b2PolygonShape::b2PolygonShape(const b2ShapeDef* def)
: b2Shape(def)
{
b2Assert(def->type == e_polygonShape);
m_type = e_polygonShape;
const b2PolygonDef* poly = (const b2PolygonDef*)def;
// Get the vertices transformed into the body frame.
m_vertexCount = poly->vertexCount;
b2Assert(3 <= m_vertexCount && m_vertexCount <= b2_maxPolygonVertices);
// Copy vertices.
for (int32 i = 0; i < m_vertexCount; ++i)
{
m_vertices[i] = poly->vertices[i];
}
// Compute normals. Ensure the edges have non-zero length.
for (int32 i = 0; i < m_vertexCount; ++i)
{
int32 i1 = i;
int32 i2 = i + 1 < m_vertexCount ? i + 1 : 0;
b2Vec2 edge = m_vertices[i2] - m_vertices[i1];
b2Assert(edge.LengthSquared() > B2_FLT_EPSILON * B2_FLT_EPSILON);
m_normals[i] = b2Cross(edge, 1.0f);
m_normals[i].Normalize();
}
#ifdef _DEBUG
// Ensure the polygon is convex.
for (int32 i = 0; i < m_vertexCount; ++i)
{
for (int32 j = 0; j < m_vertexCount; ++j)
{
// Don't check vertices on the current edge.
if (j == i || j == (i + 1) % m_vertexCount)
{
continue;
}
// Your polygon is non-convex (it has an indentation).
// Or your polygon is too skinny.
float32 s = b2Dot(m_normals[i], m_vertices[j] - m_vertices[i]);
b2Assert(s < -b2_linearSlop);
}
}
// Ensure the polygon is counter-clockwise.
for (int32 i = 1; i < m_vertexCount; ++i)
{
float32 cross = b2Cross(m_normals[i-1], m_normals[i]);
// Keep asinf happy.
cross = b2Clamp(cross, -1.0f, 1.0f);
// You have consecutive edges that are almost parallel on your polygon.
float32 angle = asinf(cross);
b2Assert(angle > b2_angularSlop);
}
#endif
// Compute the polygon centroid.
m_centroid = ComputeCentroid(poly->vertices, poly->vertexCount);
// Compute the oriented bounding box.
ComputeOBB(&m_obb, m_vertices, m_vertexCount);
// Create core polygon shape by shifting edges inward.
// Also compute the min/max radius for CCD.
for (int32 i = 0; i < m_vertexCount; ++i)
{
int32 i1 = i - 1 >= 0 ? i - 1 : m_vertexCount - 1;
int32 i2 = i;
b2Vec2 n1 = m_normals[i1];
b2Vec2 n2 = m_normals[i2];
b2Vec2 v = m_vertices[i] - m_centroid;;
b2Vec2 d;
d.x = b2Dot(n1, v) - b2_toiSlop;
d.y = b2Dot(n2, v) - b2_toiSlop;
// Shifting the edge inward by b2_toiSlop should
// not cause the plane to pass the centroid.
// Your shape has a radius/extent less than b2_toiSlop.
//TME printf("dx=%f dy=%f\n",(float)d.x,(float)d.y);
b2Assert(d.x >= 0.0f);
b2Assert(d.y >= 0.0f);
b2Mat22 A;
A.col1.x = n1.x; A.col2.x = n1.y;
A.col1.y = n2.x; A.col2.y = n2.y;
m_coreVertices[i] = A.Solve(d) + m_centroid;
}
}
void b2ContactSolver::SolveVelocityConstraints()
{
for (int32 i = 0; i < m_count; ++i)
{
b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
int32 indexA = vc->indexA;
int32 indexB = vc->indexB;
float32 mA = vc->invMassA;
float32 iA = vc->invIA;
float32 mB = vc->invMassB;
float32 iB = vc->invIB;
int32 pointCount = vc->pointCount;
b2Vec2 vA = m_velocities[indexA].v;
float32 wA = m_velocities[indexA].w;
b2Vec2 vB = m_velocities[indexB].v;
float32 wB = m_velocities[indexB].w;
b2Vec2 normal = vc->normal;
b2Vec2 tangent = b2Cross(normal, 1.0f);
float32 friction = vc->friction;
b2Assert(pointCount == 1 || pointCount == 2);
// Solve tangent constraints first because non-penetration is more important
// than friction.
for (int32 j = 0; j < pointCount; ++j)
{
b2VelocityConstraintPoint* vcp = vc->points + j;
// Relative velocity at contact
b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA);
// Compute tangent force
float32 vt = b2Dot(dv, tangent);
float32 lambda = vcp->tangentMass * (-vt);
// b2Clamp the accumulated force
float32 maxFriction = friction * vcp->normalImpulse;
float32 newImpulse = b2Clamp(vcp->tangentImpulse + lambda, -maxFriction, maxFriction);
lambda = newImpulse - vcp->tangentImpulse;
vcp->tangentImpulse = newImpulse;
// Apply contact impulse
b2Vec2 P = lambda * tangent;
vA -= mA * P;
wA -= iA * b2Cross(vcp->rA, P);
vB += mB * P;
wB += iB * b2Cross(vcp->rB, P);
}
// Solve normal constraints
if (vc->pointCount == 1)
{
b2VelocityConstraintPoint* vcp = vc->points + 0;
// Relative velocity at contact
b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA);
// Compute normal impulse
float32 vn = b2Dot(dv, normal);
float32 lambda = -vcp->normalMass * (vn - vcp->velocityBias);
// b2Clamp the accumulated impulse
float32 newImpulse = b2Max(vcp->normalImpulse + lambda, 0.0f);
lambda = newImpulse - vcp->normalImpulse;
vcp->normalImpulse = newImpulse;
// Apply contact impulse
b2Vec2 P = lambda * normal;
vA -= mA * P;
wA -= iA * b2Cross(vcp->rA, P);
vB += mB * P;
wB += iB * b2Cross(vcp->rB, P);
}
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 = vn0 - 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 = a + d
//
// a := old total impulse
// x := new total impulse
// d := incremental impulse
//
// For the current iteration we extend the formula for the incremental impulse
// to compute the new total impulse:
//
// vn = A * d + b
// = A * (x - a) + b
// = A * x + b - A * a
// = A * x + b'
// b' = b - A * a;
b2VelocityConstraintPoint* cp1 = vc->points + 0;
b2VelocityConstraintPoint* cp2 = vc->points + 1;
b2Vec2 a(cp1->normalImpulse, cp2->normalImpulse);
b2Assert(a.x >= 0.0f && a.y >= 0.0f);
// Relative velocity at contact
b2Vec2 dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
b2Vec2 dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
float32 vn1 = b2Dot(dv1, normal);
float32 vn2 = b2Dot(dv2, normal);
b2Vec2 b;
b.x = vn1 - cp1->velocityBias;
b.y = vn2 - cp2->velocityBias;
// Compute b'
b -= b2Mul(vc->K, a);
const float32 k_errorTol = 1e-3f;
B2_NOT_USED(k_errorTol);
for (;;)
{
//
// Case 1: vn = 0
//
// 0 = A * x + b'
//
// Solve for x:
//
// x = - inv(A) * b'
//
b2Vec2 x = - b2Mul(vc->normalMass, b);
if (x.x >= 0.0f && x.y >= 0.0f)
{
// Get the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += mB * (P1 + P2);
wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
vn1 = b2Dot(dv1, normal);
vn2 = b2Dot(dv2, normal);
b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
b2Assert(b2Abs(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'
//
x.x = - cp1->normalMass * b.x;
x.y = 0.0f;
vn1 = 0.0f;
vn2 = vc->K.ex.y * x.x + b.y;
if (x.x >= 0.0f && vn2 >= 0.0f)
{
// Get the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += mB * (P1 + P2);
wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
// Compute normal velocity
vn1 = b2Dot(dv1, normal);
b2Assert(b2Abs(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'
//
x.x = 0.0f;
x.y = - cp2->normalMass * b.y;
vn1 = vc->K.ey.x * x.y + b.x;
vn2 = 0.0f;
if (x.y >= 0.0f && vn1 >= 0.0f)
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += mB * (P1 + P2);
wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
vn2 = b2Dot(dv2, normal);
b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 4: x1 = 0 and x2 = 0
//
// vn1 = b1
// vn2 = b2;
x.x = 0.0f;
x.y = 0.0f;
vn1 = b.x;
vn2 = b.y;
if (vn1 >= 0.0f && vn2 >= 0.0f )
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= mA * (P1 + P2);
wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += mB * (P1 + P2);
wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
break;
}
// No solution, give up. This is hit sometimes, but it doesn't seem to matter.
break;
}
}
m_velocities[indexA].v = vA;
m_velocities[indexA].w = wA;
m_velocities[indexB].v = vB;
m_velocities[indexB].w = wB;
}
}
void b2CollidePolygonAndCircle(
b2Manifold* manifold,
const b2PolygonShape* polygon, const b2Transform& xf1,
const b2CircleShape* circle, const b2Transform& xf2)
{
manifold->m_pointCount = 0;
// Compute circle position in the frame of the polygon.
b2Vec2 c = b2Mul(xf2, circle->m_p);
b2Vec2 cLocal = b2MulT(xf1, c);
// Find the min separating edge.
int32 normalIndex = 0;
float32 separation = -b2_maxFloat;
float32 radius = polygon->m_radius + circle->m_radius;
int32 vertexCount = polygon->m_vertexCount;
const b2Vec2* vertices = polygon->m_vertices;
const b2Vec2* normals = polygon->m_normals;
for (int32 i = 0; i < vertexCount; ++i)
{
float32 s = b2Dot(normals[i], cLocal - vertices[i]);
if (s > radius)
{
// Early out.
return;
}
if (s > separation)
{
separation = s;
normalIndex = i;
}
}
// Vertices that subtend the incident face.
int32 vertIndex1 = normalIndex;
int32 vertIndex2 = vertIndex1 + 1 < vertexCount ? vertIndex1 + 1 : 0;
b2Vec2 v1 = vertices[vertIndex1];
b2Vec2 v2 = vertices[vertIndex2];
// If the center is inside the polygon ...
if (separation < b2_epsilon)
{
manifold->m_pointCount = 1;
manifold->m_type = b2Manifold::e_faceA;
manifold->m_localPlaneNormal = normals[normalIndex];
manifold->m_localPoint = 0.5f * (v1 + v2);
manifold->m_points[0].m_localPoint = circle->m_p;
manifold->m_points[0].m_id.key = 0;
return;
}
// Compute barycentric coordinates
float32 u1 = b2Dot(cLocal - v1, v2 - v1);
float32 u2 = b2Dot(cLocal - v2, v1 - v2);
if (u1 <= 0.0f)
{
if (b2DistanceSquared(cLocal, v1) > radius * radius)
{
return;
}
manifold->m_pointCount = 1;
manifold->m_type = b2Manifold::e_faceA;
manifold->m_localPlaneNormal = cLocal - v1;
manifold->m_localPlaneNormal.Normalize();
manifold->m_localPoint = v1;
manifold->m_points[0].m_localPoint = circle->m_p;
manifold->m_points[0].m_id.key = 0;
}
else if (u2 <= 0.0f)
{
if (b2DistanceSquared(cLocal, v2) > radius * radius)
{
return;
}
manifold->m_pointCount = 1;
manifold->m_type = b2Manifold::e_faceA;
manifold->m_localPlaneNormal = cLocal - v2;
manifold->m_localPlaneNormal.Normalize();
manifold->m_localPoint = v2;
manifold->m_points[0].m_localPoint = circle->m_p;
manifold->m_points[0].m_id.key = 0;
}
else
{
b2Vec2 faceCenter = 0.5f * (v1 + v2);
float32 separation = b2Dot(cLocal - faceCenter, normals[vertIndex1]);
if (separation > radius)
{
return;
}
manifold->m_pointCount = 1;
manifold->m_type = b2Manifold::e_faceA;
manifold->m_localPlaneNormal = normals[vertIndex1];
manifold->m_localPoint = faceCenter;
manifold->m_points[0].m_localPoint = circle->m_p;
manifold->m_points[0].m_id.key = 0;
}
}
void b2Island::Solve(b2Profile* profile, const b2TimeStep& step, const b2Vec2& gravity, bool allowSleep)
{
b2Timer timer;
float32 h = step.dt;
// Integrate velocities and apply damping. Initialize the body state.
for (int32 i = 0; i < m_bodyCount; ++i)
{
b2Body* b = m_bodies[i];
b2Vec2 c = b->m_sweep.c;
float32 a = b->m_sweep.a;
b2Vec2 v = b->m_linearVelocity;
float32 w = b->m_angularVelocity;
// Store positions for continuous collision.
b->m_sweep.c0 = b->m_sweep.c;
b->m_sweep.a0 = b->m_sweep.a;
if (b->m_type == b2_dynamicBody)
{
if (b->IsGravitated())
{
v += h * b->m_gravityScale * gravity;
}
// Integrate velocities.
v += h * (b->m_invMass * b->m_force);
w += h * b->m_invI * b->m_torque;
// Apply damping.
// ODE: dv/dt + c * v = 0
// Solution: v(t) = v0 * exp(-c * t)
// Time step: v(t + dt) = v0 * exp(-c * (t + dt)) = v0 * exp(-c * t) * exp(-c * dt) = v * exp(-c * dt)
// v2 = exp(-c * dt) * v1
// Taylor expansion:
// v2 = (1.0f - c * dt) * v1
v *= b2Clamp(1.0f - h * b->m_linearDamping, 0.0f, 1.0f);
w *= b2Clamp(1.0f - h * b->m_angularDamping, 0.0f, 1.0f);
}
m_positions[i].c = c;
m_positions[i].a = a;
m_velocities[i].v = v;
m_velocities[i].w = w;
}
timer.Reset();
// Solver data
b2SolverData solverData;
solverData.step = step;
solverData.positions = m_positions;
solverData.velocities = m_velocities;
// Initialize velocity constraints.
b2ContactSolverDef contactSolverDef;
contactSolverDef.step = step;
contactSolverDef.contacts = m_contacts;
contactSolverDef.count = m_contactCount;
contactSolverDef.positions = m_positions;
contactSolverDef.velocities = m_velocities;
contactSolverDef.allocator = m_allocator;
b2ContactSolver contactSolver(&contactSolverDef);
contactSolver.InitializeVelocityConstraints();
if (step.warmStarting)
{
contactSolver.WarmStart();
}
for (int32 i = 0; i < m_jointCount; ++i)
{
m_joints[i]->InitVelocityConstraints(solverData);
}
profile->solveInit = timer.GetMilliseconds();
// Solve velocity constraints
timer.Reset();
for (int32 i = 0; i < step.velocityIterations; ++i)
{
for (int32 j = 0; j < m_jointCount; ++j)
{
m_joints[j]->SolveVelocityConstraints(solverData);
}
contactSolver.SolveVelocityConstraints();
}
// Store impulses for warm starting
contactSolver.StoreImpulses();
profile->solveVelocity = timer.GetMilliseconds();
// Integrate positions
for (int32 i = 0; i < m_bodyCount; ++i)
{
b2Vec2 c = m_positions[i].c;
float32 a = m_positions[i].a;
b2Vec2 v = m_velocities[i].v;
float32 w = m_velocities[i].w;
// Check for large velocities
b2Vec2 translation = h * v;
if (b2Dot(translation, translation) > b2_maxTranslationSquared)
{
float32 ratio = b2_maxTranslation / translation.Length();
v *= ratio;
}
float32 rotation = h * w;
if (rotation * rotation > b2_maxRotationSquared)
{
float32 ratio = b2_maxRotation / b2Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
m_positions[i].c = c;
m_positions[i].a = a;
m_velocities[i].v = v;
m_velocities[i].w = w;
}
// Solve position constraints
timer.Reset();
bool positionSolved = false;
for (int32 i = 0; i < step.positionIterations; ++i)
{
bool contactsOkay = contactSolver.SolvePositionConstraints();
bool jointsOkay = true;
for (int32 i = 0; i < m_jointCount; ++i)
{
bool jointOkay = m_joints[i]->SolvePositionConstraints(solverData);
jointsOkay = jointsOkay && jointOkay;
}
if (contactsOkay && jointsOkay)
{
// Exit early if the position errors are small.
positionSolved = true;
break;
}
}
// Copy state buffers back to the bodies
for (int32 i = 0; i < m_bodyCount; ++i)
{
b2Body* body = m_bodies[i];
body->m_sweep.c = m_positions[i].c;
body->m_sweep.a = m_positions[i].a;
body->m_linearVelocity = m_velocities[i].v;
body->m_angularVelocity = m_velocities[i].w;
body->SynchronizeTransform();
}
profile->solvePosition = timer.GetMilliseconds();
Report(contactSolver.m_velocityConstraints);
if (allowSleep)
{
float32 minSleepTime = b2_maxFloat;
const float32 linTolSqr = b2_linearSleepTolerance * b2_linearSleepTolerance;
const float32 angTolSqr = b2_angularSleepTolerance * b2_angularSleepTolerance;
for (int32 i = 0; i < m_bodyCount; ++i)
{
b2Body* b = m_bodies[i];
if (b->GetType() == b2_staticBody)
{
continue;
}
if ((b->m_flags & b2Body::e_autoSleepFlag) == 0 ||
b->m_angularVelocity * b->m_angularVelocity > angTolSqr ||
b2Dot(b->m_linearVelocity, b->m_linearVelocity) > linTolSqr)
{
b->m_sleepTime = 0.0f;
minSleepTime = 0.0f;
}
else
{
b->m_sleepTime += h;
minSleepTime = b2Min(minSleepTime, b->m_sleepTime);
}
}
if (minSleepTime >= b2_timeToSleep && positionSolved)
{
for (int32 i = 0; i < m_bodyCount; ++i)
{
b2Body* b = m_bodies[i];
b->SetAwake(false);
}
}
}
}
// Possible regions:
// - points[2]
// - edge points[0]-points[2]
// - edge points[1]-points[2]
// - inside the triangle
void b2Simplex::Solve3()
{
b2Vec2 w1 = m_v1.w;
b2Vec2 w2 = m_v2.w;
b2Vec2 w3 = m_v3.w;
// Edge12
// [1 1 ][a1] = [1]
// [w1.e12 w2.e12][a2] = [0]
// a3 = 0
b2Vec2 e12 = w2 - w1;
float32 w1e12 = b2Dot(w1, e12);
float32 w2e12 = b2Dot(w2, e12);
float32 d12_1 = w2e12;
float32 d12_2 = -w1e12;
// Edge13
// [1 1 ][a1] = [1]
// [w1.e13 w3.e13][a3] = [0]
// a2 = 0
b2Vec2 e13 = w3 - w1;
float32 w1e13 = b2Dot(w1, e13);
float32 w3e13 = b2Dot(w3, e13);
float32 d13_1 = w3e13;
float32 d13_2 = -w1e13;
// Edge23
// [1 1 ][a2] = [1]
// [w2.e23 w3.e23][a3] = [0]
// a1 = 0
b2Vec2 e23 = w3 - w2;
float32 w2e23 = b2Dot(w2, e23);
float32 w3e23 = b2Dot(w3, e23);
float32 d23_1 = w3e23;
float32 d23_2 = -w2e23;
// Triangle123
float32 n123 = b2Cross(e12, e13);
float32 d123_1 = n123 * b2Cross(w2, w3);
float32 d123_2 = n123 * b2Cross(w3, w1);
float32 d123_3 = n123 * b2Cross(w1, w2);
// w1 region
if (d12_2 <= 0.0f && d13_2 <= 0.0f)
{
m_v1.a = 1.0f;
m_count = 1;
return;
}
// e12
if (d12_1 > 0.0f && d12_2 > 0.0f && d123_3 <= 0.0f)
{
float32 inv_d12 = 1.0f / (d12_1 + d12_2);
m_v1.a = d12_1 * inv_d12;
m_v2.a = d12_2 * inv_d12;
m_count = 2;
return;
}
// e13
if (d13_1 > 0.0f && d13_2 > 0.0f && d123_2 <= 0.0f)
{
float32 inv_d13 = 1.0f / (d13_1 + d13_2);
m_v1.a = d13_1 * inv_d13;
m_v3.a = d13_2 * inv_d13;
m_count = 2;
m_v2 = m_v3;
return;
}
// w2 region
if (d12_1 <= 0.0f && d23_2 <= 0.0f)
{
m_v2.a = 1.0f;
m_count = 1;
m_v1 = m_v2;
return;
}
// w3 region
if (d13_1 <= 0.0f && d23_1 <= 0.0f)
{
m_v3.a = 1.0f;
m_count = 1;
m_v1 = m_v3;
return;
}
// e23
if (d23_1 > 0.0f && d23_2 > 0.0f && d123_1 <= 0.0f)
{
float32 inv_d23 = 1.0f / (d23_1 + d23_2);
m_v2.a = d23_1 * inv_d23;
m_v3.a = d23_2 * inv_d23;
m_count = 2;
m_v1 = m_v3;
return;
}
// Must be in triangle123
float32 inv_d123 = 1.0f / (d123_1 + d123_2 + d123_3);
m_v1.a = d123_1 * inv_d123;
m_v2.a = d123_2 * inv_d123;
m_v3.a = d123_3 * inv_d123;
m_count = 3;
}
void b2LineJoint::SolveVelocityConstraints(const b2TimeStep& step)
{
b2Body* b1 = m_bodyA;
b2Body* b2 = m_bodyB;
b2vec2 v1 = b1->m_linearVelocity;
float32 w1 = b1->m_angularVelocity;
b2vec2 v2 = b2->m_linearVelocity;
float32 w2 = b2->m_angularVelocity;
// Solve linear motor constraint.
if (m_enableMotor && m_limitState != e_equalLimits)
{
float32 Cdot = b2Dot(m_axis, v2 - v1) + m_a2 * w2 - m_a1 * w1;
float32 impulse = m_motorMass * (m_motorSpeed - Cdot);
float32 oldImpulse = m_motorImpulse;
float32 maxImpulse = step.dt * m_maxMotorForce;
m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
b2vec2 P = impulse * m_axis;
float32 L1 = impulse * m_a1;
float32 L2 = impulse * m_a2;
v1 -= m_invMassA * P;
w1 -= m_invIA * L1;
v2 += m_invMassB * P;
w2 += m_invIB * L2;
}
float32 Cdot1 = b2Dot(m_perp, v2 - v1) + m_s2 * w2 - m_s1 * w1;
if (m_enableLimit && m_limitState != e_inactiveLimit)
{
// Solve prismatic and limit constraint in block form.
float32 Cdot2 = b2Dot(m_axis, v2 - v1) + m_a2 * w2 - m_a1 * w1;
b2vec2 Cdot(Cdot1, Cdot2);
b2vec2 f1 = m_impulse;
b2vec2 df = m_K.Solve(-Cdot);
m_impulse += df;
if (m_limitState == e_atLowerLimit)
{
m_impulse.y = b2Max(m_impulse.y, 0.0f);
}
else if (m_limitState == e_atUpperLimit)
{
m_impulse.y = b2Min(m_impulse.y, 0.0f);
}
// f2(1) = invK(1,1) * (-Cdot(1) - K(1,2) * (f2(2) - f1(2))) + f1(1)
float32 b = -Cdot1 - (m_impulse.y - f1.y) * m_K.col2.x;
float32 f2r;
if (m_K.col1.x != 0.0f)
{
f2r = b / m_K.col1.x + f1.x;
}
else
{
f2r = f1.x;
}
m_impulse.x = f2r;
df = m_impulse - f1;
b2vec2 P = df.x * m_perp + df.y * m_axis;
float32 L1 = df.x * m_s1 + df.y * m_a1;
float32 L2 = df.x * m_s2 + df.y * m_a2;
v1 -= m_invMassA * P;
w1 -= m_invIA * L1;
v2 += m_invMassB * P;
w2 += m_invIB * L2;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
float32 df;
if (m_K.col1.x != 0.0f)
{
df = - Cdot1 / m_K.col1.x;
}
else
{
df = 0.0f;
}
m_impulse.x += df;
b2vec2 P = df * m_perp;
float32 L1 = df * m_s1;
float32 L2 = df * m_s2;
v1 -= m_invMassA * P;
w1 -= m_invIA * L1;
v2 += m_invMassB * P;
w2 += m_invIB * L2;
}
b1->m_linearVelocity = v1;
b1->m_angularVelocity = w1;
b2->m_linearVelocity = v2;
b2->m_angularVelocity = w2;
}
float32 FindMinSeparation(int32* indexA, int32* indexB, float32 t) const
{
b2Transform xfA, xfB;
m_sweepA.GetTransform(&xfA, t);
m_sweepB.GetTransform(&xfB, t);
switch (m_type)
{
case e_points:
{
b2Vec2 axisA = b2MulT(xfA.R, m_axis);
b2Vec2 axisB = b2MulT(xfB.R, -m_axis);
*indexA = m_proxyA->GetSupport(axisA);
*indexB = m_proxyB->GetSupport(axisB);
b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
b2Vec2 pointA = b2Mul(xfA, localPointA);
b2Vec2 pointB = b2Mul(xfB, localPointB);
float32 separation = b2Dot(pointB - pointA, m_axis);
return separation;
}
case e_faceA:
{
b2Vec2 normal = b2Mul(xfA.R, m_axis);
b2Vec2 pointA = b2Mul(xfA, m_localPoint);
b2Vec2 axisB = b2MulT(xfB.R, -normal);
*indexA = -1;
*indexB = m_proxyB->GetSupport(axisB);
b2Vec2 localPointB = m_proxyB->GetVertex(*indexB);
b2Vec2 pointB = b2Mul(xfB, localPointB);
float32 separation = b2Dot(pointB - pointA, normal);
return separation;
}
case e_faceB:
{
b2Vec2 normal = b2Mul(xfB.R, m_axis);
b2Vec2 pointB = b2Mul(xfB, m_localPoint);
b2Vec2 axisA = b2MulT(xfA.R, -normal);
*indexB = -1;
*indexA = m_proxyA->GetSupport(axisA);
b2Vec2 localPointA = m_proxyA->GetVertex(*indexA);
b2Vec2 pointA = b2Mul(xfA, localPointA);
float32 separation = b2Dot(pointA - pointB, normal);
return separation;
}
default:
b2Assert(false);
*indexA = -1;
*indexB = -1;
return 0.0f;
}
}
// Compute contact points for edge versus circle.
// This accounts for edge connectivity.
void b2CollideEdgeAndCircle(b2Manifold* manifold,
const b2EdgeShape* edgeA, const b2Transform& xfA,
const b2CircleShape* circleB, const b2Transform& xfB)
{
manifold->pointCount = 0;
// Compute circle in frame of edge
b2Vec2 Q = b2MulT(xfA, b2Mul(xfB, circleB->m_p));
b2Vec2 A = edgeA->m_vertex1, B = edgeA->m_vertex2;
b2Vec2 e = B - A;
// Barycentric coordinates
float32 u = b2Dot(e, B - Q);
float32 v = b2Dot(e, Q - A);
float32 radius = edgeA->m_radius + circleB->m_radius;
b2ContactFeature cf;
cf.indexB = 0;
cf.typeB = b2ContactFeature::e_vertex;
// Region A
if (v <= 0.0f)
{
b2Vec2 P = A;
b2Vec2 d = Q - P;
float32 dd = b2Dot(d, d);
if (dd > radius * radius)
{
return;
}
// Is there an edge connected to A?
if (edgeA->m_hasVertex0)
{
b2Vec2 A1 = edgeA->m_vertex0;
b2Vec2 B1 = A;
b2Vec2 e1 = B1 - A1;
float32 u1 = b2Dot(e1, B1 - Q);
// Is the circle in Region AB of the previous edge?
if (u1 > 0.0f)
{
return;
}
}
cf.indexA = 0;
cf.typeA = b2ContactFeature::e_vertex;
manifold->pointCount = 1;
manifold->type = b2Manifold::e_circles;
manifold->localNormal.SetZero();
manifold->localPoint = P;
manifold->points[0].id.key = 0;
manifold->points[0].id.cf = cf;
manifold->points[0].localPoint = circleB->m_p;
return;
}
// Region B
if (u <= 0.0f)
{
b2Vec2 P = B;
b2Vec2 d = Q - P;
float32 dd = b2Dot(d, d);
if (dd > radius * radius)
{
return;
}
// Is there an edge connected to B?
if (edgeA->m_hasVertex3)
{
b2Vec2 B2 = edgeA->m_vertex3;
b2Vec2 A2 = B;
b2Vec2 e2 = B2 - A2;
float32 v2 = b2Dot(e2, Q - A2);
// Is the circle in Region AB of the next edge?
if (v2 > 0.0f)
{
return;
}
}
cf.indexA = 1;
cf.typeA = b2ContactFeature::e_vertex;
manifold->pointCount = 1;
manifold->type = b2Manifold::e_circles;
manifold->localNormal.SetZero();
manifold->localPoint = P;
manifold->points[0].id.key = 0;
manifold->points[0].id.cf = cf;
manifold->points[0].localPoint = circleB->m_p;
return;
}
// Region AB
float32 den = b2Dot(e, e);
b2Assert(den > 0.0f);
b2Vec2 P = (1.0f / den) * (u * A + v * B);
b2Vec2 d = Q - P;
float32 dd = b2Dot(d, d);
if (dd > radius * radius)
{
return;
}
b2Vec2 n(-e.y, e.x);
if (b2Dot(n, Q - A) < 0.0f)
{
n.Set(-n.x, -n.y);
}
n.Normalize();
cf.indexA = 0;
cf.typeA = b2ContactFeature::e_face;
manifold->pointCount = 1;
manifold->type = b2Manifold::e_faceA;
manifold->localNormal = n;
manifold->localPoint = A;
manifold->points[0].id.key = 0;
manifold->points[0].id.cf = cf;
manifold->points[0].localPoint = circleB->m_p;
}
b2Vec2 CarModel::getLateralVelocity()
{
b2Vec2 currentRightNormal = m_body->GetWorldVector(b2Vec2(1, 0));
return b2Dot(currentRightNormal, m_body->GetLinearVelocity()) * currentRightNormal;
}
// p = p1 + t * d
// v = v1 + s * e
// p1 + t * d = v1 + s * e
// s * e - t * d = p1 - v1
bool b2EdgeShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
const b2Transform& xf, int32 childIndex) const
{
B2_NOT_USED(childIndex);
// Put the ray into the edge's frame of reference.
b2Vec2 p1 = b2MulT(xf.q, input.p1 - xf.p);
b2Vec2 p2 = b2MulT(xf.q, input.p2 - xf.p);
b2Vec2 d = p2 - p1;
b2Vec2 v1 = m_vertex1;
b2Vec2 v2 = m_vertex2;
b2Vec2 e = v2 - v1;
b2Vec2 normal(e.y, -e.x);
normal.Normalize();
// q = p1 + t * d
// dot(normal, q - v1) = 0
// dot(normal, p1 - v1) + t * dot(normal, d) = 0
float32 numerator = b2Dot(normal, v1 - p1);
float32 denominator = b2Dot(normal, d);
if (denominator == 0.0f)
{
return false;
}
float32 t = numerator / denominator;
if (t < 0.0f || input.maxFraction < t)
{
return false;
}
b2Vec2 q = p1 + t * d;
// q = v1 + s * r
// s = dot(q - v1, r) / dot(r, r)
b2Vec2 r = v2 - v1;
float32 rr = b2Dot(r, r);
if (rr == 0.0f)
{
return false;
}
float32 s = b2Dot(q - v1, r) / rr;
if (s < 0.0f || 1.0f < s)
{
return false;
}
output->fraction = t;
if (numerator > 0.0f)
{
output->normal = -b2Mul(xf.q, normal);
}
else
{
output->normal = b2Mul(xf.q, normal);
}
return true;
}
// Algorithm:
// 1. Classify v1 and v2
// 2. Classify polygon centroid as front or back
// 3. Flip normal if necessary
// 4. Initialize normal range to [-pi, pi] about face normal
// 5. Adjust normal range according to adjacent edges
// 6. Visit each separating axes, only accept axes within the range
// 7. Return if _any_ axis indicates separation
// 8. Clip
void b2EPCollider::Collide(b2Manifold* manifold, const b2EdgeShape* edgeA, const b2Transform& xfA,
const b2PolygonShape* polygonB, const b2Transform& xfB)
{
m_xf = b2MulT(xfA, xfB);
m_centroidB = b2Mul(m_xf, polygonB->m_centroid);
m_v0 = edgeA->m_vertex0;
m_v1 = edgeA->m_vertex1;
m_v2 = edgeA->m_vertex2;
m_v3 = edgeA->m_vertex3;
bool hasVertex0 = edgeA->m_hasVertex0;
bool hasVertex3 = edgeA->m_hasVertex3;
b2Vec2 edge1 = m_v2 - m_v1;
edge1.Normalize();
m_normal1.Set(edge1.y, -edge1.x);
float32 offset1 = b2Dot(m_normal1, m_centroidB - m_v1);
float32 offset0 = 0.0f, offset2 = 0.0f;
bool convex1 = false, convex2 = false;
// Is there a preceding edge?
if (hasVertex0)
{
b2Vec2 edge0 = m_v1 - m_v0;
edge0.Normalize();
m_normal0.Set(edge0.y, -edge0.x);
convex1 = b2Cross(edge0, edge1) >= 0.0f;
offset0 = b2Dot(m_normal0, m_centroidB - m_v0);
}
// Is there a following edge?
if (hasVertex3)
{
b2Vec2 edge2 = m_v3 - m_v2;
edge2.Normalize();
m_normal2.Set(edge2.y, -edge2.x);
convex2 = b2Cross(edge1, edge2) > 0.0f;
offset2 = b2Dot(m_normal2, m_centroidB - m_v2);
}
// Determine front or back collision. Determine collision normal limits.
if (hasVertex0 && hasVertex3)
{
if (convex1 && convex2)
{
m_front = offset0 >= 0.0f || offset1 >= 0.0f || offset2 >= 0.0f;
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = m_normal0;
m_upperLimit = m_normal2;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = -m_normal1;
m_upperLimit = -m_normal1;
}
}
else if (convex1)
{
m_front = offset0 >= 0.0f || (offset1 >= 0.0f && offset2 >= 0.0f);
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = m_normal0;
m_upperLimit = m_normal1;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = -m_normal2;
m_upperLimit = -m_normal1;
}
}
else if (convex2)
{
m_front = offset2 >= 0.0f || (offset0 >= 0.0f && offset1 >= 0.0f);
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = m_normal1;
m_upperLimit = m_normal2;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = -m_normal1;
m_upperLimit = -m_normal0;
}
}
else
{
m_front = offset0 >= 0.0f && offset1 >= 0.0f && offset2 >= 0.0f;
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = m_normal1;
m_upperLimit = m_normal1;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = -m_normal2;
m_upperLimit = -m_normal0;
}
}
}
else if (hasVertex0)
{
if (convex1)
{
m_front = offset0 >= 0.0f || offset1 >= 0.0f;
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = m_normal0;
m_upperLimit = -m_normal1;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = m_normal1;
m_upperLimit = -m_normal1;
}
}
else
{
m_front = offset0 >= 0.0f && offset1 >= 0.0f;
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = m_normal1;
m_upperLimit = -m_normal1;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = m_normal1;
m_upperLimit = -m_normal0;
}
}
}
else if (hasVertex3)
{
if (convex2)
{
m_front = offset1 >= 0.0f || offset2 >= 0.0f;
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = -m_normal1;
m_upperLimit = m_normal2;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = -m_normal1;
m_upperLimit = m_normal1;
}
}
else
{
m_front = offset1 >= 0.0f && offset2 >= 0.0f;
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = -m_normal1;
m_upperLimit = m_normal1;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = -m_normal2;
m_upperLimit = m_normal1;
}
}
}
else
{
m_front = offset1 >= 0.0f;
if (m_front)
{
m_normal = m_normal1;
m_lowerLimit = -m_normal1;
m_upperLimit = -m_normal1;
}
else
{
m_normal = -m_normal1;
m_lowerLimit = m_normal1;
m_upperLimit = m_normal1;
}
}
// Get polygonB in frameA
m_polygonB.count = polygonB->m_vertexCount;
for (int32 i = 0; i < polygonB->m_vertexCount; ++i)
{
m_polygonB.vertices[i] = b2Mul(m_xf, polygonB->m_vertices[i]);
m_polygonB.normals[i] = b2Mul(m_xf.q, polygonB->m_normals[i]);
}
m_radius = 2.0f * b2_polygonRadius;
manifold->pointCount = 0;
b2EPAxis edgeAxis = ComputeEdgeSeparation();
// If no valid normal can be found than this edge should not collide.
if (edgeAxis.type == b2EPAxis::e_unknown)
{
return;
}
if (edgeAxis.separation > m_radius)
{
return;
}
b2EPAxis polygonAxis = ComputePolygonSeparation();
if (polygonAxis.type != b2EPAxis::e_unknown && polygonAxis.separation > m_radius)
{
return;
}
// Use hysteresis for jitter reduction.
const float32 k_relativeTol = 0.98f;
const float32 k_absoluteTol = 0.001f;
b2EPAxis primaryAxis;
if (polygonAxis.type == b2EPAxis::e_unknown)
{
primaryAxis = edgeAxis;
}
else if (polygonAxis.separation > k_relativeTol * edgeAxis.separation + k_absoluteTol)
{
primaryAxis = polygonAxis;
}
else
{
primaryAxis = edgeAxis;
}
b2ClipVertex ie[2];
b2ReferenceFace rf;
if (primaryAxis.type == b2EPAxis::e_edgeA)
{
manifold->type = b2Manifold::e_faceA;
// Search for the polygon normal that is most anti-parallel to the edge normal.
int32 bestIndex = 0;
float32 bestValue = b2Dot(m_normal, m_polygonB.normals[0]);
for (int32 i = 1; i < m_polygonB.count; ++i)
{
float32 value = b2Dot(m_normal, m_polygonB.normals[i]);
if (value < bestValue)
{
bestValue = value;
bestIndex = i;
}
}
int32 i1 = bestIndex;
int32 i2 = i1 + 1 < m_polygonB.count ? i1 + 1 : 0;
ie[0].v = m_polygonB.vertices[i1];
ie[0].id.cf.indexA = 0;
ie[0].id.cf.indexB = i1;
ie[0].id.cf.typeA = b2ContactFeature::e_face;
ie[0].id.cf.typeB = b2ContactFeature::e_vertex;
ie[1].v = m_polygonB.vertices[i2];
ie[1].id.cf.indexA = 0;
ie[1].id.cf.indexB = i2;
ie[1].id.cf.typeA = b2ContactFeature::e_face;
ie[1].id.cf.typeB = b2ContactFeature::e_vertex;
if (m_front)
{
rf.i1 = 0;
rf.i2 = 1;
rf.v1 = m_v1;
rf.v2 = m_v2;
rf.normal = m_normal1;
}
else
{
rf.i1 = 1;
rf.i2 = 0;
rf.v1 = m_v2;
rf.v2 = m_v1;
rf.normal = -m_normal1;
}
}
else
{
manifold->type = b2Manifold::e_faceB;
ie[0].v = m_v1;
ie[0].id.cf.indexA = 0;
ie[0].id.cf.indexB = primaryAxis.index;
ie[0].id.cf.typeA = b2ContactFeature::e_vertex;
ie[0].id.cf.typeB = b2ContactFeature::e_face;
ie[1].v = m_v2;
ie[1].id.cf.indexA = 0;
ie[1].id.cf.indexB = primaryAxis.index;
ie[1].id.cf.typeA = b2ContactFeature::e_vertex;
ie[1].id.cf.typeB = b2ContactFeature::e_face;
rf.i1 = primaryAxis.index;
rf.i2 = rf.i1 + 1 < m_polygonB.count ? rf.i1 + 1 : 0;
rf.v1 = m_polygonB.vertices[rf.i1];
rf.v2 = m_polygonB.vertices[rf.i2];
rf.normal = m_polygonB.normals[rf.i1];
}
rf.sideNormal1.Set(rf.normal.y, -rf.normal.x);
rf.sideNormal2 = -rf.sideNormal1;
rf.sideOffset1 = b2Dot(rf.sideNormal1, rf.v1);
rf.sideOffset2 = b2Dot(rf.sideNormal2, rf.v2);
// Clip incident edge against extruded edge1 side edges.
b2ClipVertex clipPoints1[2];
b2ClipVertex clipPoints2[2];
int32 np;
// Clip to box side 1
np = b2ClipSegmentToLine(clipPoints1, ie, rf.sideNormal1, rf.sideOffset1, rf.i1);
if (np < b2_maxManifoldPoints)
{
return;
}
// Clip to negative box side 1
np = b2ClipSegmentToLine(clipPoints2, clipPoints1, rf.sideNormal2, rf.sideOffset2, rf.i2);
if (np < b2_maxManifoldPoints)
{
return;
}
// Now clipPoints2 contains the clipped points.
if (primaryAxis.type == b2EPAxis::e_edgeA)
{
manifold->localNormal = rf.normal;
manifold->localPoint = rf.v1;
}
else
{
manifold->localNormal = polygonB->m_normals[rf.i1];
manifold->localPoint = polygonB->m_vertices[rf.i1];
}
int32 pointCount = 0;
for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
{
float32 separation;
separation = b2Dot(rf.normal, clipPoints2[i].v - rf.v1);
if (separation <= m_radius)
{
b2ManifoldPoint* cp = manifold->points + pointCount;
if (primaryAxis.type == b2EPAxis::e_edgeA)
{
cp->localPoint = b2MulT(m_xf, clipPoints2[i].v);
cp->id = clipPoints2[i].id;
}
else
{
cp->localPoint = clipPoints2[i].v;
cp->id.cf.typeA = clipPoints2[i].id.cf.typeB;
cp->id.cf.typeB = clipPoints2[i].id.cf.typeA;
cp->id.cf.indexA = clipPoints2[i].id.cf.indexB;
cp->id.cf.indexB = clipPoints2[i].id.cf.indexA;
}
++pointCount;
}
}
manifold->pointCount = pointCount;
}
void b2WorldManifold::Initialize(const b2Manifold* manifold,
const b2Transform& xfA, float32 radiusA,
const b2Transform& xfB, float32 radiusB)
{
if (manifold->m_pointCount == 0)
{
return;
}
switch (manifold->m_type)
{
case b2Manifold::e_circles:
{
b2Vec2 pointA = b2Mul(xfA, manifold->m_localPoint);
b2Vec2 pointB = b2Mul(xfB, manifold->m_points[0].m_localPoint);
b2Vec2 normal(1.0f, 0.0f);
if (b2DistanceSquared(pointA, pointB) > b2_epsilon * b2_epsilon)
{
normal = pointB - pointA;
normal.Normalize();
}
m_normal = normal;
b2Vec2 cA = pointA + radiusA * normal;
b2Vec2 cB = pointB - radiusB * normal;
m_points[0] = 0.5f * (cA + cB);
}
break;
case b2Manifold::e_faceA:
{
b2Vec2 normal = b2Mul(xfA.R, manifold->m_localPlaneNormal);
b2Vec2 planePoint = b2Mul(xfA, manifold->m_localPoint);
// Ensure normal points from A to B.
m_normal = normal;
for (int32 i = 0; i < manifold->m_pointCount; ++i)
{
b2Vec2 clipPoint = b2Mul(xfB, manifold->m_points[i].m_localPoint);
b2Vec2 cA = clipPoint + (radiusA - b2Dot(clipPoint - planePoint, normal)) * normal;
b2Vec2 cB = clipPoint - radiusB * normal;
m_points[i] = 0.5f * (cA + cB);
}
}
break;
case b2Manifold::e_faceB:
{
b2Vec2 normal = b2Mul(xfB.R, manifold->m_localPlaneNormal);
b2Vec2 planePoint = b2Mul(xfB, manifold->m_localPoint);
// Ensure normal points from A to B.
m_normal = -normal;
for (int32 i = 0; i < manifold->m_pointCount; ++i)
{
b2Vec2 clipPoint = b2Mul(xfA, manifold->m_points[i].m_localPoint);
b2Vec2 cA = clipPoint - radiusA * normal;
b2Vec2 cB = clipPoint + (radiusB - b2Dot(clipPoint - planePoint, normal)) * normal;
m_points[i] = 0.5f * (cA + cB);
}
}
break;
}
}
// Find the max separation between poly1 and poly2 using edge normals from poly1.
static float32 b2FindMaxSeparation(int32* edgeIndex,
const b2PolygonShape* poly1, const b2Transform& xf1,
const b2PolygonShape* poly2, const b2Transform& xf2)
{
int32 count1 = poly1->m_vertexCount;
const b2Vec2* normals1 = poly1->m_normals;
// Vector pointing from the centroid of poly1 to the centroid of poly2.
b2Vec2 d = b2Mul(xf2, poly2->m_centroid) - b2Mul(xf1, poly1->m_centroid);
b2Vec2 dLocal1 = b2MulT(xf1.R, d);
// Find edge normal on poly1 that has the largest projection onto d.
int32 edge = 0;
float32 maxDot = -b2_maxFloat;
for (int32 i = 0; i < count1; ++i)
{
float32 dot = b2Dot(normals1[i], dLocal1);
if (dot > maxDot)
{
maxDot = dot;
edge = i;
}
}
// Get the separation for the edge normal.
float32 s = b2EdgeSeparation(poly1, xf1, edge, poly2, xf2);
// Check the separation for the previous edge normal.
int32 prevEdge = edge - 1 >= 0 ? edge - 1 : count1 - 1;
float32 sPrev = b2EdgeSeparation(poly1, xf1, prevEdge, poly2, xf2);
// Check the separation for the next edge normal.
int32 nextEdge = edge + 1 < count1 ? edge + 1 : 0;
float32 sNext = b2EdgeSeparation(poly1, xf1, nextEdge, poly2, xf2);
// Find the best edge and the search direction.
int32 bestEdge;
float32 bestSeparation;
int32 increment;
if (sPrev > s && sPrev > sNext)
{
increment = -1;
bestEdge = prevEdge;
bestSeparation = sPrev;
}
else if (sNext > s)
{
increment = 1;
bestEdge = nextEdge;
bestSeparation = sNext;
}
else
{
*edgeIndex = edge;
return s;
}
// Perform a local search for the best edge normal.
for ( ; ; )
{
if (increment == -1)
edge = bestEdge - 1 >= 0 ? bestEdge - 1 : count1 - 1;
else
edge = bestEdge + 1 < count1 ? bestEdge + 1 : 0;
s = b2EdgeSeparation(poly1, xf1, edge, poly2, xf2);
if (s > bestSeparation)
{
bestEdge = edge;
bestSeparation = s;
}
else
{
break;
}
}
*edgeIndex = bestEdge;
return bestSeparation;
}
// The normal points from 1 to 2
void b2CollidePolygons(b2Manifold* manifold,
const b2PolygonShape* polyA, const b2Transform& xfA,
const b2PolygonShape* polyB, const b2Transform& xfB)
{
manifold->pointCount = 0;
float32 totalRadius = polyA->m_radius + polyB->m_radius;
int32 edgeA = 0;
float32 separationA = b2FindMaxSeparation(&edgeA, polyA, xfA, polyB, xfB);
if (separationA > totalRadius)
return;
int32 edgeB = 0;
float32 separationB = b2FindMaxSeparation(&edgeB, polyB, xfB, polyA, xfA);
if (separationB > totalRadius)
return;
const b2PolygonShape* poly1; // reference polygon
const b2PolygonShape* poly2; // incident polygon
b2Transform xf1, xf2;
int32 edge1; // reference edge
uint8 flip;
const float32 k_relativeTol = 0.98f;
const float32 k_absoluteTol = 0.001f;
if (separationB > k_relativeTol * separationA + k_absoluteTol)
{
poly1 = polyB;
poly2 = polyA;
xf1 = xfB;
xf2 = xfA;
edge1 = edgeB;
manifold->type = b2Manifold::e_faceB;
flip = 1;
}
else
{
poly1 = polyA;
poly2 = polyB;
xf1 = xfA;
xf2 = xfB;
edge1 = edgeA;
manifold->type = b2Manifold::e_faceA;
flip = 0;
}
b2ClipVertex incidentEdge[2];
b2FindIncidentEdge(incidentEdge, poly1, xf1, edge1, poly2, xf2);
int32 count1 = poly1->m_vertexCount;
const b2Vec2* vertices1 = poly1->m_vertices;
b2Vec2 v11 = vertices1[edge1];
b2Vec2 v12 = edge1 + 1 < count1 ? vertices1[edge1+1] : vertices1[0];
b2Vec2 localTangent = v12 - v11;
localTangent.Normalize();
b2Vec2 localNormal = b2Cross(localTangent, 1.0f);
b2Vec2 planePoint = 0.5f * (v11 + v12);
b2Vec2 tangent = b2Mul(xf1.R, localTangent);
b2Vec2 normal = b2Cross(tangent, 1.0f);
v11 = b2Mul(xf1, v11);
v12 = b2Mul(xf1, v12);
// Face offset.
float32 frontOffset = b2Dot(normal, v11);
// Side offsets, extended by polytope skin thickness.
float32 sideOffset1 = -b2Dot(tangent, v11) + totalRadius;
float32 sideOffset2 = b2Dot(tangent, v12) + totalRadius;
// Clip incident edge against extruded edge1 side edges.
b2ClipVertex clipPoints1[2];
b2ClipVertex clipPoints2[2];
int np;
// Clip to box side 1
np = b2ClipSegmentToLine(clipPoints1, incidentEdge, -tangent, sideOffset1);
if (np < 2)
return;
// Clip to negative box side 1
np = b2ClipSegmentToLine(clipPoints2, clipPoints1, tangent, sideOffset2);
if (np < 2)
{
return;
}
// Now clipPoints2 contains the clipped points.
manifold->localNormal = localNormal;
manifold->localPoint = planePoint;
int32 pointCount = 0;
for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
{
float32 separation = b2Dot(normal, clipPoints2[i].v) - frontOffset;
if (separation <= totalRadius)
{
b2ManifoldPoint* cp = manifold->points + pointCount;
cp->localPoint = b2MulT(xf2, clipPoints2[i].v);
cp->id = clipPoints2[i].id;
cp->id.features.flip = flip;
++pointCount;
}
}
manifold->pointCount = pointCount;
}
void b2PolygonShape::ComputeMass(b2MassData* massData, float32 density) const
{
// Polygon mass, centroid, and inertia.
// Let rho be the polygon density in mass per unit area.
// Then:
// mass = rho * int(dA)
// centroid.x = (1/mass) * rho * int(x * dA)
// centroid.y = (1/mass) * rho * int(y * dA)
// I = rho * int((x*x + y*y) * dA)
//
// We can compute these integrals by summing all the integrals
// for each triangle of the polygon. To evaluate the integral
// for a single triangle, we make a change of variables to
// the (u,v) coordinates of the triangle:
// x = x0 + e1x * u + e2x * v
// y = y0 + e1y * u + e2y * v
// where 0 <= u && 0 <= v && u + v <= 1.
//
// We integrate u from [0,1-v] and then v from [0,1].
// We also need to use the Jacobian of the transformation:
// D = cross(e1, e2)
//
// Simplification: triangle centroid = (1/3) * (p1 + p2 + p3)
//
// The rest of the derivation is handled by computer algebra.
b2Assert(m_count >= 3);
b2Vec2 center; center.Set(0.0f, 0.0f);
float32 area = 0.0f;
float32 I = 0.0f;
// s is the reference point for forming triangles.
// It's location doesn't change the result (except for rounding error).
b2Vec2 s(0.0f, 0.0f);
// This code would put the reference point inside the polygon.
for (int32 i = 0; i < m_count; ++i)
{
s += m_vertices[i];
}
s *= 1.0f / m_count;
const float32 k_inv3 = 1.0f / 3.0f;
for (int32 i = 0; i < m_count; ++i)
{
// Triangle vertices.
b2Vec2 e1 = m_vertices[i] - s;
b2Vec2 e2 = i + 1 < m_count ? m_vertices[i+1] - s : m_vertices[0] - s;
float32 D = b2Cross(e1, e2);
float32 triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
center += triangleArea * k_inv3 * (e1 + e2);
float32 ex1 = e1.x, ey1 = e1.y;
float32 ex2 = e2.x, ey2 = e2.y;
float32 intx2 = ex1*ex1 + ex2*ex1 + ex2*ex2;
float32 inty2 = ey1*ey1 + ey2*ey1 + ey2*ey2;
I += (0.25f * k_inv3 * D) * (intx2 + inty2);
}
// Total mass
massData->mass = density * area;
// Center of mass
b2Assert(area > b2_epsilon);
center *= 1.0f / area;
massData->center = center + s;
// Inertia tensor relative to the local origin (point s).
massData->I = density * I;
// Shift to center of mass then to original body origin.
massData->I += massData->mass * (b2Dot(massData->center, massData->center) - b2Dot(center, center));
}
b2Vec2 CarModel::getForwardVelocity()
{
b2Vec2 currentForwardNormal = m_body->GetWorldVector(b2Vec2(0, 1));
return b2Dot(currentForwardNormal, m_body->GetLinearVelocity()) * currentForwardNormal;
}
void b2LineJoint::InitVelocityConstraints(const b2TimeStep& step)
{
b2Body* b1 = m_bodyA;
b2Body* b2 = m_bodyB;
m_localCenterA = b1->GetLocalCenter();
m_localCenterB = b2->GetLocalCenter();
b2Transform xf1 = b1->GetTransform();
b2Transform xf2 = b2->GetTransform();
// Compute the effective masses.
b2vec2 r1 = b2Mul(xf1.R, m_localAnchor1 - m_localCenterA);
b2vec2 r2 = b2Mul(xf2.R, m_localAnchor2 - m_localCenterB);
b2vec2 d = b2->m_sweep.c + r2 - b1->m_sweep.c - r1;
m_invMassA = b1->m_invMass;
m_invIA = b1->m_invI;
m_invMassB = b2->m_invMass;
m_invIB = b2->m_invI;
// Compute motor Jacobian and effective mass.
{
m_axis = b2Mul(xf1.R, m_localXAxis1);
m_a1 = b2Cross(d + r1, m_axis);
m_a2 = b2Cross(r2, m_axis);
m_motorMass = m_invMassA + m_invMassB + m_invIA * m_a1 * m_a1 + m_invIB * m_a2 * m_a2;
if (m_motorMass > b2_epsilon)
{
m_motorMass = 1.0f / m_motorMass;
}
else
{
m_motorMass = 0.0f;
}
}
// Prismatic constraint.
{
m_perp = b2Mul(xf1.R, m_localYAxis1);
m_s1 = b2Cross(d + r1, m_perp);
m_s2 = b2Cross(r2, m_perp);
float32 m1 = m_invMassA, m2 = m_invMassB;
float32 i1 = m_invIA, i2 = m_invIB;
float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
float32 k12 = i1 * m_s1 * m_a1 + i2 * m_s2 * m_a2;
float32 k22 = m1 + m2 + i1 * m_a1 * m_a1 + i2 * m_a2 * m_a2;
m_K.col1.Set(k11, k12);
m_K.col2.Set(k12, k22);
}
// Compute motor and limit terms.
if (m_enableLimit)
{
float32 jointTranslation = b2Dot(m_axis, d);
if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
{
m_limitState = e_equalLimits;
}
else if (jointTranslation <= m_lowerTranslation)
{
if (m_limitState != e_atLowerLimit)
{
m_limitState = e_atLowerLimit;
m_impulse.y = 0.0f;
}
}
else if (jointTranslation >= m_upperTranslation)
{
if (m_limitState != e_atUpperLimit)
{
m_limitState = e_atUpperLimit;
m_impulse.y = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.y = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
}
if (m_enableMotor == false)
{
m_motorImpulse = 0.0f;
}
if (step.warmStarting)
{
// Account for variable time step.
m_impulse *= step.dtRatio;
m_motorImpulse *= step.dtRatio;
b2vec2 P = m_impulse.x * m_perp + (m_motorImpulse + m_impulse.y) * m_axis;
float32 L1 = m_impulse.x * m_s1 + (m_motorImpulse + m_impulse.y) * m_a1;
float32 L2 = m_impulse.x * m_s2 + (m_motorImpulse + m_impulse.y) * m_a2;
b1->m_linearVelocity -= m_invMassA * P;
b1->m_angularVelocity -= m_invIA * L1;
b2->m_linearVelocity += m_invMassB * P;
b2->m_angularVelocity += m_invIB * L2;
}
else
{
m_impulse.SetZero();
m_motorImpulse = 0.0f;
}
}
void b2PrismaticJoint::InitVelocityConstraints(const b2SolverData& data)
{
m_indexA = m_bodyA->m_islandIndex;
m_indexB = m_bodyB->m_islandIndex;
m_localCenterA = m_bodyA->m_sweep.localCenter;
m_localCenterB = 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;
b2Vec2 cA = data.positions[m_indexA].c;
float32 aA = data.positions[m_indexA].a;
b2Vec2 vA = data.velocities[m_indexA].v;
float32 wA = data.velocities[m_indexA].w;
b2Vec2 cB = data.positions[m_indexB].c;
float32 aB = data.positions[m_indexB].a;
b2Vec2 vB = data.velocities[m_indexB].v;
float32 wB = data.velocities[m_indexB].w;
b2Rot qA(aA), qB(aB);
// Compute the effective masses.
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
b2Vec2 d = (cB - cA) + rB - rA;
float32 mA = m_invMassA, mB = m_invMassB;
float32 iA = m_invIA, iB = m_invIB;
// Compute motor Jacobian and effective mass.
{
m_axis = b2Mul(qA, m_localXAxisA);
m_a1 = b2Cross(d + rA, m_axis);
m_a2 = b2Cross(rB, m_axis);
m_motorMass = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
if (m_motorMass > 0.0f)
{
m_motorMass = 1.0f / m_motorMass;
}
}
// Prismatic constraint.
{
m_perp = b2Mul(qA, m_localYAxisA);
m_s1 = b2Cross(d + rA, m_perp);
m_s2 = b2Cross(rB, m_perp);
float32 s1test;
s1test = b2Cross(rA, m_perp);
float32 k11 = mA + mB + iA * m_s1 * m_s1 + iB * m_s2 * m_s2;
float32 k12 = iA * m_s1 + iB * m_s2;
float32 k13 = iA * m_s1 * m_a1 + iB * m_s2 * m_a2;
float32 k22 = iA + iB;
if (k22 == 0.0f)
{
// For bodies with fixed rotation.
k22 = 1.0f;
}
float32 k23 = iA * m_a1 + iB * m_a2;
float32 k33 = mA + mB + iA * m_a1 * m_a1 + iB * m_a2 * m_a2;
m_K.ex.Set(k11, k12, k13);
m_K.ey.Set(k12, k22, k23);
m_K.ez.Set(k13, k23, k33);
}
// Compute motor and limit terms.
if (m_enableLimit)
{
float32 jointTranslation = b2Dot(m_axis, d);
if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
{
m_limitState = e_equalLimits;
}
else if (jointTranslation <= m_lowerTranslation)
{
if (m_limitState != e_atLowerLimit)
{
m_limitState = e_atLowerLimit;
m_impulse.z = 0.0f;
}
}
else if (jointTranslation >= m_upperTranslation)
{
if (m_limitState != e_atUpperLimit)
{
m_limitState = e_atUpperLimit;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.z = 0.0f;
}
}
else
{
m_limitState = e_inactiveLimit;
m_impulse.z = 0.0f;
}
if (m_enableMotor == false)
{
m_motorImpulse = 0.0f;
}
if (data.step.warmStarting)
{
// Account for variable time step.
m_impulse *= data.step.dtRatio;
m_motorImpulse *= data.step.dtRatio;
b2Vec2 P = m_impulse.x * m_perp + (m_motorImpulse + m_impulse.z) * m_axis;
float32 LA = m_impulse.x * m_s1 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a1;
float32 LB = m_impulse.x * m_s2 + m_impulse.y + (m_motorImpulse + m_impulse.z) * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
m_impulse.SetZero();
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;
}
bool b2LineJoint::SolvePositionConstraints(float32 baumgarte)
{
B2_NOT_USED(baumgarte);
b2Body* b1 = m_bodyA;
b2Body* b2 = m_bodyB;
b2vec2 c1 = b1->m_sweep.c;
float32 a1 = b1->m_sweep.a;
b2vec2 c2 = b2->m_sweep.c;
float32 a2 = b2->m_sweep.a;
// Solve linear limit constraint.
float32 linearError = 0.0f, angularError = 0.0f;
bool active = false;
float32 C2 = 0.0f;
b2Mat22 R1(a1), R2(a2);
b2vec2 r1 = b2Mul(R1, m_localAnchor1 - m_localCenterA);
b2vec2 r2 = b2Mul(R2, m_localAnchor2 - m_localCenterB);
b2vec2 d = c2 + r2 - c1 - r1;
if (m_enableLimit)
{
m_axis = b2Mul(R1, m_localXAxis1);
m_a1 = b2Cross(d + r1, m_axis);
m_a2 = b2Cross(r2, m_axis);
float32 translation = b2Dot(m_axis, d);
if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
{
// Prevent large angular corrections
C2 = b2Clamp(translation, -b2_maxLinearCorrection, b2_maxLinearCorrection);
linearError = b2Abs(translation);
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = b2Clamp(translation - m_lowerTranslation + b2_linearSlop, -b2_maxLinearCorrection, 0.0f);
linearError = m_lowerTranslation - translation;
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = b2Clamp(translation - m_upperTranslation - b2_linearSlop, 0.0f, b2_maxLinearCorrection);
linearError = translation - m_upperTranslation;
active = true;
}
}
m_perp = b2Mul(R1, m_localYAxis1);
m_s1 = b2Cross(d + r1, m_perp);
m_s2 = b2Cross(r2, m_perp);
b2vec2 impulse;
float32 C1;
C1 = b2Dot(m_perp, d);
linearError = b2Max(linearError, b2Abs(C1));
angularError = 0.0f;
if (active)
{
float32 m1 = m_invMassA, m2 = m_invMassB;
float32 i1 = m_invIA, i2 = m_invIB;
float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
float32 k12 = i1 * m_s1 * m_a1 + i2 * m_s2 * m_a2;
float32 k22 = m1 + m2 + i1 * m_a1 * m_a1 + i2 * m_a2 * m_a2;
m_K.col1.Set(k11, k12);
m_K.col2.Set(k12, k22);
b2vec2 C;
C.x = C1;
C.y = C2;
impulse = m_K.Solve(-C);
}
else
{
float32 m1 = m_invMassA, m2 = m_invMassB;
float32 i1 = m_invIA, i2 = m_invIB;
float32 k11 = m1 + m2 + i1 * m_s1 * m_s1 + i2 * m_s2 * m_s2;
float32 impulse1;
if (k11 != 0.0f)
{
impulse1 = - C1 / k11;
}
else
{
impulse1 = 0.0f;
}
impulse.x = impulse1;
impulse.y = 0.0f;
}
b2vec2 P = impulse.x * m_perp + impulse.y * m_axis;
float32 L1 = impulse.x * m_s1 + impulse.y * m_a1;
float32 L2 = impulse.x * m_s2 + impulse.y * m_a2;
c1 -= m_invMassA * P;
a1 -= m_invIA * L1;
c2 += m_invMassB * P;
a2 += m_invIB * L2;
// TODO_ERIN remove need for this.
b1->m_sweep.c = c1;
b1->m_sweep.a = a1;
b2->m_sweep.c = c2;
b2->m_sweep.a = a2;
b1->SynchronizeTransform();
b2->SynchronizeTransform();
return linearError <= b2_linearSlop && angularError <= b2_angularSlop;
}
void b2PrismaticJoint::SolveVelocityConstraints(const b2SolverData& data)
{
b2Vec2 vA = data.velocities[m_indexA].v;
float32 wA = data.velocities[m_indexA].w;
b2Vec2 vB = data.velocities[m_indexB].v;
float32 wB = data.velocities[m_indexB].w;
float32 mA = m_invMassA, mB = m_invMassB;
float32 iA = m_invIA, iB = m_invIB;
// Solve linear motor constraint.
if (m_enableMotor && m_limitState != e_equalLimits)
{
float32 Cdot = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
float32 impulse = m_motorMass * (m_motorSpeed - Cdot);
float32 oldImpulse = m_motorImpulse;
float32 maxImpulse = data.step.dt * m_maxMotorForce;
m_motorImpulse = b2Clamp(m_motorImpulse + impulse, -maxImpulse, maxImpulse);
impulse = m_motorImpulse - oldImpulse;
b2Vec2 P = impulse * m_axis;
float32 LA = impulse * m_a1;
float32 LB = impulse * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
b2Vec2 Cdot1;
Cdot1.x = b2Dot(m_perp, vB - vA) + m_s2 * wB - m_s1 * wA;
Cdot1.y = wB - wA;
if (m_enableLimit && m_limitState != e_inactiveLimit)
{
// Solve prismatic and limit constraint in block form.
float32 Cdot2;
Cdot2 = b2Dot(m_axis, vB - vA) + m_a2 * wB - m_a1 * wA;
b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);
b2Vec3 f1 = m_impulse;
b2Vec3 df = m_K.Solve33(-Cdot);
m_impulse += df;
if (m_limitState == e_atLowerLimit)
{
m_impulse.z = b2Max(m_impulse.z, 0.0f);
}
else if (m_limitState == e_atUpperLimit)
{
m_impulse.z = b2Min(m_impulse.z, 0.0f);
}
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
b2Vec2 b = -Cdot1 - (m_impulse.z - f1.z) * b2Vec2(m_K.ez.x, m_K.ez.y);
b2Vec2 f2r = m_K.Solve22(b) + b2Vec2(f1.x, f1.y);
m_impulse.x = f2r.x;
m_impulse.y = f2r.y;
df = m_impulse - f1;
b2Vec2 P = df.x * m_perp + df.z * m_axis;
float32 LA = df.x * m_s1 + df.y + df.z * m_a1;
float32 LB = df.x * m_s2 + df.y + df.z * m_a2;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
b2Vec2 df = m_K.Solve22(-Cdot1);
m_impulse.x += df.x;
m_impulse.y += df.y;
b2Vec2 P = df.x * m_perp;
float32 LA = df.x * m_s1 + df.y;
float32 LB = df.x * m_s2 + df.y;
vA -= mA * P;
wA -= iA * LA;
vB += mB * P;
wB += iB * LB;
}
data.velocities[m_indexA].v = vA;
data.velocities[m_indexA].w = wA;
data.velocities[m_indexB].v = vB;
data.velocities[m_indexB].w = wB;
}
float32 Initialize(const b2SimplexCache* cache,
const b2DistanceProxy* proxyA, const b2Sweep& sweepA,
const b2DistanceProxy* proxyB, const b2Sweep& sweepB)
{
m_proxyA = proxyA;
m_proxyB = proxyB;
int32 count = cache->count;
b2Assert(0 < count && count < 3);
m_sweepA = sweepA;
m_sweepB = sweepB;
b2Transform xfA, xfB;
m_sweepA.GetTransform(&xfA, 0.0f);
m_sweepB.GetTransform(&xfB, 0.0f);
if (count == 1)
{
m_type = e_points;
b2Vec2 localPointA = m_proxyA->GetVertex(cache->indexA[0]);
b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
b2Vec2 pointA = b2Mul(xfA, localPointA);
b2Vec2 pointB = b2Mul(xfB, localPointB);
m_axis = pointB - pointA;
float32 s = m_axis.Normalize();
return s;
}
else if (cache->indexA[0] == cache->indexA[1])
{
// Two points on B and one on A.
m_type = e_faceB;
b2Vec2 localPointB1 = proxyB->GetVertex(cache->indexB[0]);
b2Vec2 localPointB2 = proxyB->GetVertex(cache->indexB[1]);
m_axis = b2Cross(localPointB2 - localPointB1, 1.0f);
m_axis.Normalize();
b2Vec2 normal = b2Mul(xfB.R, m_axis);
m_localPoint = 0.5f * (localPointB1 + localPointB2);
b2Vec2 pointB = b2Mul(xfB, m_localPoint);
b2Vec2 localPointA = proxyA->GetVertex(cache->indexA[0]);
b2Vec2 pointA = b2Mul(xfA, localPointA);
float32 s = b2Dot(pointA - pointB, normal);
if (s < 0.0f)
{
m_axis = -m_axis;
s = -s;
}
return s;
}
else
{
// Two points on A and one or two points on B.
m_type = e_faceA;
b2Vec2 localPointA1 = m_proxyA->GetVertex(cache->indexA[0]);
b2Vec2 localPointA2 = m_proxyA->GetVertex(cache->indexA[1]);
m_axis = b2Cross(localPointA2 - localPointA1, 1.0f);
m_axis.Normalize();
b2Vec2 normal = b2Mul(xfA.R, m_axis);
m_localPoint = 0.5f * (localPointA1 + localPointA2);
b2Vec2 pointA = b2Mul(xfA, m_localPoint);
b2Vec2 localPointB = m_proxyB->GetVertex(cache->indexB[0]);
b2Vec2 pointB = b2Mul(xfB, localPointB);
float32 s = b2Dot(pointB - pointA, normal);
if (s < 0.0f)
{
m_axis = -m_axis;
s = -s;
}
return s;
}
}
bool b2PrismaticJoint::SolvePositionConstraints(const b2SolverData& data)
{
b2Vec2 cA = data.positions[m_indexA].c;
float32 aA = data.positions[m_indexA].a;
b2Vec2 cB = data.positions[m_indexB].c;
float32 aB = data.positions[m_indexB].a;
b2Rot qA(aA), qB(aB);
float32 mA = m_invMassA, mB = m_invMassB;
float32 iA = m_invIA, iB = m_invIB;
// Compute fresh Jacobians
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
b2Vec2 d = cB + rB - cA - rA;
b2Vec2 axis = b2Mul(qA, m_localXAxisA);
float32 a1 = b2Cross(d + rA, axis);
float32 a2 = b2Cross(rB, axis);
b2Vec2 perp = b2Mul(qA, m_localYAxisA);
float32 s1 = b2Cross(d + rA, perp);
float32 s2 = b2Cross(rB, perp);
b2Vec3 impulse;
b2Vec2 C1;
C1.x = b2Dot(perp, d);
C1.y = aB - aA - m_referenceAngle;
float32 linearError = b2Abs(C1.x);
float32 angularError = b2Abs(C1.y);
bool active = false;
float32 C2 = 0.0f;
if (m_enableLimit)
{
float32 translation = b2Dot(axis, d);
if (b2Abs(m_upperTranslation - m_lowerTranslation) < 2.0f * b2_linearSlop)
{
// Prevent large angular corrections
C2 = b2Clamp(translation, -b2_maxLinearCorrection, b2_maxLinearCorrection);
linearError = b2Max(linearError, b2Abs(translation));
active = true;
}
else if (translation <= m_lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = b2Clamp(translation - m_lowerTranslation + b2_linearSlop, -b2_maxLinearCorrection, 0.0f);
linearError = b2Max(linearError, m_lowerTranslation - translation);
active = true;
}
else if (translation >= m_upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = b2Clamp(translation - m_upperTranslation - b2_linearSlop, 0.0f, b2_maxLinearCorrection);
linearError = b2Max(linearError, translation - m_upperTranslation);
active = true;
}
}
if (active)
{
float32 k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float32 k12 = iA * s1 + iB * s2;
float32 k13 = iA * s1 * a1 + iB * s2 * a2;
float32 k22 = iA + iB;
if (k22 == 0.0f)
{
// For fixed rotation
k22 = 1.0f;
}
float32 k23 = iA * a1 + iB * a2;
float32 k33 = mA + mB + iA * a1 * a1 + iB * a2 * a2;
b2Mat33 K;
K.ex.Set(k11, k12, k13);
K.ey.Set(k12, k22, k23);
K.ez.Set(k13, k23, k33);
b2Vec3 C;
C.x = C1.x;
C.y = C1.y;
C.z = C2;
impulse = K.Solve33(-C);
}
else
{
float32 k11 = mA + mB + iA * s1 * s1 + iB * s2 * s2;
float32 k12 = iA * s1 + iB * s2;
float32 k22 = iA + iB;
if (k22 == 0.0f)
{
k22 = 1.0f;
}
b2Mat22 K;
K.ex.Set(k11, k12);
K.ey.Set(k12, k22);
b2Vec2 impulse1 = K.Solve(-C1);
impulse.x = impulse1.x;
impulse.y = impulse1.y;
impulse.z = 0.0f;
}
b2Vec2 P = impulse.x * perp + impulse.z * axis;
float32 LA = impulse.x * s1 + impulse.y + impulse.z * a1;
float32 LB = impulse.x * s2 + impulse.y + impulse.z * a2;
cA -= mA * P;
aA -= iA * LA;
cB += mB * P;
aB += iB * LB;
data.positions[m_indexA].c = cA;
data.positions[m_indexA].a = aA;
data.positions[m_indexB].c = cB;
data.positions[m_indexB].a = aB;
return linearError <= b2_linearSlop && angularError <= b2_angularSlop;
}
void b2Island::SolveTOI(const b2TimeStep& subStep, int32 toiIndexA, int32 toiIndexB)
{
b2Assert(toiIndexA < m_bodyCount);
b2Assert(toiIndexB < m_bodyCount);
// Initialize the body state.
for (int32 i = 0; i < m_bodyCount; ++i)
{
b2Body* b = m_bodies[i];
m_positions[i].c = b->m_sweep.c;
m_positions[i].a = b->m_sweep.a;
m_velocities[i].v = b->m_linearVelocity;
m_velocities[i].w = b->m_angularVelocity;
}
b2ContactSolverDef contactSolverDef;
contactSolverDef.contacts = m_contacts;
contactSolverDef.count = m_contactCount;
contactSolverDef.allocator = m_allocator;
contactSolverDef.step = subStep;
contactSolverDef.positions = m_positions;
contactSolverDef.velocities = m_velocities;
b2ContactSolver contactSolver(&contactSolverDef);
// Solve position constraints.
for (int32 i = 0; i < subStep.positionIterations; ++i)
{
bool contactsOkay = contactSolver.SolveTOIPositionConstraints(toiIndexA, toiIndexB);
if (contactsOkay)
{
break;
}
}
#if 0
// Is the new position really safe?
for (int32 i = 0; i < m_contactCount; ++i)
{
b2Contact* c = m_contacts[i];
b2Fixture* fA = c->GetFixtureA();
b2Fixture* fB = c->GetFixtureB();
b2Body* bA = fA->GetBody();
b2Body* bB = fB->GetBody();
int32 indexA = c->GetChildIndexA();
int32 indexB = c->GetChildIndexB();
b2DistanceInput input;
input.proxyA.Set(fA->GetShape(), indexA);
input.proxyB.Set(fB->GetShape(), indexB);
input.transformA = bA->GetTransform();
input.transformB = bB->GetTransform();
input.useRadii = false;
b2DistanceOutput output;
b2SimplexCache cache;
cache.count = 0;
b2Distance(&output, &cache, &input);
if (output.distance == 0 || cache.count == 3)
{
cache.count += 0;
}
}
#endif
// Leap of faith to new safe state.
m_bodies[toiIndexA]->m_sweep.c0 = m_positions[toiIndexA].c;
m_bodies[toiIndexA]->m_sweep.a0 = m_positions[toiIndexA].a;
m_bodies[toiIndexB]->m_sweep.c0 = m_positions[toiIndexB].c;
m_bodies[toiIndexB]->m_sweep.a0 = m_positions[toiIndexB].a;
// No warm starting is needed for TOI events because warm
// starting impulses were applied in the discrete solver.
contactSolver.InitializeVelocityConstraints();
// Solve velocity constraints.
for (int32 i = 0; i < subStep.velocityIterations; ++i)
{
contactSolver.SolveVelocityConstraints();
}
// Don't store the TOI contact forces for warm starting
// because they can be quite large.
float32 h = subStep.dt;
// Integrate positions
for (int32 i = 0; i < m_bodyCount; ++i)
{
b2Vec2 c = m_positions[i].c;
float32 a = m_positions[i].a;
b2Vec2 v = m_velocities[i].v;
float32 w = m_velocities[i].w;
// Check for large velocities
b2Vec2 translation = h * v;
if (b2Dot(translation, translation) > b2_maxTranslationSquared)
{
float32 ratio = b2_maxTranslation / translation.Length();
v *= ratio;
}
float32 rotation = h * w;
if (rotation * rotation > b2_maxRotationSquared)
{
float32 ratio = b2_maxRotation / b2Abs(rotation);
w *= ratio;
}
// Integrate
c += h * v;
a += h * w;
m_positions[i].c = c;
m_positions[i].a = a;
m_velocities[i].v = v;
m_velocities[i].w = w;
// Sync bodies
b2Body* body = m_bodies[i];
body->m_sweep.c = c;
body->m_sweep.a = a;
body->m_linearVelocity = v;
body->m_angularVelocity = w;
body->SynchronizeTransform();
}
Report(contactSolver.m_velocityConstraints);
}
bool b2GearJoint::SolvePositionConstraints(const b2SolverData& data)
{
b2Vec2 cA = data.positions[m_indexA].c;
float32 aA = data.positions[m_indexA].a;
b2Vec2 cB = data.positions[m_indexB].c;
float32 aB = data.positions[m_indexB].a;
b2Vec2 cC = data.positions[m_indexC].c;
float32 aC = data.positions[m_indexC].a;
b2Vec2 cD = data.positions[m_indexD].c;
float32 aD = data.positions[m_indexD].a;
b2Rot qA(aA), qB(aB), qC(aC), qD(aD);
float32 linearError = 0.0f;
float32 coordinateA, coordinateB;
b2Vec2 JvAC, JvBD;
float32 JwA, JwB, JwC, JwD;
float32 mass = 0.0f;
if (m_typeA == e_revoluteJoint)
{
JvAC.SetZero();
JwA = 1.0f;
JwC = 1.0f;
mass += m_iA + m_iC;
coordinateA = aA - aC - m_referenceAngleA;
}
else
{
b2Vec2 u = b2Mul(qC, m_localAxisC);
b2Vec2 rC = b2Mul(qC, m_localAnchorC - m_lcC);
b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_lcA);
JvAC = u;
JwC = b2Cross(rC, u);
JwA = b2Cross(rA, u);
mass += m_mC + m_mA + m_iC * JwC * JwC + m_iA * JwA * JwA;
b2Vec2 pC = m_localAnchorC - m_lcC;
b2Vec2 pA = b2MulT(qC, rA + (cA - cC));
coordinateA = b2Dot(pA - pC, m_localAxisC);
}
if (m_typeB == e_revoluteJoint)
{
JvBD.SetZero();
JwB = m_ratio;
JwD = m_ratio;
mass += m_ratio * m_ratio * (m_iB + m_iD);
coordinateB = aB - aD - m_referenceAngleB;
}
else
{
b2Vec2 u = b2Mul(qD, m_localAxisD);
b2Vec2 rD = b2Mul(qD, m_localAnchorD - m_lcD);
b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_lcB);
JvBD = m_ratio * u;
JwD = m_ratio * b2Cross(rD, u);
JwB = m_ratio * b2Cross(rB, u);
mass += m_ratio * m_ratio * (m_mD + m_mB) + m_iD * JwD * JwD + m_iB * JwB * JwB;
b2Vec2 pD = m_localAnchorD - m_lcD;
b2Vec2 pB = b2MulT(qD, rB + (cB - cD));
coordinateB = b2Dot(pB - pD, m_localAxisD);
}
float32 C = (coordinateA + m_ratio * coordinateB) - m_constant;
float32 impulse = 0.0f;
if (mass > 0.0f)
{
impulse = -C / mass;
}
cA += m_mA * impulse * JvAC;
aA += m_iA * impulse * JwA;
cB += m_mB * impulse * JvBD;
aB += m_iB * impulse * JwB;
cC -= m_mC * impulse * JvAC;
aC -= m_iC * impulse * JwC;
cD -= m_mD * impulse * JvBD;
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 < b2_linearSlop;
}
// Initialize position dependent portions of the velocity constraints.
void b2ContactSolver::InitializeVelocityConstraints()
{
for (int32 i = 0; i < m_count; ++i)
{
b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
b2ContactPositionConstraint* pc = m_positionConstraints + i;
float32 radiusA = pc->radiusA;
float32 radiusB = pc->radiusB;
b2Manifold* manifold = m_contacts[vc->contactIndex]->GetManifold();
int32 indexA = vc->indexA;
int32 indexB = vc->indexB;
float32 mA = vc->invMassA;
float32 mB = vc->invMassB;
float32 iA = vc->invIA;
float32 iB = vc->invIB;
b2Vec2 localCenterA = pc->localCenterA;
b2Vec2 localCenterB = pc->localCenterB;
b2Vec2 cA = m_positions[indexA].c;
float32 aA = m_positions[indexA].a;
b2Vec2 vA = m_velocities[indexA].v;
float32 wA = m_velocities[indexA].w;
b2Vec2 cB = m_positions[indexB].c;
float32 aB = m_positions[indexB].a;
b2Vec2 vB = m_velocities[indexB].v;
float32 wB = m_velocities[indexB].w;
b2Assert(manifold->pointCount > 0);
b2Transform xfA, xfB;
xfA.q.Set(aA);
xfB.q.Set(aB);
xfA.p = cA - b2Mul(xfA.q, localCenterA);
xfB.p = cB - b2Mul(xfB.q, localCenterB);
b2WorldManifold worldManifold;
worldManifold.Initialize(manifold, xfA, radiusA, xfB, radiusB);
vc->normal = worldManifold.normal;
int32 pointCount = vc->pointCount;
for (int32 j = 0; j < pointCount; ++j)
{
b2VelocityConstraintPoint* vcp = vc->points + j;
vcp->rA = worldManifold.points[j] - cA;
vcp->rB = worldManifold.points[j] - cB;
float32 rnA = b2Cross(vcp->rA, vc->normal);
float32 rnB = b2Cross(vcp->rB, vc->normal);
float32 kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
vcp->normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;
b2Vec2 tangent = b2Cross(vc->normal, 1.0f);
float32 rtA = b2Cross(vcp->rA, tangent);
float32 rtB = b2Cross(vcp->rB, tangent);
float32 kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
vcp->tangentMass = kTangent > 0.0f ? 1.0f / kTangent : 0.0f;
// Setup a velocity bias for restitution.
vcp->velocityBias = 0.0f;
float32 vRel = b2Dot(vc->normal, vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA));
if (vRel < -b2_velocityThreshold)
{
vcp->velocityBias = -vc->restitution * vRel;
}
}
// If we have two points, then prepare the block solver.
if (vc->pointCount == 2)
{
b2VelocityConstraintPoint* vcp1 = vc->points + 0;
b2VelocityConstraintPoint* vcp2 = vc->points + 1;
float32 rn1A = b2Cross(vcp1->rA, vc->normal);
float32 rn1B = b2Cross(vcp1->rB, vc->normal);
float32 rn2A = b2Cross(vcp2->rA, vc->normal);
float32 rn2B = b2Cross(vcp2->rB, vc->normal);
float32 k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
float32 k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
float32 k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;
// Ensure a reasonable condition number.
const float32 k_maxConditionNumber = 1000.0f;
if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12))
{
// K is safe to invert.
vc->K.ex.Set(k11, k12);
vc->K.ey.Set(k12, k22);
vc->normalMass = vc->K.GetInverse();
}
else
{
// The constraints are redundant, just use one.
// TODO_ERIN use deepest?
vc->pointCount = 1;
}
}
}
}
b2GearJoint::b2GearJoint(const b2GearJointDef* def)
: b2Joint(def)
{
m_joint1 = def->joint1;
m_joint2 = def->joint2;
m_typeA = m_joint1->GetType();
m_typeB = m_joint2->GetType();
b2Assert(m_typeA == e_revoluteJoint || m_typeA == e_prismaticJoint);
b2Assert(m_typeB == e_revoluteJoint || m_typeB == e_prismaticJoint);
float32 coordinateA, coordinateB;
// TODO_ERIN there might be some problem with the joint edges in b2Joint.
m_bodyC = m_joint1->GetBodyA();
m_bodyA = m_joint1->GetBodyB();
// Get geometry of joint1
b2Transform xfA = m_bodyA->m_xf;
float32 aA = m_bodyA->m_sweep.a;
b2Transform xfC = m_bodyC->m_xf;
float32 aC = m_bodyC->m_sweep.a;
if (m_typeA == e_revoluteJoint)
{
b2RevoluteJoint* revolute = (b2RevoluteJoint*)def->joint1;
m_localAnchorC = revolute->m_localAnchorA;
m_localAnchorA = revolute->m_localAnchorB;
m_referenceAngleA = revolute->m_referenceAngle;
m_localAxisC.SetZero();
coordinateA = aA - aC - m_referenceAngleA;
}
else
{
b2PrismaticJoint* prismatic = (b2PrismaticJoint*)def->joint1;
m_localAnchorC = prismatic->m_localAnchorA;
m_localAnchorA = prismatic->m_localAnchorB;
m_referenceAngleA = prismatic->m_referenceAngle;
m_localAxisC = prismatic->m_localXAxisA;
b2Vec2 pC = m_localAnchorC;
b2Vec2 pA = b2MulT(xfC.q, b2Mul(xfA.q, m_localAnchorA) + (xfA.p - xfC.p));
coordinateA = b2Dot(pA - pC, m_localAxisC);
}
m_bodyD = m_joint2->GetBodyA();
m_bodyB = m_joint2->GetBodyB();
// Get geometry of joint2
b2Transform xfB = m_bodyB->m_xf;
float32 aB = m_bodyB->m_sweep.a;
b2Transform xfD = m_bodyD->m_xf;
float32 aD = m_bodyD->m_sweep.a;
if (m_typeB == e_revoluteJoint)
{
b2RevoluteJoint* revolute = (b2RevoluteJoint*)def->joint2;
m_localAnchorD = revolute->m_localAnchorA;
m_localAnchorB = revolute->m_localAnchorB;
m_referenceAngleB = revolute->m_referenceAngle;
m_localAxisD.SetZero();
coordinateB = aB - aD - m_referenceAngleB;
}
else
{
b2PrismaticJoint* prismatic = (b2PrismaticJoint*)def->joint2;
m_localAnchorD = prismatic->m_localAnchorA;
m_localAnchorB = prismatic->m_localAnchorB;
m_referenceAngleB = prismatic->m_referenceAngle;
m_localAxisD = prismatic->m_localXAxisA;
b2Vec2 pD = m_localAnchorD;
b2Vec2 pB = b2MulT(xfD.q, b2Mul(xfB.q, m_localAnchorB) + (xfB.p - xfD.p));
coordinateB = b2Dot(pB - pD, m_localAxisD);
}
m_ratio = def->ratio;
m_constant = coordinateA + m_ratio * coordinateB;
m_impulse = 0.0f;
}
bool b2CircleShape::TestPoint(const b2XForm& transform, const b2Vec2& p) const
{
b2Vec2 center = transform.position + b2Mul(transform.R, m_p);
b2Vec2 d = p - center;
return b2Dot(d, d) <= m_radius * m_radius;
}
bool b2PolygonShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input,
const b2Transform& xf, int32 childIndex) const
{
B2_NOT_USED(childIndex);
// Put the ray into the polygon's frame of reference.
b2Vec2 p1 = b2MulT(xf.q, input.p1 - xf.p);
b2Vec2 p2 = b2MulT(xf.q, input.p2 - xf.p);
b2Vec2 d = p2 - p1;
float32 lower = 0.0f, upper = input.maxFraction;
int32 index = -1;
for (int32 i = 0; i < m_count; ++i)
{
// p = p1 + a * d
// dot(normal, p - v) = 0
// dot(normal, p1 - v) + a * dot(normal, d) = 0
float32 numerator = b2Dot(m_normals[i], m_vertices[i] - p1);
float32 denominator = b2Dot(m_normals[i], d);
if (denominator == 0.0f)
{
if (numerator < 0.0f)
{
return false;
}
}
else
{
// Note: we want this predicate without division:
// lower < numerator / denominator, where denominator < 0
// Since denominator < 0, we have to flip the inequality:
// lower < numerator / denominator <==> denominator * lower > numerator.
if (denominator < 0.0f && numerator < lower * denominator)
{
// Increase lower.
// The segment enters this half-space.
lower = numerator / denominator;
index = i;
}
else if (denominator > 0.0f && numerator < upper * denominator)
{
// Decrease upper.
// The segment exits this half-space.
upper = numerator / denominator;
}
}
// The use of epsilon here causes the assert on lower to trip
// in some cases. Apparently the use of epsilon was to make edge
// shapes work, but now those are handled separately.
//if (upper < lower - b2_epsilon)
if (upper < lower)
{
return false;
}
}
b2Assert(0.0f <= lower && lower <= input.maxFraction);
if (index >= 0)
{
output->fraction = lower;
output->normal = b2Mul(xf.q, m_normals[index]);
return true;
}
return false;
}
void b2ContactSolver::SolveVelocityConstraints()
{
for (int32 i = 0; i < m_constraintCount; ++i)
{
b2ContactConstraint* c = m_constraints + i;
b2Body* bodyA = c->bodyA;
b2Body* bodyB = c->bodyB;
float32 wA = bodyA->m_angularVelocity;
float32 wB = bodyB->m_angularVelocity;
b2Vec2 vA = bodyA->m_linearVelocity;
b2Vec2 vB = bodyB->m_linearVelocity;
float32 invMassA = bodyA->m_invMass;
float32 invIA = bodyA->m_invI;
float32 invMassB = bodyB->m_invMass;
float32 invIB = bodyB->m_invI;
b2Vec2 normal = c->normal;
b2Vec2 tangent = b2Cross(normal, 1.0f);
float32 friction = c->friction;
b2Assert(c->pointCount == 1 || c->pointCount == 2);
// Solve tangent constraints
for (int32 j = 0; j < c->pointCount; ++j)
{
b2ContactConstraintPoint* ccp = c->points + j;
// Relative velocity at contact
b2Vec2 dv = vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA);
// Compute tangent force
float32 vt = b2Dot(dv, tangent);
float32 lambda = ccp->tangentMass * (-vt);
// b2Clamp the accumulated force
float32 maxFriction = friction * ccp->normalImpulse;
float32 newImpulse = b2Clamp(ccp->tangentImpulse + lambda, -maxFriction, maxFriction);
lambda = newImpulse - ccp->tangentImpulse;
// Apply contact impulse
b2Vec2 P = lambda * tangent;
vA -= invMassA * P;
wA -= invIA * b2Cross(ccp->rA, P);
vB += invMassB * P;
wB += invIB * b2Cross(ccp->rB, P);
ccp->tangentImpulse = newImpulse;
}
// Solve normal constraints
if (c->pointCount == 1)
{
b2ContactConstraintPoint* ccp = c->points + 0;
// Relative velocity at contact
b2Vec2 dv = vB + b2Cross(wB, ccp->rB) - vA - b2Cross(wA, ccp->rA);
// Compute normal impulse
float32 vn = b2Dot(dv, normal);
float32 lambda = -ccp->normalMass * (vn - ccp->velocityBias);
// b2Clamp the accumulated impulse
float32 newImpulse = b2Max(ccp->normalImpulse + lambda, 0.0f);
lambda = newImpulse - ccp->normalImpulse;
// Apply contact impulse
b2Vec2 P = lambda * normal;
vA -= invMassA * P;
wA -= invIA * b2Cross(ccp->rA, P);
vB += invMassB * P;
wB += invIB * b2Cross(ccp->rB, P);
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;
b2ContactConstraintPoint* cp1 = c->points + 0;
b2ContactConstraintPoint* cp2 = c->points + 1;
b2Vec2 a(cp1->normalImpulse, cp2->normalImpulse);
b2Assert(a.x >= 0.0f && a.y >= 0.0f);
// Relative velocity at contact
b2Vec2 dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
b2Vec2 dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
float32 vn1 = b2Dot(dv1, normal);
float32 vn2 = b2Dot(dv2, normal);
b2Vec2 b;
b.x = vn1 - cp1->velocityBias;
b.y = vn2 - cp2->velocityBias;
b -= b2Mul(c->K, a);
const float32 k_errorTol = 1e-3f;
B2_NOT_USED(k_errorTol);
for (;;)
{
//
// Case 1: vn = 0
//
// 0 = A * x' + b'
//
// Solve for x':
//
// x' = - inv(A) * b'
//
b2Vec2 x = - b2Mul(c->normalMass, b);
if (x.x >= 0.0f && x.y >= 0.0f)
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= invMassA * (P1 + P2);
wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += invMassB * (P1 + P2);
wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
vn1 = b2Dot(dv1, normal);
vn2 = b2Dot(dv2, normal);
b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
b2Assert(b2Abs(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'
//
x.x = - cp1->normalMass * b.x;
x.y = 0.0f;
vn1 = 0.0f;
vn2 = c->K.col1.y * x.x + b.y;
if (x.x >= 0.0f && vn2 >= 0.0f)
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= invMassA * (P1 + P2);
wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += invMassB * (P1 + P2);
wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
// Compute normal velocity
vn1 = b2Dot(dv1, normal);
b2Assert(b2Abs(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'
//
x.x = 0.0f;
x.y = - cp2->normalMass * b.y;
vn1 = c->K.col2.x * x.y + b.x;
vn2 = 0.0f;
if (x.y >= 0.0f && vn1 >= 0.0f)
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= invMassA * (P1 + P2);
wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += invMassB * (P1 + P2);
wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
#if B2_DEBUG_SOLVER == 1
// Postconditions
dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
// Compute normal velocity
vn2 = b2Dot(dv2, normal);
b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
#endif
break;
}
//
// Case 4: x1 = 0 and x2 = 0
//
// vn1 = b1
// vn2 = b2;
x.x = 0.0f;
x.y = 0.0f;
vn1 = b.x;
vn2 = b.y;
if (vn1 >= 0.0f && vn2 >= 0.0f )
{
// Resubstitute for the incremental impulse
b2Vec2 d = x - a;
// Apply incremental impulse
b2Vec2 P1 = d.x * normal;
b2Vec2 P2 = d.y * normal;
vA -= invMassA * (P1 + P2);
wA -= invIA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
vB += invMassB * (P1 + P2);
wB += invIB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
// Accumulate
cp1->normalImpulse = x.x;
cp2->normalImpulse = x.y;
break;
}
// No solution, give up. This is hit sometimes, but it doesn't seem to matter.
break;
}
}
bodyA->m_linearVelocity = vA;
bodyA->m_angularVelocity = wA;
bodyB->m_linearVelocity = vB;
bodyB->m_angularVelocity = wB;
}
}
bool b2PolygonShape::RayCast(b2RayCastOutput* output, const b2RayCastInput& input, const b2Transform& xf) const
{
// Put the ray into the polygon's frame of reference.
b2Vec2 p1 = b2MulT(xf.R, input.p1 - xf.position);
b2Vec2 p2 = b2MulT(xf.R, input.p2 - xf.position);
b2Vec2 d = p2 - p1;
if (m_vertexCount == 2)
{
b2Vec2 v1 = m_vertices[0];
b2Vec2 v2 = m_vertices[1];
b2Vec2 normal = m_normals[0];
// q = p1 + t * d
// dot(normal, q - v1) = 0
// dot(normal, p1 - v1) + t * dot(normal, d) = 0
float32 numerator = b2Dot(normal, v1 - p1);
float32 denominator = b2Dot(normal, d);
if (denominator == 0.0f)
{
return false;
}
float32 t = numerator / denominator;
if (t < 0.0f || 1.0f < t)
{
return false;
}
b2Vec2 q = p1 + t * d;
// q = v1 + s * r
// s = dot(q - v1, r) / dot(r, r)
b2Vec2 r = v2 - v1;
float32 rr = b2Dot(r, r);
if (rr == 0.0f)
{
return false;
}
float32 s = b2Dot(q - v1, r) / rr;
if (s < 0.0f || 1.0f < s)
{
return false;
}
output->fraction = t;
if (numerator > 0.0f)
{
output->normal = -normal;
}
else
{
output->normal = normal;
}
return true;
}
else
{
float32 lower = 0.0f, upper = input.maxFraction;
int32 index = -1;
for (int32 i = 0; i < m_vertexCount; ++i)
{
// p = p1 + a * d
// dot(normal, p - v) = 0
// dot(normal, p1 - v) + a * dot(normal, d) = 0
float32 numerator = b2Dot(m_normals[i], m_vertices[i] - p1);
float32 denominator = b2Dot(m_normals[i], d);
if (denominator == 0.0f)
{
if (numerator < 0.0f)
{
return false;
}
}
else
{
// Note: we want this predicate without division:
// lower < numerator / denominator, where denominator < 0
// Since denominator < 0, we have to flip the inequality:
// lower < numerator / denominator <==> denominator * lower > numerator.
if (denominator < 0.0f && numerator < lower * denominator)
{
// Increase lower.
// The segment enters this half-space.
lower = numerator / denominator;
index = i;
}
else if (denominator > 0.0f && numerator < upper * denominator)
{
// Decrease upper.
// The segment exits this half-space.
upper = numerator / denominator;
}
}
// The use of epsilon here causes the assert on lower to trip
// in some cases. Apparently the use of epsilon was to make edge
// shapes work, but now those are handled separately.
//if (upper < lower - b2_epsilon)
if (upper < lower)
{
return false;
}
}
b2Assert(0.0f <= lower && lower <= input.maxFraction);
if (index >= 0)
{
output->fraction = lower;
output->normal = b2Mul(xf.R, m_normals[index]);
return true;
}
}
return false;
}