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1/*************************************************************************
2 * *
3 * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
4 * All rights reserved. Email: russ@q12.org Web: www.q12.org *
5 * *
6 * Fast iterative solver, David Whittaker. Email: david@csworkbench.com *
7 * *
8 * This library is free software; you can redistribute it and/or *
9 * modify it under the terms of EITHER: *
10 * (1) The GNU Lesser General Public License as published by the Free *
11 * Software Foundation; either version 2.1 of the License, or (at *
12 * your option) any later version. The text of the GNU Lesser *
13 * General Public License is included with this library in the *
14 * file LICENSE.TXT. *
15 * (2) The BSD-style license that is included with this library in *
16 * the file LICENSE-BSD.TXT. *
17 * *
18 * This library is distributed in the hope that it will be useful, *
19 * but WITHOUT ANY WARRANTY; without even the implied warranty of *
20 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files *
21 * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
22 * *
23 *************************************************************************/
24
25// This is the StepFast code by David Whittaker. This code is faster, but
26// sometimes less stable than, the original "big matrix" code.
27// Refer to the user's manual for more information.
28// Note that this source file duplicates a lot of stuff from step.cpp,
29// eventually we should move the common code to a third file.
30
31#include "objects.h"
32#include "joint.h"
33#include <ode/config.h>
34#include <ode/objects.h>
35#include <ode/odemath.h>
36#include <ode/rotation.h>
37#include <ode/timer.h>
38#include <ode/error.h>
39#include <ode/matrix.h>
40#include <ode/misc.h>
41#include "lcp.h"
42#include "step.h"
43#include "util.h"
44
45
46// misc defines
47
48#define ALLOCA dALLOCA16
49
50#define RANDOM_JOINT_ORDER
51//#define FAST_FACTOR //use a factorization approximation to the LCP solver (fast, theoretically less accurate)
52#define SLOW_LCP //use the old LCP solver
53//#define NO_ISLANDS //does not perform island creation code (3~4% of simulation time), body disabling doesn't work
54//#define TIMING
55
56
57static int autoEnableDepth = 2;
58
59void dWorldSetAutoEnableDepthSF1 (dxWorld *world, int autodepth)
60{
61 if (autodepth > 0)
62 autoEnableDepth = autodepth;
63 else
64 autoEnableDepth = 0;
65}
66
67int dWorldGetAutoEnableDepthSF1 (dxWorld *world)
68{
69 return autoEnableDepth;
70}
71
72//little bit of math.... the _sym_ functions assume the return matrix will be symmetric
73static void
74Multiply2_sym_p8p (dReal * A, dReal * B, dReal * C, int p, int Askip)
75{
76 int i, j;
77 dReal sum, *aa, *ad, *bb, *cc;
78 dIASSERT (p > 0 && A && B && C);
79 bb = B;
80 for (i = 0; i < p; i++)
81 {
82 //aa is going accross the matrix, ad down
83 aa = ad = A;
84 cc = C;
85 for (j = i; j < p; j++)
86 {
87 sum = bb[0] * cc[0];
88 sum += bb[1] * cc[1];
89 sum += bb[2] * cc[2];
90 sum += bb[4] * cc[4];
91 sum += bb[5] * cc[5];
92 sum += bb[6] * cc[6];
93 *(aa++) = *ad = sum;
94 ad += Askip;
95 cc += 8;
96 }
97 bb += 8;
98 A += Askip + 1;
99 C += 8;
100 }
101}
102
103static void
104MultiplyAdd2_sym_p8p (dReal * A, dReal * B, dReal * C, int p, int Askip)
105{
106 int i, j;
107 dReal sum, *aa, *ad, *bb, *cc;
108 dIASSERT (p > 0 && A && B && C);
109 bb = B;
110 for (i = 0; i < p; i++)
111 {
112 //aa is going accross the matrix, ad down
113 aa = ad = A;
114 cc = C;
115 for (j = i; j < p; j++)
116 {
117 sum = bb[0] * cc[0];
118 sum += bb[1] * cc[1];
119 sum += bb[2] * cc[2];
120 sum += bb[4] * cc[4];
121 sum += bb[5] * cc[5];
122 sum += bb[6] * cc[6];
123 *(aa++) += sum;
124 *ad += sum;
125 ad += Askip;
126 cc += 8;
127 }
128 bb += 8;
129 A += Askip + 1;
130 C += 8;
131 }
132}
133
134
135// this assumes the 4th and 8th rows of B are zero.
136
137static void
138Multiply0_p81 (dReal * A, dReal * B, dReal * C, int p)
139{
140 int i;
141 dIASSERT (p > 0 && A && B && C);
142 dReal sum;
143 for (i = p; i; i--)
144 {
145 sum = B[0] * C[0];
146 sum += B[1] * C[1];
147 sum += B[2] * C[2];
148 sum += B[4] * C[4];
149 sum += B[5] * C[5];
150 sum += B[6] * C[6];
151 *(A++) = sum;
152 B += 8;
153 }
154}
155
156
157// this assumes the 4th and 8th rows of B are zero.
158
159static void
160MultiplyAdd0_p81 (dReal * A, dReal * B, dReal * C, int p)
161{
162 int i;
163 dIASSERT (p > 0 && A && B && C);
164 dReal sum;
165 for (i = p; i; i--)
166 {
167 sum = B[0] * C[0];
168 sum += B[1] * C[1];
169 sum += B[2] * C[2];
170 sum += B[4] * C[4];
171 sum += B[5] * C[5];
172 sum += B[6] * C[6];
173 *(A++) += sum;
174 B += 8;
175 }
176}
177
178
179// this assumes the 4th and 8th rows of B are zero.
180
181static void
182Multiply1_8q1 (dReal * A, dReal * B, dReal * C, int q)
183{
184 int k;
185 dReal sum;
186 dIASSERT (q > 0 && A && B && C);
187 sum = 0;
188 for (k = 0; k < q; k++)
189 sum += B[k * 8] * C[k];
190 A[0] = sum;
191 sum = 0;
192 for (k = 0; k < q; k++)
193 sum += B[1 + k * 8] * C[k];
194 A[1] = sum;
195 sum = 0;
196 for (k = 0; k < q; k++)
197 sum += B[2 + k * 8] * C[k];
198 A[2] = sum;
199 sum = 0;
200 for (k = 0; k < q; k++)
201 sum += B[4 + k * 8] * C[k];
202 A[4] = sum;
203 sum = 0;
204 for (k = 0; k < q; k++)
205 sum += B[5 + k * 8] * C[k];
206 A[5] = sum;
207 sum = 0;
208 for (k = 0; k < q; k++)
209 sum += B[6 + k * 8] * C[k];
210 A[6] = sum;
211}
212
213//****************************************************************************
214// body rotation
215
216// return sin(x)/x. this has a singularity at 0 so special handling is needed
217// for small arguments.
218
219static inline dReal
220sinc (dReal x)
221{
222 // if |x| < 1e-4 then use a taylor series expansion. this two term expansion
223 // is actually accurate to one LS bit within this range if double precision
224 // is being used - so don't worry!
225 if (dFabs (x) < 1.0e-4)
226 return REAL (1.0) - x * x * REAL (0.166666666666666666667);
227 else
228 return dSin (x) / x;
229}
230
231
232// given a body b, apply its linear and angular rotation over the time
233// interval h, thereby adjusting its position and orientation.
234
235static inline void
236moveAndRotateBody (dxBody * b, dReal h)
237{
238 int j;
239
240 // handle linear velocity
241 for (j = 0; j < 3; j++)
242 b->posr.pos[j] += h * b->lvel[j];
243
244 if (b->flags & dxBodyFlagFiniteRotation)
245 {
246 dVector3 irv; // infitesimal rotation vector
247 dQuaternion q; // quaternion for finite rotation
248
249 if (b->flags & dxBodyFlagFiniteRotationAxis)
250 {
251 // split the angular velocity vector into a component along the finite
252 // rotation axis, and a component orthogonal to it.
253 dVector3 frv, irv; // finite rotation vector
254 dReal k = dDOT (b->finite_rot_axis, b->avel);
255 frv[0] = b->finite_rot_axis[0] * k;
256 frv[1] = b->finite_rot_axis[1] * k;
257 frv[2] = b->finite_rot_axis[2] * k;
258 irv[0] = b->avel[0] - frv[0];
259 irv[1] = b->avel[1] - frv[1];
260 irv[2] = b->avel[2] - frv[2];
261
262 // make a rotation quaternion q that corresponds to frv * h.
263 // compare this with the full-finite-rotation case below.
264 h *= REAL (0.5);
265 dReal theta = k * h;
266 q[0] = dCos (theta);
267 dReal s = sinc (theta) * h;
268 q[1] = frv[0] * s;
269 q[2] = frv[1] * s;
270 q[3] = frv[2] * s;
271 }
272 else
273 {
274 // make a rotation quaternion q that corresponds to w * h
275 dReal wlen = dSqrt (b->avel[0] * b->avel[0] + b->avel[1] * b->avel[1] + b->avel[2] * b->avel[2]);
276 h *= REAL (0.5);
277 dReal theta = wlen * h;
278 q[0] = dCos (theta);
279 dReal s = sinc (theta) * h;
280 q[1] = b->avel[0] * s;
281 q[2] = b->avel[1] * s;
282 q[3] = b->avel[2] * s;
283 }
284
285 // do the finite rotation
286 dQuaternion q2;
287 dQMultiply0 (q2, q, b->q);
288 for (j = 0; j < 4; j++)
289 b->q[j] = q2[j];
290
291 // do the infitesimal rotation if required
292 if (b->flags & dxBodyFlagFiniteRotationAxis)
293 {
294 dReal dq[4];
295 dWtoDQ (irv, b->q, dq);
296 for (j = 0; j < 4; j++)
297 b->q[j] += h * dq[j];
298 }
299 }
300 else
301 {
302 // the normal way - do an infitesimal rotation
303 dReal dq[4];
304 dWtoDQ (b->avel, b->q, dq);
305 for (j = 0; j < 4; j++)
306 b->q[j] += h * dq[j];
307 }
308
309 // normalize the quaternion and convert it to a rotation matrix
310 dNormalize4 (b->q);
311 dQtoR (b->q, b->posr.R);
312
313 // notify all attached geoms that this body has moved
314 for (dxGeom * geom = b->geom; geom; geom = dGeomGetBodyNext (geom))
315 dGeomMoved (geom);
316}
317
318//****************************************************************************
319//This is an implementation of the iterated/relaxation algorithm.
320//Here is a quick overview of the algorithm per Sergi Valverde's posts to the
321//mailing list:
322//
323// for i=0..N-1 do
324// for c = 0..C-1 do
325// Solve constraint c-th
326// Apply forces to constraint bodies
327// next
328// next
329// Integrate bodies
330
331void
332dInternalStepFast (dxWorld * world, dxBody * body[2], dReal * GI[2], dReal * GinvI[2], dxJoint * joint, dxJoint::Info1 info, dxJoint::Info2 Jinfo, dReal stepsize)
333{
334 int i, j, k;
335# ifdef TIMING
336 dTimerNow ("constraint preprocessing");
337# endif
338
339 dReal stepsize1 = dRecip (stepsize);
340
341 int m = info.m;
342 // nothing to do if no constraints.
343 if (m <= 0)
344 return;
345
346 int nub = 0;
347 if (info.nub == info.m)
348 nub = m;
349
350 // compute A = J*invM*J'. first compute JinvM = J*invM. this has the same
351 // format as J so we just go through the constraints in J multiplying by
352 // the appropriate scalars and matrices.
353# ifdef TIMING
354 dTimerNow ("compute A");
355# endif
356 dReal JinvM[2 * 6 * 8];
357 //dSetZero (JinvM, 2 * m * 8);
358
359 dReal *Jsrc = Jinfo.J1l;
360 dReal *Jdst = JinvM;
361 if (body[0])
362 {
363 for (j = m - 1; j >= 0; j--)
364 {
365 for (k = 0; k < 3; k++)
366 Jdst[k] = Jsrc[k] * body[0]->invMass;
367 dMULTIPLY0_133 (Jdst + 4, Jsrc + 4, GinvI[0]);
368 Jsrc += 8;
369 Jdst += 8;
370 }
371 }
372 if (body[1])
373 {
374 Jsrc = Jinfo.J2l;
375 Jdst = JinvM + 8 * m;
376 for (j = m - 1; j >= 0; j--)
377 {
378 for (k = 0; k < 3; k++)
379 Jdst[k] = Jsrc[k] * body[1]->invMass;
380 dMULTIPLY0_133 (Jdst + 4, Jsrc + 4, GinvI[1]);
381 Jsrc += 8;
382 Jdst += 8;
383 }
384 }
385
386
387 // now compute A = JinvM * J'.
388 int mskip = dPAD (m);
389 dReal A[6 * 8];
390 //dSetZero (A, 6 * 8);
391
392 if (body[0]) {
393 Multiply2_sym_p8p (A, JinvM, Jinfo.J1l, m, mskip);
394 if (body[1])
395 MultiplyAdd2_sym_p8p (A, JinvM + 8 * m, Jinfo.J2l,
396 m, mskip);
397 } else {
398 if (body[1])
399 Multiply2_sym_p8p (A, JinvM + 8 * m, Jinfo.J2l,
400 m, mskip);
401 }
402
403 // add cfm to the diagonal of A
404 for (i = 0; i < m; i++)
405 A[i * mskip + i] += Jinfo.cfm[i] * stepsize1;
406
407 // compute the right hand side `rhs'
408# ifdef TIMING
409 dTimerNow ("compute rhs");
410# endif
411 dReal tmp1[16];
412 //dSetZero (tmp1, 16);
413 // put v/h + invM*fe into tmp1
414 for (i = 0; i < 2; i++)
415 {
416 if (!body[i])
417 continue;
418 for (j = 0; j < 3; j++)
419 tmp1[i * 8 + j] = body[i]->facc[j] * body[i]->invMass + body[i]->lvel[j] * stepsize1;
420 dMULTIPLY0_331 (tmp1 + i * 8 + 4, GinvI[i], body[i]->tacc);
421 for (j = 0; j < 3; j++)
422 tmp1[i * 8 + 4 + j] += body[i]->avel[j] * stepsize1;
423 }
424 // put J*tmp1 into rhs
425 dReal rhs[6];
426 //dSetZero (rhs, 6);
427
428 if (body[0]) {
429 Multiply0_p81 (rhs, Jinfo.J1l, tmp1, m);
430 if (body[1])
431 MultiplyAdd0_p81 (rhs, Jinfo.J2l, tmp1 + 8, m);
432 } else {
433 if (body[1])
434 Multiply0_p81 (rhs, Jinfo.J2l, tmp1 + 8, m);
435 }
436
437 // complete rhs
438 for (i = 0; i < m; i++)
439 rhs[i] = Jinfo.c[i] * stepsize1 - rhs[i];
440
441#ifdef SLOW_LCP
442 // solve the LCP problem and get lambda.
443 // this will destroy A but that's okay
444# ifdef TIMING
445 dTimerNow ("solving LCP problem");
446# endif
447 dReal *lambda = (dReal *) ALLOCA (m * sizeof (dReal));
448 dReal *residual = (dReal *) ALLOCA (m * sizeof (dReal));
449 dReal lo[6], hi[6];
450 memcpy (lo, Jinfo.lo, m * sizeof (dReal));
451 memcpy (hi, Jinfo.hi, m * sizeof (dReal));
452 dSolveLCP (m, A, lambda, rhs, residual, nub, lo, hi, Jinfo.findex);
453#endif
454
455 // LCP Solver replacement:
456 // This algorithm goes like this:
457 // Do a straightforward LDLT factorization of the matrix A, solving for
458 // A*x = rhs
459 // For each x[i] that is outside of the bounds of lo[i] and hi[i],
460 // clamp x[i] into that range.
461 // Substitute into A the now known x's
462 // subtract the residual away from the rhs.
463 // Remove row and column i from L, updating the factorization
464 // place the known x's at the end of the array, keeping up with location in p
465 // Repeat until all constraints have been clamped or all are within bounds
466 //
467 // This is probably only faster in the single joint case where only one repeat is
468 // the norm.
469
470#ifdef FAST_FACTOR
471 // factorize A (L*D*L'=A)
472# ifdef TIMING
473 dTimerNow ("factorize A");
474# endif
475 dReal d[6];
476 dReal L[6 * 8];
477 memcpy (L, A, m * mskip * sizeof (dReal));
478 dFactorLDLT (L, d, m, mskip);
479
480 // compute lambda
481# ifdef TIMING
482 dTimerNow ("compute lambda");
483# endif
484
485 int left = m; //constraints left to solve.
486 int remove[6];
487 dReal lambda[6];
488 dReal x[6];
489 int p[6];
490 for (i = 0; i < 6; i++)
491 p[i] = i;
492 while (true)
493 {
494 memcpy (x, rhs, left * sizeof (dReal));
495 dSolveLDLT (L, d, x, left, mskip);
496
497 int fixed = 0;
498 for (i = 0; i < left; i++)
499 {
500 j = p[i];
501 remove[i] = false;
502 // This isn't the exact same use of findex as dSolveLCP.... since x[findex]
503 // may change after I've already clamped x[i], but it should be close
504 if (Jinfo.findex[j] > -1)
505 {
506 dReal f = fabs (Jinfo.hi[j] * x[p[Jinfo.findex[j]]]);
507 if (x[i] > f)
508 x[i] = f;
509 else if (x[i] < -f)
510 x[i] = -f;
511 else
512 continue;
513 }
514 else
515 {
516 if (x[i] > Jinfo.hi[j])
517 x[i] = Jinfo.hi[j];
518 else if (x[i] < Jinfo.lo[j])
519 x[i] = Jinfo.lo[j];
520 else
521 continue;
522 }
523 remove[i] = true;
524 fixed++;
525 }
526 if (fixed == 0 || fixed == left) //no change or all constraints solved
527 break;
528
529 for (i = 0; i < left; i++) //sub in to right hand side.
530 if (remove[i])
531 for (j = 0; j < left; j++)
532 if (!remove[j])
533 rhs[j] -= A[j * mskip + i] * x[i];
534
535 for (int r = left - 1; r >= 0; r--) //eliminate row/col for fixed variables
536 {
537 if (remove[r])
538 {
539 //dRemoveLDLT adapted for use without row pointers.
540 if (r == left - 1)
541 {
542 left--;
543 continue; // deleting last row/col is easy
544 }
545 else if (r == 0)
546 {
547 dReal a[6];
548 for (i = 0; i < left; i++)
549 a[i] = -A[i * mskip];
550 a[0] += REAL (1.0);
551 dLDLTAddTL (L, d, a, left, mskip);
552 }
553 else
554 {
555 dReal t[6];
556 dReal a[6];
557 for (i = 0; i < r; i++)
558 t[i] = L[r * mskip + i] / d[i];
559 for (i = 0; i < left - r; i++)
560 a[i] = dDot (L + (r + i) * mskip, t, r) - A[(r + i) * mskip + r];
561 a[0] += REAL (1.0);
562 dLDLTAddTL (L + r * mskip + r, d + r, a, left - r, mskip);
563 }
564
565 dRemoveRowCol (L, left, mskip, r);
566 //end dRemoveLDLT
567
568 left--;
569 if (r < (left - 1))
570 {
571 dReal tx = x[r];
572 memmove (d + r, d + r + 1, (left - r) * sizeof (dReal));
573 memmove (rhs + r, rhs + r + 1, (left - r) * sizeof (dReal));
574 //x will get written over by rhs anyway, no need to move it around
575 //just store the fixed value we just discovered in it.
576 x[left] = tx;
577 for (i = 0; i < m; i++)
578 if (p[i] > r && p[i] <= left)
579 p[i]--;
580 p[r] = left;
581 }
582 }
583 }
584 }
585
586 for (i = 0; i < m; i++)
587 lambda[i] = x[p[i]];
588# endif
589 // compute the constraint force `cforce'
590# ifdef TIMING
591 dTimerNow ("compute constraint force");
592#endif
593
594 // compute cforce = J'*lambda
595 dJointFeedback *fb = joint->feedback;
596 dReal cforce[16];
597 //dSetZero (cforce, 16);
598
599 if (fb)
600 {
601 // the user has requested feedback on the amount of force that this
602 // joint is applying to the bodies. we use a slightly slower
603 // computation that splits out the force components and puts them
604 // in the feedback structure.
605 dReal data1[8], data2[8];
606 if (body[0])
607 {
608 Multiply1_8q1 (data1, Jinfo.J1l, lambda, m);
609 dReal *cf1 = cforce;
610 cf1[0] = (fb->f1[0] = data1[0]);
611 cf1[1] = (fb->f1[1] = data1[1]);
612 cf1[2] = (fb->f1[2] = data1[2]);
613 cf1[4] = (fb->t1[0] = data1[4]);
614 cf1[5] = (fb->t1[1] = data1[5]);
615 cf1[6] = (fb->t1[2] = data1[6]);
616 }
617 if (body[1])
618 {
619 Multiply1_8q1 (data2, Jinfo.J2l, lambda, m);
620 dReal *cf2 = cforce + 8;
621 cf2[0] = (fb->f2[0] = data2[0]);
622 cf2[1] = (fb->f2[1] = data2[1]);
623 cf2[2] = (fb->f2[2] = data2[2]);
624 cf2[4] = (fb->t2[0] = data2[4]);
625 cf2[5] = (fb->t2[1] = data2[5]);
626 cf2[6] = (fb->t2[2] = data2[6]);
627 }
628 }
629 else
630 {
631 // no feedback is required, let's compute cforce the faster way
632 if (body[0])
633 Multiply1_8q1 (cforce, Jinfo.J1l, lambda, m);
634 if (body[1])
635 Multiply1_8q1 (cforce + 8, Jinfo.J2l, lambda, m);
636 }
637
638 for (i = 0; i < 2; i++)
639 {
640 if (!body[i])
641 continue;
642 for (j = 0; j < 3; j++)
643 {
644 body[i]->facc[j] += cforce[i * 8 + j];
645 body[i]->tacc[j] += cforce[i * 8 + 4 + j];
646 }
647 }
648}
649
650void
651dInternalStepIslandFast (dxWorld * world, dxBody * const *bodies, int nb, dxJoint * const *_joints, int nj, dReal stepsize, int maxiterations)
652{
653# ifdef TIMING
654 dTimerNow ("preprocessing");
655# endif
656 dxBody *bodyPair[2], *body;
657 dReal *GIPair[2], *GinvIPair[2];
658 dxJoint *joint;
659 int iter, b, j, i;
660 dReal ministep = stepsize / maxiterations;
661
662 // make a local copy of the joint array, because we might want to modify it.
663 // (the "dxJoint *const*" declaration says we're allowed to modify the joints
664 // but not the joint array, because the caller might need it unchanged).
665 dxJoint **joints = (dxJoint **) ALLOCA (nj * sizeof (dxJoint *));
666 memcpy (joints, _joints, nj * sizeof (dxJoint *));
667
668 // get m = total constraint dimension, nub = number of unbounded variables.
669 // create constraint offset array and number-of-rows array for all joints.
670 // the constraints are re-ordered as follows: the purely unbounded
671 // constraints, the mixed unbounded + LCP constraints, and last the purely
672 // LCP constraints. this assists the LCP solver to put all unbounded
673 // variables at the start for a quick factorization.
674 //
675 // joints with m=0 are inactive and are removed from the joints array
676 // entirely, so that the code that follows does not consider them.
677 // also number all active joints in the joint list (set their tag values).
678 // inactive joints receive a tag value of -1.
679
680 int m = 0;
681 dxJoint::Info1 * info = (dxJoint::Info1 *) ALLOCA (nj * sizeof (dxJoint::Info1));
682 int *ofs = (int *) ALLOCA (nj * sizeof (int));
683 for (i = 0, j = 0; j < nj; j++)
684 { // i=dest, j=src
685 joints[j]->vtable->getInfo1 (joints[j], info + i);
686 dIASSERT (info[i].m >= 0 && info[i].m <= 6 && info[i].nub >= 0 && info[i].nub <= info[i].m);
687 if (info[i].m > 0)
688 {
689 joints[i] = joints[j];
690 joints[i]->tag = i;
691 i++;
692 }
693 else
694 {
695 joints[j]->tag = -1;
696 }
697 }
698 nj = i;
699
700 // the purely unbounded constraints
701 for (i = 0; i < nj; i++)
702 {
703 ofs[i] = m;
704 m += info[i].m;
705 }
706 dReal *c = NULL;
707 dReal *cfm = NULL;
708 dReal *lo = NULL;
709 dReal *hi = NULL;
710 int *findex = NULL;
711
712 dReal *J = NULL;
713 dxJoint::Info2 * Jinfo = NULL;
714
715 if (m)
716 {
717 // create a constraint equation right hand side vector `c', a constraint
718 // force mixing vector `cfm', and LCP low and high bound vectors, and an
719 // 'findex' vector.
720 c = (dReal *) ALLOCA (m * sizeof (dReal));
721 cfm = (dReal *) ALLOCA (m * sizeof (dReal));
722 lo = (dReal *) ALLOCA (m * sizeof (dReal));
723 hi = (dReal *) ALLOCA (m * sizeof (dReal));
724 findex = (int *) ALLOCA (m * sizeof (int));
725 dSetZero (c, m);
726 dSetValue (cfm, m, world->global_cfm);
727 dSetValue (lo, m, -dInfinity);
728 dSetValue (hi, m, dInfinity);
729 for (i = 0; i < m; i++)
730 findex[i] = -1;
731
732 // get jacobian data from constraints. a (2*m)x8 matrix will be created
733 // to store the two jacobian blocks from each constraint. it has this
734 // format:
735 //
736 // l l l 0 a a a 0 \ .
737 // l l l 0 a a a 0 }-- jacobian body 1 block for joint 0 (3 rows)
738 // l l l 0 a a a 0 /
739 // l l l 0 a a a 0 \ .
740 // l l l 0 a a a 0 }-- jacobian body 2 block for joint 0 (3 rows)
741 // l l l 0 a a a 0 /
742 // l l l 0 a a a 0 }--- jacobian body 1 block for joint 1 (1 row)
743 // l l l 0 a a a 0 }--- jacobian body 2 block for joint 1 (1 row)
744 // etc...
745 //
746 // (lll) = linear jacobian data
747 // (aaa) = angular jacobian data
748 //
749# ifdef TIMING
750 dTimerNow ("create J");
751# endif
752 J = (dReal *) ALLOCA (2 * m * 8 * sizeof (dReal));
753 dSetZero (J, 2 * m * 8);
754 Jinfo = (dxJoint::Info2 *) ALLOCA (nj * sizeof (dxJoint::Info2));
755 for (i = 0; i < nj; i++)
756 {
757 Jinfo[i].rowskip = 8;
758 Jinfo[i].fps = dRecip (stepsize);
759 Jinfo[i].erp = world->global_erp;
760 Jinfo[i].J1l = J + 2 * 8 * ofs[i];
761 Jinfo[i].J1a = Jinfo[i].J1l + 4;
762 Jinfo[i].J2l = Jinfo[i].J1l + 8 * info[i].m;
763 Jinfo[i].J2a = Jinfo[i].J2l + 4;
764 Jinfo[i].c = c + ofs[i];
765 Jinfo[i].cfm = cfm + ofs[i];
766 Jinfo[i].lo = lo + ofs[i];
767 Jinfo[i].hi = hi + ofs[i];
768 Jinfo[i].findex = findex + ofs[i];
769 //joints[i]->vtable->getInfo2 (joints[i], Jinfo+i);
770 }
771
772 }
773
774 dReal *saveFacc = (dReal *) ALLOCA (nb * 4 * sizeof (dReal));
775 dReal *saveTacc = (dReal *) ALLOCA (nb * 4 * sizeof (dReal));
776 dReal *globalI = (dReal *) ALLOCA (nb * 12 * sizeof (dReal));
777 dReal *globalInvI = (dReal *) ALLOCA (nb * 12 * sizeof (dReal));
778 for (b = 0; b < nb; b++)
779 {
780 for (i = 0; i < 4; i++)
781 {
782 saveFacc[b * 4 + i] = bodies[b]->facc[i];
783 saveTacc[b * 4 + i] = bodies[b]->tacc[i];
784 }
785 bodies[b]->tag = b;
786 }
787
788 for (iter = 0; iter < maxiterations; iter++)
789 {
790# ifdef TIMING
791 dTimerNow ("applying inertia and gravity");
792# endif
793 dReal tmp[12] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
794
795 for (b = 0; b < nb; b++)
796 {
797 body = bodies[b];
798
799 // for all bodies, compute the inertia tensor and its inverse in the global
800 // frame, and compute the rotational force and add it to the torque
801 // accumulator. I and invI are vertically stacked 3x4 matrices, one per body.
802 // @@@ check computation of rotational force.
803
804 // compute inertia tensor in global frame
805 dMULTIPLY2_333 (tmp, body->mass.I, body->posr.R);
806 dMULTIPLY0_333 (globalI + b * 12, body->posr.R, tmp);
807 // compute inverse inertia tensor in global frame
808 dMULTIPLY2_333 (tmp, body->invI, body->posr.R);
809 dMULTIPLY0_333 (globalInvI + b * 12, body->posr.R, tmp);
810
811 for (i = 0; i < 4; i++)
812 body->tacc[i] = saveTacc[b * 4 + i];
813#ifdef dGYROSCOPIC
814 // compute rotational force
815 dMULTIPLY0_331 (tmp, globalI + b * 12, body->avel);
816 dCROSS (body->tacc, -=, body->avel, tmp);
817#endif
818
819 // add the gravity force to all bodies
820 if ((body->flags & dxBodyNoGravity) == 0)
821 {
822 body->facc[0] = saveFacc[b * 4 + 0] + body->mass.mass * world->gravity[0];
823 body->facc[1] = saveFacc[b * 4 + 1] + body->mass.mass * world->gravity[1];
824 body->facc[2] = saveFacc[b * 4 + 2] + body->mass.mass * world->gravity[2];
825 body->facc[3] = 0;
826 } else {
827 body->facc[0] = saveFacc[b * 4 + 0];
828 body->facc[1] = saveFacc[b * 4 + 1];
829 body->facc[2] = saveFacc[b * 4 + 2];
830 body->facc[3] = 0;
831 }
832
833 }
834
835#ifdef RANDOM_JOINT_ORDER
836#ifdef TIMING
837 dTimerNow ("randomizing joint order");
838#endif
839 //randomize the order of the joints by looping through the array
840 //and swapping the current joint pointer with a random one before it.
841 for (j = 0; j < nj; j++)
842 {
843 joint = joints[j];
844 dxJoint::Info1 i1 = info[j];
845 dxJoint::Info2 i2 = Jinfo[j];
846 const int r = dRandInt(j+1);
847 dIASSERT (r < nj);
848 joints[j] = joints[r];
849 info[j] = info[r];
850 Jinfo[j] = Jinfo[r];
851 joints[r] = joint;
852 info[r] = i1;
853 Jinfo[r] = i2;
854 }
855#endif
856
857 //now iterate through the random ordered joint array we created.
858 for (j = 0; j < nj; j++)
859 {
860#ifdef TIMING
861 dTimerNow ("setting up joint");
862#endif
863 joint = joints[j];
864 bodyPair[0] = joint->node[0].body;
865 bodyPair[1] = joint->node[1].body;
866
867 if (bodyPair[0] && (bodyPair[0]->flags & dxBodyDisabled))
868 bodyPair[0] = 0;
869 if (bodyPair[1] && (bodyPair[1]->flags & dxBodyDisabled))
870 bodyPair[1] = 0;
871
872 //if this joint is not connected to any enabled bodies, skip it.
873 if (!bodyPair[0] && !bodyPair[1])
874 continue;
875
876 if (bodyPair[0])
877 {
878 GIPair[0] = globalI + bodyPair[0]->tag * 12;
879 GinvIPair[0] = globalInvI + bodyPair[0]->tag * 12;
880 }
881 if (bodyPair[1])
882 {
883 GIPair[1] = globalI + bodyPair[1]->tag * 12;
884 GinvIPair[1] = globalInvI + bodyPair[1]->tag * 12;
885 }
886
887 joints[j]->vtable->getInfo2 (joints[j], Jinfo + j);
888
889 //dInternalStepIslandFast is an exact copy of the old routine with one
890 //modification: the calculated forces are added back to the facc and tacc
891 //vectors instead of applying them to the bodies and moving them.
892 if (info[j].m > 0)
893 {
894 dInternalStepFast (world, bodyPair, GIPair, GinvIPair, joint, info[j], Jinfo[j], ministep);
895 }
896 }
897 // }
898# ifdef TIMING
899 dTimerNow ("moving bodies");
900# endif
901 //Now we can simulate all the free floating bodies, and move them.
902 for (b = 0; b < nb; b++)
903 {
904 body = bodies[b];
905
906 for (i = 0; i < 4; i++)
907 {
908 body->facc[i] *= ministep;
909 body->tacc[i] *= ministep;
910 }
911
912 //apply torque
913 dMULTIPLYADD0_331 (body->avel, globalInvI + b * 12, body->tacc);
914
915 //apply force
916 for (i = 0; i < 3; i++)
917 body->lvel[i] += body->invMass * body->facc[i];
918
919 //move It!
920 moveAndRotateBody (body, ministep);
921 }
922 }
923 for (b = 0; b < nb; b++)
924 for (j = 0; j < 4; j++)
925 bodies[b]->facc[j] = bodies[b]->tacc[j] = 0;
926}
927
928
929#ifdef NO_ISLANDS
930
931// Since the iterative algorithm doesn't care about islands of bodies, this is a
932// faster algorithm that just sends it all the joints and bodies in one array.
933// It's downfall is it's inability to handle disabled bodies as well as the old one.
934static void
935processIslandsFast (dxWorld * world, dReal stepsize, int maxiterations)
936{
937 // nothing to do if no bodies
938 if (world->nb <= 0)
939 return;
940
941 dInternalHandleAutoDisabling (world,stepsize);
942
943# ifdef TIMING
944 dTimerStart ("creating joint and body arrays");
945# endif
946 dxBody **bodies, *body;
947 dxJoint **joints, *joint;
948 joints = (dxJoint **) ALLOCA (world->nj * sizeof (dxJoint *));
949 bodies = (dxBody **) ALLOCA (world->nb * sizeof (dxBody *));
950
951 int nj = 0;
952 for (joint = world->firstjoint; joint; joint = (dxJoint *) joint->next)
953 joints[nj++] = joint;
954
955 int nb = 0;
956 for (body = world->firstbody; body; body = (dxBody *) body->next)
957 bodies[nb++] = body;
958
959 dInternalStepIslandFast (world, bodies, nb, joints, nj, stepsize, maxiterations);
960# ifdef TIMING
961 dTimerEnd ();
962 dTimerReport (stdout, 1);
963# endif
964}
965
966#else
967
968//****************************************************************************
969// island processing
970
971// this groups all joints and bodies in a world into islands. all objects
972// in an island are reachable by going through connected bodies and joints.
973// each island can be simulated separately.
974// note that joints that are not attached to anything will not be included
975// in any island, an so they do not affect the simulation.
976//
977// this function starts new island from unvisited bodies. however, it will
978// never start a new islands from a disabled body. thus islands of disabled
979// bodies will not be included in the simulation. disabled bodies are
980// re-enabled if they are found to be part of an active island.
981
982static void
983processIslandsFast (dxWorld * world, dReal stepsize, int maxiterations)
984{
985#ifdef TIMING
986 dTimerStart ("Island Setup");
987#endif
988 dxBody *b, *bb, **body;
989 dxJoint *j, **joint;
990
991 // nothing to do if no bodies
992 if (world->nb <= 0)
993 return;
994
995 dInternalHandleAutoDisabling (world,stepsize);
996
997 // make arrays for body and joint lists (for a single island) to go into
998 body = (dxBody **) ALLOCA (world->nb * sizeof (dxBody *));
999 joint = (dxJoint **) ALLOCA (world->nj * sizeof (dxJoint *));
1000 int bcount = 0; // number of bodies in `body'
1001 int jcount = 0; // number of joints in `joint'
1002 int tbcount = 0;
1003 int tjcount = 0;
1004
1005 // set all body/joint tags to 0
1006 for (b = world->firstbody; b; b = (dxBody *) b->next)
1007 b->tag = 0;
1008 for (j = world->firstjoint; j; j = (dxJoint *) j->next)
1009 j->tag = 0;
1010
1011 // allocate a stack of unvisited bodies in the island. the maximum size of
1012 // the stack can be the lesser of the number of bodies or joints, because
1013 // new bodies are only ever added to the stack by going through untagged
1014 // joints. all the bodies in the stack must be tagged!
1015 int stackalloc = (world->nj < world->nb) ? world->nj : world->nb;
1016 dxBody **stack = (dxBody **) ALLOCA (stackalloc * sizeof (dxBody *));
1017 int *autostack = (int *) ALLOCA (stackalloc * sizeof (int));
1018
1019 for (bb = world->firstbody; bb; bb = (dxBody *) bb->next)
1020 {
1021#ifdef TIMING
1022 dTimerNow ("Island Processing");
1023#endif
1024 // get bb = the next enabled, untagged body, and tag it
1025 if (bb->tag || (bb->flags & dxBodyDisabled))
1026 continue;
1027 bb->tag = 1;
1028
1029 // tag all bodies and joints starting from bb.
1030 int stacksize = 0;
1031 int autoDepth = autoEnableDepth;
1032 b = bb;
1033 body[0] = bb;
1034 bcount = 1;
1035 jcount = 0;
1036 goto quickstart;
1037 while (stacksize > 0)
1038 {
1039 b = stack[--stacksize]; // pop body off stack
1040 autoDepth = autostack[stacksize];
1041 body[bcount++] = b; // put body on body list
1042 quickstart:
1043
1044 // traverse and tag all body's joints, add untagged connected bodies
1045 // to stack
1046 for (dxJointNode * n = b->firstjoint; n; n = n->next)
1047 {
1048 if (!n->joint->tag)
1049 {
1050 int thisDepth = autoEnableDepth;
1051 n->joint->tag = 1;
1052 joint[jcount++] = n->joint;
1053 if (n->body && !n->body->tag)
1054 {
1055 if (n->body->flags & dxBodyDisabled)
1056 thisDepth = autoDepth - 1;
1057 if (thisDepth < 0)
1058 continue;
1059 n->body->flags &= ~dxBodyDisabled;
1060 n->body->tag = 1;
1061 autostack[stacksize] = thisDepth;
1062 stack[stacksize++] = n->body;
1063 }
1064 }
1065 }
1066 dIASSERT (stacksize <= world->nb);
1067 dIASSERT (stacksize <= world->nj);
1068 }
1069
1070 // now do something with body and joint lists
1071 dInternalStepIslandFast (world, body, bcount, joint, jcount, stepsize, maxiterations);
1072
1073 // what we've just done may have altered the body/joint tag values.
1074 // we must make sure that these tags are nonzero.
1075 // also make sure all bodies are in the enabled state.
1076 int i;
1077 for (i = 0; i < bcount; i++)
1078 {
1079 body[i]->tag = 1;
1080 body[i]->flags &= ~dxBodyDisabled;
1081 }
1082 for (i = 0; i < jcount; i++)
1083 joint[i]->tag = 1;
1084
1085 tbcount += bcount;
1086 tjcount += jcount;
1087 }
1088
1089#ifdef TIMING
1090 dMessage(0, "Total joints processed: %i, bodies: %i", tjcount, tbcount);
1091#endif
1092
1093 // if debugging, check that all objects (except for disabled bodies,
1094 // unconnected joints, and joints that are connected to disabled bodies)
1095 // were tagged.
1096# ifndef dNODEBUG
1097 for (b = world->firstbody; b; b = (dxBody *) b->next)
1098 {
1099 if (b->flags & dxBodyDisabled)
1100 {
1101 if (b->tag)
1102 dDebug (0, "disabled body tagged");
1103 }
1104 else
1105 {
1106 if (!b->tag)
1107 dDebug (0, "enabled body not tagged");
1108 }
1109 }
1110 for (j = world->firstjoint; j; j = (dxJoint *) j->next)
1111 {
1112 if ((j->node[0].body && (j->node[0].body->flags & dxBodyDisabled) == 0) || (j->node[1].body && (j->node[1].body->flags & dxBodyDisabled) == 0))
1113 {
1114 if (!j->tag)
1115 dDebug (0, "attached enabled joint not tagged");
1116 }
1117 else
1118 {
1119 if (j->tag)
1120 dDebug (0, "unattached or disabled joint tagged");
1121 }
1122 }
1123# endif
1124
1125# ifdef TIMING
1126 dTimerEnd ();
1127 dTimerReport (stdout, 1);
1128# endif
1129}
1130
1131#endif
1132
1133
1134void dWorldStepFast1 (dWorldID w, dReal stepsize, int maxiterations)
1135{
1136 dUASSERT (w, "bad world argument");
1137 dUASSERT (stepsize > 0, "stepsize must be > 0");
1138 processIslandsFast (w, stepsize, maxiterations);
1139}
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