelocityBias = 0.0f;
float vRel = cc.Normal.X * (vB.X + -wB * ccp.rB.Y - vA.X - -wA * ccp.rA.Y) +
cc.Normal.Y * (vB.Y + wB * ccp.rB.X - vA.Y - wA * ccp.rA.X);
if (vRel < -Settings.VelocityThreshold)
{
ccp.VelocityBias = -cc.Restitution * vRel;
}
}
// If we have two points, then prepare the block solver.
if (cc.PointCount == 2)
{
ContactConstraintPoint ccp1 = cc.Points[0];
ContactConstraintPoint ccp2 = cc.Points[1];
float invMassA = bodyA.InvMass;
float invIA = bodyA.InvI;
float invMassB = bodyB.InvMass;
float invIB = bodyB.InvI;
float rn1A = ccp1.rA.X * cc.Normal.Y - ccp1.rA.Y * cc.Normal.X;
float rn1B = ccp1.rB.X * cc.Normal.Y - ccp1.rB.Y * cc.Normal.X;
float rn2A = ccp2.rA.X * cc.Normal.Y - ccp2.rA.Y * cc.Normal.X;
float rn2B = ccp2.rB.X * cc.Normal.Y - ccp2.rB.Y * cc.Normal.X;
float k11 = invMassA + invMassB + invIA * rn1A * rn1A + invIB * rn1B * rn1B;
float k22 = invMassA + invMassB + invIA * rn2A * rn2A + invIB * rn2B * rn2B;
float k12 = invMassA + invMassB + invIA * rn1A * rn2A + invIB * rn1B * rn2B;
// Ensure a reasonable condition number.
const float k_maxConditionNumber = 100.0f;
if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12))
{
// K is safe to invert.
cc.K.Col1.X = k11;
cc.K.Col1.Y = k12;
cc.K.Col2.X = k12;
cc.K.Col2.Y = k22;
float a = cc.K.Col1.X, b = cc.K.Col2.X, c = cc.K.Col1.Y, d = cc.K.Col2.Y;
float det = a * d - b * c;
if (det != 0.0f)
{
det = 1.0f / det;
}
cc.NormalMass.Col1.X = det * d;
cc.NormalMass.Col1.Y = -det * c;
cc.NormalMass.Col2.X = -det * b;
cc.NormalMass.Col2.Y = det * a;
}
else
{
// The constraints are redundant, just use one.
// TODO_ERIN use deepest?
cc.PointCount = 1;
}
}
}
}