1 /*
2 * Copyright (c) 2006-2011 Erin Catto http://www.box2d.org
3 *
4 * This software is provided 'as-is', without any express or implied
5 * warranty. In no event will the authors be held liable for any damages
6 * arising from the use of this software.
7 * Permission is granted to anyone to use this software for any purpose,
8 * including commercial applications, and to alter it and redistribute it
9 * freely, subject to the following restrictions:
10 * 1. The origin of this software must not be misrepresented; you must not
11 * claim that you wrote the original software. If you use this software
12 * in a product, an acknowledgment in the product documentation would be
13 * appreciated but is not required.
14 * 2. Altered source versions must be plainly marked as such, and must not be
15 * misrepresented as being the original software.
16 * 3. This notice may not be removed or altered from any source distribution.
17 */
18
19 #include "b2ContactSolver.h"
20
21 #include "b2Contact.h"
22 #include "../b2Body.h"
23 #include "../b2Fixture.h"
24 #include "../b2World.h"
25 #include "../../Common/b2StackAllocator.h"
26
27 #define B2_DEBUG_SOLVER 0
28
29 struct b2ContactPositionConstraint
30 {
31 b2Vec2 localPoints[b2_maxManifoldPoints];
32 b2Vec2 localNormal;
33 b2Vec2 localPoint;
34 int32 indexA;
35 int32 indexB;
36 float32 invMassA, invMassB;
37 b2Vec2 localCenterA, localCenterB;
38 float32 invIA, invIB;
39 b2Manifold::Type type;
40 float32 radiusA, radiusB;
41 int32 pointCount;
42 };
43
b2ContactSolver(b2ContactSolverDef * def)44 b2ContactSolver::b2ContactSolver(b2ContactSolverDef* def)
45 {
46 m_step = def->step;
47 m_allocator = def->allocator;
48 m_count = def->count;
49 m_positionConstraints = (b2ContactPositionConstraint*)m_allocator->Allocate(m_count * sizeof(b2ContactPositionConstraint));
50 m_velocityConstraints = (b2ContactVelocityConstraint*)m_allocator->Allocate(m_count * sizeof(b2ContactVelocityConstraint));
51 m_positions = def->positions;
52 m_velocities = def->velocities;
53 m_contacts = def->contacts;
54
55 // Initialize position independent portions of the constraints.
56 for (int32 i = 0; i < m_count; ++i)
57 {
58 b2Contact* contact = m_contacts[i];
59
60 b2Fixture* fixtureA = contact->m_fixtureA;
61 b2Fixture* fixtureB = contact->m_fixtureB;
62 b2Shape* shapeA = fixtureA->GetShape();
63 b2Shape* shapeB = fixtureB->GetShape();
64 float32 radiusA = shapeA->m_radius;
65 float32 radiusB = shapeB->m_radius;
66 b2Body* bodyA = fixtureA->GetBody();
67 b2Body* bodyB = fixtureB->GetBody();
68 b2Manifold* manifold = contact->GetManifold();
69
70 int32 pointCount = manifold->pointCount;
71 b2Assert(pointCount > 0);
72
73 b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
74 vc->friction = contact->m_friction;
75 vc->restitution = contact->m_restitution;
76 vc->indexA = bodyA->m_islandIndex;
77 vc->indexB = bodyB->m_islandIndex;
78 vc->invMassA = bodyA->m_invMass;
79 vc->invMassB = bodyB->m_invMass;
80 vc->invIA = bodyA->m_invI;
81 vc->invIB = bodyB->m_invI;
82 vc->contactIndex = i;
83 vc->pointCount = pointCount;
84 vc->K.SetZero();
85 vc->normalMass.SetZero();
86
87 b2ContactPositionConstraint* pc = m_positionConstraints + i;
88 pc->indexA = bodyA->m_islandIndex;
89 pc->indexB = bodyB->m_islandIndex;
90 pc->invMassA = bodyA->m_invMass;
91 pc->invMassB = bodyB->m_invMass;
92 pc->localCenterA = bodyA->m_sweep.localCenter;
93 pc->localCenterB = bodyB->m_sweep.localCenter;
94 pc->invIA = bodyA->m_invI;
95 pc->invIB = bodyB->m_invI;
96 pc->localNormal = manifold->localNormal;
97 pc->localPoint = manifold->localPoint;
98 pc->pointCount = pointCount;
99 pc->radiusA = radiusA;
100 pc->radiusB = radiusB;
101 pc->type = manifold->type;
102
103 for (int32 j = 0; j < pointCount; ++j)
104 {
105 b2ManifoldPoint* cp = manifold->points + j;
106 b2VelocityConstraintPoint* vcp = vc->points + j;
107
108 if (m_step.warmStarting)
109 {
110 vcp->normalImpulse = m_step.dtRatio * cp->normalImpulse;
111 vcp->tangentImpulse = m_step.dtRatio * cp->tangentImpulse;
112 }
113 else
114 {
115 vcp->normalImpulse = 0.0f;
116 vcp->tangentImpulse = 0.0f;
117 }
118
119 vcp->rA.SetZero();
120 vcp->rB.SetZero();
121 vcp->normalMass = 0.0f;
122 vcp->tangentMass = 0.0f;
123 vcp->velocityBias = 0.0f;
124
125 pc->localPoints[j] = cp->localPoint;
126 }
127 }
128 }
129
~b2ContactSolver()130 b2ContactSolver::~b2ContactSolver()
131 {
132 m_allocator->Free(m_velocityConstraints);
133 m_allocator->Free(m_positionConstraints);
134 }
135
136 // Initialize position dependent portions of the velocity constraints.
InitializeVelocityConstraints()137 void b2ContactSolver::InitializeVelocityConstraints()
138 {
139 for (int32 i = 0; i < m_count; ++i)
140 {
141 b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
142 b2ContactPositionConstraint* pc = m_positionConstraints + i;
143
144 float32 radiusA = pc->radiusA;
145 float32 radiusB = pc->radiusB;
146 b2Manifold* manifold = m_contacts[vc->contactIndex]->GetManifold();
147
148 int32 indexA = vc->indexA;
149 int32 indexB = vc->indexB;
150
151 float32 mA = vc->invMassA;
152 float32 mB = vc->invMassB;
153 float32 iA = vc->invIA;
154 float32 iB = vc->invIB;
155 b2Vec2 localCenterA = pc->localCenterA;
156 b2Vec2 localCenterB = pc->localCenterB;
157
158 b2Vec2 cA = m_positions[indexA].c;
159 float32 aA = m_positions[indexA].a;
160 b2Vec2 vA = m_velocities[indexA].v;
161 float32 wA = m_velocities[indexA].w;
162
163 b2Vec2 cB = m_positions[indexB].c;
164 float32 aB = m_positions[indexB].a;
165 b2Vec2 vB = m_velocities[indexB].v;
166 float32 wB = m_velocities[indexB].w;
167
168 b2Assert(manifold->pointCount > 0);
169
170 b2Transform xfA, xfB;
171 xfA.q.Set(aA);
172 xfB.q.Set(aB);
173 xfA.p = cA - b2Mul(xfA.q, localCenterA);
174 xfB.p = cB - b2Mul(xfB.q, localCenterB);
175
176 b2WorldManifold worldManifold;
177 worldManifold.Initialize(manifold, xfA, radiusA, xfB, radiusB);
178
179 vc->normal = worldManifold.normal;
180
181 int32 pointCount = vc->pointCount;
182 for (int32 j = 0; j < pointCount; ++j)
183 {
184 b2VelocityConstraintPoint* vcp = vc->points + j;
185
186 vcp->rA = worldManifold.points[j] - cA;
187 vcp->rB = worldManifold.points[j] - cB;
188
189 float32 rnA = b2Cross(vcp->rA, vc->normal);
190 float32 rnB = b2Cross(vcp->rB, vc->normal);
191
192 float32 kNormal = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
193
194 vcp->normalMass = kNormal > 0.0f ? 1.0f / kNormal : 0.0f;
195
196 b2Vec2 tangent = b2Cross(vc->normal, 1.0f);
197
198 float32 rtA = b2Cross(vcp->rA, tangent);
199 float32 rtB = b2Cross(vcp->rB, tangent);
200
201 float32 kTangent = mA + mB + iA * rtA * rtA + iB * rtB * rtB;
202
203 vcp->tangentMass = kTangent > 0.0f ? 1.0f / kTangent : 0.0f;
204
205 // Setup a velocity bias for restitution.
206 vcp->velocityBias = 0.0f;
207 float32 vRel = b2Dot(vc->normal, vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA));
208 if (vRel < -b2_velocityThreshold)
209 {
210 vcp->velocityBias = -vc->restitution * vRel;
211 }
212 }
213
214 // If we have two points, then prepare the block solver.
215 if (vc->pointCount == 2)
216 {
217 b2VelocityConstraintPoint* vcp1 = vc->points + 0;
218 b2VelocityConstraintPoint* vcp2 = vc->points + 1;
219
220 float32 rn1A = b2Cross(vcp1->rA, vc->normal);
221 float32 rn1B = b2Cross(vcp1->rB, vc->normal);
222 float32 rn2A = b2Cross(vcp2->rA, vc->normal);
223 float32 rn2B = b2Cross(vcp2->rB, vc->normal);
224
225 float32 k11 = mA + mB + iA * rn1A * rn1A + iB * rn1B * rn1B;
226 float32 k22 = mA + mB + iA * rn2A * rn2A + iB * rn2B * rn2B;
227 float32 k12 = mA + mB + iA * rn1A * rn2A + iB * rn1B * rn2B;
228
229 // Ensure a reasonable condition number.
230 const float32 k_maxConditionNumber = 1000.0f;
231 if (k11 * k11 < k_maxConditionNumber * (k11 * k22 - k12 * k12))
232 {
233 // K is safe to invert.
234 vc->K.ex.Set(k11, k12);
235 vc->K.ey.Set(k12, k22);
236 vc->normalMass = vc->K.GetInverse();
237 }
238 else
239 {
240 // The constraints are redundant, just use one.
241 // TODO_ERIN use deepest?
242 vc->pointCount = 1;
243 }
244 }
245 }
246 }
247
WarmStart()248 void b2ContactSolver::WarmStart()
249 {
250 // Warm start.
251 for (int32 i = 0; i < m_count; ++i)
252 {
253 b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
254
255 int32 indexA = vc->indexA;
256 int32 indexB = vc->indexB;
257 float32 mA = vc->invMassA;
258 float32 iA = vc->invIA;
259 float32 mB = vc->invMassB;
260 float32 iB = vc->invIB;
261 int32 pointCount = vc->pointCount;
262
263 b2Vec2 vA = m_velocities[indexA].v;
264 float32 wA = m_velocities[indexA].w;
265 b2Vec2 vB = m_velocities[indexB].v;
266 float32 wB = m_velocities[indexB].w;
267
268 b2Vec2 normal = vc->normal;
269 b2Vec2 tangent = b2Cross(normal, 1.0f);
270
271 for (int32 j = 0; j < pointCount; ++j)
272 {
273 b2VelocityConstraintPoint* vcp = vc->points + j;
274 b2Vec2 P = vcp->normalImpulse * normal + vcp->tangentImpulse * tangent;
275 wA -= iA * b2Cross(vcp->rA, P);
276 vA -= mA * P;
277 wB += iB * b2Cross(vcp->rB, P);
278 vB += mB * P;
279 }
280
281 m_velocities[indexA].v = vA;
282 m_velocities[indexA].w = wA;
283 m_velocities[indexB].v = vB;
284 m_velocities[indexB].w = wB;
285 }
286 }
287
SolveVelocityConstraints()288 void b2ContactSolver::SolveVelocityConstraints()
289 {
290 for (int32 i = 0; i < m_count; ++i)
291 {
292 b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
293
294 int32 indexA = vc->indexA;
295 int32 indexB = vc->indexB;
296 float32 mA = vc->invMassA;
297 float32 iA = vc->invIA;
298 float32 mB = vc->invMassB;
299 float32 iB = vc->invIB;
300 int32 pointCount = vc->pointCount;
301
302 b2Vec2 vA = m_velocities[indexA].v;
303 float32 wA = m_velocities[indexA].w;
304 b2Vec2 vB = m_velocities[indexB].v;
305 float32 wB = m_velocities[indexB].w;
306
307 b2Vec2 normal = vc->normal;
308 b2Vec2 tangent = b2Cross(normal, 1.0f);
309 float32 friction = vc->friction;
310
311 b2Assert(pointCount == 1 || pointCount == 2);
312
313 // Solve tangent constraints first because non-penetration is more important
314 // than friction.
315 for (int32 j = 0; j < pointCount; ++j)
316 {
317 b2VelocityConstraintPoint* vcp = vc->points + j;
318
319 // Relative velocity at contact
320 b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA);
321
322 // Compute tangent force
323 float32 vt = b2Dot(dv, tangent);
324 float32 lambda = vcp->tangentMass * (-vt);
325
326 // b2Clamp the accumulated force
327 float32 maxFriction = friction * vcp->normalImpulse;
328 float32 newImpulse = b2Clamp(vcp->tangentImpulse + lambda, -maxFriction, maxFriction);
329 lambda = newImpulse - vcp->tangentImpulse;
330 vcp->tangentImpulse = newImpulse;
331
332 // Apply contact impulse
333 b2Vec2 P = lambda * tangent;
334
335 vA -= mA * P;
336 wA -= iA * b2Cross(vcp->rA, P);
337
338 vB += mB * P;
339 wB += iB * b2Cross(vcp->rB, P);
340 }
341
342 // Solve normal constraints
343 if (vc->pointCount == 1)
344 {
345 b2VelocityConstraintPoint* vcp = vc->points + 0;
346
347 // Relative velocity at contact
348 b2Vec2 dv = vB + b2Cross(wB, vcp->rB) - vA - b2Cross(wA, vcp->rA);
349
350 // Compute normal impulse
351 float32 vn = b2Dot(dv, normal);
352 float32 lambda = -vcp->normalMass * (vn - vcp->velocityBias);
353
354 // b2Clamp the accumulated impulse
355 float32 newImpulse = b2Max(vcp->normalImpulse + lambda, 0.0f);
356 lambda = newImpulse - vcp->normalImpulse;
357 vcp->normalImpulse = newImpulse;
358
359 // Apply contact impulse
360 b2Vec2 P = lambda * normal;
361 vA -= mA * P;
362 wA -= iA * b2Cross(vcp->rA, P);
363
364 vB += mB * P;
365 wB += iB * b2Cross(vcp->rB, P);
366 }
367 else
368 {
369 // Block solver developed in collaboration with Dirk Gregorius (back in 01/07 on Box2D_Lite).
370 // Build the mini LCP for this contact patch
371 //
372 // vn = A * x + b, vn >= 0, , vn >= 0, x >= 0 and vn_i * x_i = 0 with i = 1..2
373 //
374 // A = J * W * JT and J = ( -n, -r1 x n, n, r2 x n )
375 // b = vn0 - velocityBias
376 //
377 // The system is solved using the "Total enumeration method" (s. Murty). The complementary constraint vn_i * x_i
378 // implies that we must have in any solution either vn_i = 0 or x_i = 0. So for the 2D contact problem the cases
379 // 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
380 // solution that satisfies the problem is chosen.
381 //
382 // In order to account of the accumulated impulse 'a' (because of the iterative nature of the solver which only requires
383 // that the accumulated impulse is clamped and not the incremental impulse) we change the impulse variable (x_i).
384 //
385 // Substitute:
386 //
387 // x = a + d
388 //
389 // a := old total impulse
390 // x := new total impulse
391 // d := incremental impulse
392 //
393 // For the current iteration we extend the formula for the incremental impulse
394 // to compute the new total impulse:
395 //
396 // vn = A * d + b
397 // = A * (x - a) + b
398 // = A * x + b - A * a
399 // = A * x + b'
400 // b' = b - A * a;
401
402 b2VelocityConstraintPoint* cp1 = vc->points + 0;
403 b2VelocityConstraintPoint* cp2 = vc->points + 1;
404
405 b2Vec2 a(cp1->normalImpulse, cp2->normalImpulse);
406 b2Assert(a.x >= 0.0f && a.y >= 0.0f);
407
408 // Relative velocity at contact
409 b2Vec2 dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
410 b2Vec2 dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
411
412 // Compute normal velocity
413 float32 vn1 = b2Dot(dv1, normal);
414 float32 vn2 = b2Dot(dv2, normal);
415
416 b2Vec2 b;
417 b.x = vn1 - cp1->velocityBias;
418 b.y = vn2 - cp2->velocityBias;
419
420 // Compute b'
421 b -= b2Mul(vc->K, a);
422
423 const float32 k_errorTol = 1e-3f;
424 B2_NOT_USED(k_errorTol);
425
426 for (;;)
427 {
428 //
429 // Case 1: vn = 0
430 //
431 // 0 = A * x + b'
432 //
433 // Solve for x:
434 //
435 // x = - inv(A) * b'
436 //
437 b2Vec2 x = - b2Mul(vc->normalMass, b);
438
439 if (x.x >= 0.0f && x.y >= 0.0f)
440 {
441 // Get the incremental impulse
442 b2Vec2 d = x - a;
443
444 // Apply incremental impulse
445 b2Vec2 P1 = d.x * normal;
446 b2Vec2 P2 = d.y * normal;
447 vA -= mA * (P1 + P2);
448 wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
449
450 vB += mB * (P1 + P2);
451 wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
452
453 // Accumulate
454 cp1->normalImpulse = x.x;
455 cp2->normalImpulse = x.y;
456
457 #if B2_DEBUG_SOLVER == 1
458 // Postconditions
459 dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
460 dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
461
462 // Compute normal velocity
463 vn1 = b2Dot(dv1, normal);
464 vn2 = b2Dot(dv2, normal);
465
466 b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
467 b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
468 #endif
469 break;
470 }
471
472 //
473 // Case 2: vn1 = 0 and x2 = 0
474 //
475 // 0 = a11 * x1 + a12 * 0 + b1'
476 // vn2 = a21 * x1 + a22 * 0 + b2'
477 //
478 x.x = - cp1->normalMass * b.x;
479 x.y = 0.0f;
480 //vn1 = 0.0f;
481 vn2 = vc->K.ex.y * x.x + b.y;
482
483 if (x.x >= 0.0f && vn2 >= 0.0f)
484 {
485 // Get the incremental impulse
486 b2Vec2 d = x - a;
487
488 // Apply incremental impulse
489 b2Vec2 P1 = d.x * normal;
490 b2Vec2 P2 = d.y * normal;
491 vA -= mA * (P1 + P2);
492 wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
493
494 vB += mB * (P1 + P2);
495 wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
496
497 // Accumulate
498 cp1->normalImpulse = x.x;
499 cp2->normalImpulse = x.y;
500
501 #if B2_DEBUG_SOLVER == 1
502 // Postconditions
503 dv1 = vB + b2Cross(wB, cp1->rB) - vA - b2Cross(wA, cp1->rA);
504
505 // Compute normal velocity
506 vn1 = b2Dot(dv1, normal);
507
508 b2Assert(b2Abs(vn1 - cp1->velocityBias) < k_errorTol);
509 #endif
510 break;
511 }
512
513
514 //
515 // Case 3: vn2 = 0 and x1 = 0
516 //
517 // vn1 = a11 * 0 + a12 * x2 + b1'
518 // 0 = a21 * 0 + a22 * x2 + b2'
519 //
520 x.x = 0.0f;
521 x.y = - cp2->normalMass * b.y;
522 vn1 = vc->K.ey.x * x.y + b.x;
523 //vn2 = 0.0f;
524
525 if (x.y >= 0.0f && vn1 >= 0.0f)
526 {
527 // Resubstitute for the incremental impulse
528 b2Vec2 d = x - a;
529
530 // Apply incremental impulse
531 b2Vec2 P1 = d.x * normal;
532 b2Vec2 P2 = d.y * normal;
533 vA -= mA * (P1 + P2);
534 wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
535
536 vB += mB * (P1 + P2);
537 wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
538
539 // Accumulate
540 cp1->normalImpulse = x.x;
541 cp2->normalImpulse = x.y;
542
543 #if B2_DEBUG_SOLVER == 1
544 // Postconditions
545 dv2 = vB + b2Cross(wB, cp2->rB) - vA - b2Cross(wA, cp2->rA);
546
547 // Compute normal velocity
548 vn2 = b2Dot(dv2, normal);
549
550 b2Assert(b2Abs(vn2 - cp2->velocityBias) < k_errorTol);
551 #endif
552 break;
553 }
554
555 //
556 // Case 4: x1 = 0 and x2 = 0
557 //
558 // vn1 = b1
559 // vn2 = b2;
560 x.x = 0.0f;
561 x.y = 0.0f;
562 vn1 = b.x;
563 vn2 = b.y;
564
565 if (vn1 >= 0.0f && vn2 >= 0.0f )
566 {
567 // Resubstitute for the incremental impulse
568 b2Vec2 d = x - a;
569
570 // Apply incremental impulse
571 b2Vec2 P1 = d.x * normal;
572 b2Vec2 P2 = d.y * normal;
573 vA -= mA * (P1 + P2);
574 wA -= iA * (b2Cross(cp1->rA, P1) + b2Cross(cp2->rA, P2));
575
576 vB += mB * (P1 + P2);
577 wB += iB * (b2Cross(cp1->rB, P1) + b2Cross(cp2->rB, P2));
578
579 // Accumulate
580 cp1->normalImpulse = x.x;
581 cp2->normalImpulse = x.y;
582
583 break;
584 }
585
586 // No solution, give up. This is hit sometimes, but it doesn't seem to matter.
587 break;
588 }
589 }
590
591 m_velocities[indexA].v = vA;
592 m_velocities[indexA].w = wA;
593 m_velocities[indexB].v = vB;
594 m_velocities[indexB].w = wB;
595 }
596 }
597
StoreImpulses()598 void b2ContactSolver::StoreImpulses()
599 {
600 for (int32 i = 0; i < m_count; ++i)
601 {
602 b2ContactVelocityConstraint* vc = m_velocityConstraints + i;
603 b2Manifold* manifold = m_contacts[vc->contactIndex]->GetManifold();
604
605 for (int32 j = 0; j < vc->pointCount; ++j)
606 {
607 manifold->points[j].normalImpulse = vc->points[j].normalImpulse;
608 manifold->points[j].tangentImpulse = vc->points[j].tangentImpulse;
609 }
610 }
611 }
612
613 struct b2PositionSolverManifold
614 {
Initializeb2PositionSolverManifold615 void Initialize(b2ContactPositionConstraint* pc, const b2Transform& xfA, const b2Transform& xfB, int32 index)
616 {
617 b2Assert(pc->pointCount > 0);
618
619 switch (pc->type)
620 {
621 case b2Manifold::e_circles:
622 {
623 b2Vec2 pointA = b2Mul(xfA, pc->localPoint);
624 b2Vec2 pointB = b2Mul(xfB, pc->localPoints[0]);
625 normal = pointB - pointA;
626 normal.Normalize();
627 point = 0.5f * (pointA + pointB);
628 separation = b2Dot(pointB - pointA, normal) - pc->radiusA - pc->radiusB;
629 }
630 break;
631
632 case b2Manifold::e_faceA:
633 {
634 normal = b2Mul(xfA.q, pc->localNormal);
635 b2Vec2 planePoint = b2Mul(xfA, pc->localPoint);
636
637 b2Vec2 clipPoint = b2Mul(xfB, pc->localPoints[index]);
638 separation = b2Dot(clipPoint - planePoint, normal) - pc->radiusA - pc->radiusB;
639 point = clipPoint;
640 }
641 break;
642
643 case b2Manifold::e_faceB:
644 {
645 normal = b2Mul(xfB.q, pc->localNormal);
646 b2Vec2 planePoint = b2Mul(xfB, pc->localPoint);
647
648 b2Vec2 clipPoint = b2Mul(xfA, pc->localPoints[index]);
649 separation = b2Dot(clipPoint - planePoint, normal) - pc->radiusA - pc->radiusB;
650 point = clipPoint;
651
652 // Ensure normal points from A to B
653 normal = -normal;
654 }
655 break;
656 }
657 }
658
659 b2Vec2 normal;
660 b2Vec2 point;
661 float32 separation;
662 };
663
664 // Sequential solver.
SolvePositionConstraints()665 bool b2ContactSolver::SolvePositionConstraints()
666 {
667 float32 minSeparation = 0.0f;
668
669 for (int32 i = 0; i < m_count; ++i)
670 {
671 b2ContactPositionConstraint* pc = m_positionConstraints + i;
672
673 int32 indexA = pc->indexA;
674 int32 indexB = pc->indexB;
675 b2Vec2 localCenterA = pc->localCenterA;
676 float32 mA = pc->invMassA;
677 float32 iA = pc->invIA;
678 b2Vec2 localCenterB = pc->localCenterB;
679 float32 mB = pc->invMassB;
680 float32 iB = pc->invIB;
681 int32 pointCount = pc->pointCount;
682
683 b2Vec2 cA = m_positions[indexA].c;
684 float32 aA = m_positions[indexA].a;
685
686 b2Vec2 cB = m_positions[indexB].c;
687 float32 aB = m_positions[indexB].a;
688
689 // Solve normal constraints
690 for (int32 j = 0; j < pointCount; ++j)
691 {
692 b2Transform xfA, xfB;
693 xfA.q.Set(aA);
694 xfB.q.Set(aB);
695 xfA.p = cA - b2Mul(xfA.q, localCenterA);
696 xfB.p = cB - b2Mul(xfB.q, localCenterB);
697
698 b2PositionSolverManifold psm;
699 psm.Initialize(pc, xfA, xfB, j);
700 b2Vec2 normal = psm.normal;
701
702 b2Vec2 point = psm.point;
703 float32 separation = psm.separation;
704
705 b2Vec2 rA = point - cA;
706 b2Vec2 rB = point - cB;
707
708 // Track max constraint error.
709 minSeparation = b2Min(minSeparation, separation);
710
711 // Prevent large corrections and allow slop.
712 float32 C = b2Clamp(b2_baumgarte * (separation + b2_linearSlop), -b2_maxLinearCorrection, 0.0f);
713
714 // Compute the effective mass.
715 float32 rnA = b2Cross(rA, normal);
716 float32 rnB = b2Cross(rB, normal);
717 float32 K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
718
719 // Compute normal impulse
720 float32 impulse = K > 0.0f ? - C / K : 0.0f;
721
722 b2Vec2 P = impulse * normal;
723
724 cA -= mA * P;
725 aA -= iA * b2Cross(rA, P);
726
727 cB += mB * P;
728 aB += iB * b2Cross(rB, P);
729 }
730
731 m_positions[indexA].c = cA;
732 m_positions[indexA].a = aA;
733
734 m_positions[indexB].c = cB;
735 m_positions[indexB].a = aB;
736 }
737
738 // We can't expect minSpeparation >= -b2_linearSlop because we don't
739 // push the separation above -b2_linearSlop.
740 return minSeparation >= -3.0f * b2_linearSlop;
741 }
742
743 // Sequential position solver for position constraints.
SolveTOIPositionConstraints(int32 toiIndexA,int32 toiIndexB)744 bool b2ContactSolver::SolveTOIPositionConstraints(int32 toiIndexA, int32 toiIndexB)
745 {
746 float32 minSeparation = 0.0f;
747
748 for (int32 i = 0; i < m_count; ++i)
749 {
750 b2ContactPositionConstraint* pc = m_positionConstraints + i;
751
752 int32 indexA = pc->indexA;
753 int32 indexB = pc->indexB;
754 b2Vec2 localCenterA = pc->localCenterA;
755 b2Vec2 localCenterB = pc->localCenterB;
756 int32 pointCount = pc->pointCount;
757
758 float32 mA = 0.0f;
759 float32 iA = 0.0f;
760 if (indexA == toiIndexA || indexA == toiIndexB)
761 {
762 mA = pc->invMassA;
763 iA = pc->invIA;
764 }
765
766 float32 mB = pc->invMassB;
767 float32 iB = pc->invIB;
768 if (indexB == toiIndexA || indexB == toiIndexB)
769 {
770 mB = pc->invMassB;
771 iB = pc->invIB;
772 }
773
774 b2Vec2 cA = m_positions[indexA].c;
775 float32 aA = m_positions[indexA].a;
776
777 b2Vec2 cB = m_positions[indexB].c;
778 float32 aB = m_positions[indexB].a;
779
780 // Solve normal constraints
781 for (int32 j = 0; j < pointCount; ++j)
782 {
783 b2Transform xfA, xfB;
784 xfA.q.Set(aA);
785 xfB.q.Set(aB);
786 xfA.p = cA - b2Mul(xfA.q, localCenterA);
787 xfB.p = cB - b2Mul(xfB.q, localCenterB);
788
789 b2PositionSolverManifold psm;
790 psm.Initialize(pc, xfA, xfB, j);
791 b2Vec2 normal = psm.normal;
792
793 b2Vec2 point = psm.point;
794 float32 separation = psm.separation;
795
796 b2Vec2 rA = point - cA;
797 b2Vec2 rB = point - cB;
798
799 // Track max constraint error.
800 minSeparation = b2Min(minSeparation, separation);
801
802 // Prevent large corrections and allow slop.
803 float32 C = b2Clamp(b2_toiBaugarte * (separation + b2_linearSlop), -b2_maxLinearCorrection, 0.0f);
804
805 // Compute the effective mass.
806 float32 rnA = b2Cross(rA, normal);
807 float32 rnB = b2Cross(rB, normal);
808 float32 K = mA + mB + iA * rnA * rnA + iB * rnB * rnB;
809
810 // Compute normal impulse
811 float32 impulse = K > 0.0f ? - C / K : 0.0f;
812
813 b2Vec2 P = impulse * normal;
814
815 cA -= mA * P;
816 aA -= iA * b2Cross(rA, P);
817
818 cB += mB * P;
819 aB += iB * b2Cross(rB, P);
820 }
821
822 m_positions[indexA].c = cA;
823 m_positions[indexA].a = aA;
824
825 m_positions[indexB].c = cB;
826 m_positions[indexB].a = aB;
827 }
828
829 // We can't expect minSpeparation >= -b2_linearSlop because we don't
830 // push the separation above -b2_linearSlop.
831 return minSeparation >= -1.5f * b2_linearSlop;
832 }
833