collision.c

   1
   2 #include "quakedef.h"
   3
   4 typedef struct
   5 {
   6         // the hull we're tracing through
   7         const hull_t *hull;
   8
   9         // the trace structure to fill in
  10         trace_t *trace;
  11
  12         // start and end of the trace (in model space)
  13         double start[3];
  14         double end[3];
  15
  16         // end - start
  17         double dist[3];
  18 }
  19 RecursiveHullCheckTraceInfo_t;
  20
  21 // 1/32 epsilon to keep floating point happy
  22 #define DIST_EPSILON (0.03125)
  23
  24 #define HULLCHECKSTATE_EMPTY 0
  25 #define HULLCHECKSTATE_SOLID 1
  26 #define HULLCHECKSTATE_DONE 2
  27
  28 static int RecursiveHullCheck(RecursiveHullCheckTraceInfo_t *t, int num, double p1f, double p2f, double p1[3], double p2[3])
  29 {
  30         // status variables, these don't need to be saved on the stack when
  31         // recursing...  but are because this should be thread-safe
  32         // (note: tracing against a bbox is not thread-safe, yet)
  33         int ret;
  34         mplane_t *plane;
  35         double t1, t2;
  36
  37         // variables that need to be stored on the stack when recursing
  38         dclipnode_t *node;
  39         int side;
  40         double midf, mid[3];
  41
  42         // LordHavoc: a goto!  everyone flee in terror... :)
  43 loc0:
  44         // check for empty
  45         if (num < 0)
  46         {
  47                 t->trace->endcontents = num;
  48                 if (t->trace->thiscontents)
  49                 {
  50                         if (num == t->trace->thiscontents)
  51                                 t->trace->allsolid = false;
  52                         else
  53                         {
  54                                 // if the first leaf is solid, set startsolid
  55                                 if (t->trace->allsolid)
  56                                         t->trace->startsolid = true;
  57                                 return HULLCHECKSTATE_SOLID;
  58                         }
  59                         return HULLCHECKSTATE_EMPTY;
  60                 }
  61                 else
  62                 {
  63                         if (num != CONTENTS_SOLID)
  64                         {
  65                                 t->trace->allsolid = false;
  66                                 if (num == CONTENTS_EMPTY)
  67                                         t->trace->inopen = true;
  68                                 else
  69                                         t->trace->inwater = true;
  70                         }
  71                         else
  72                         {
  73                                 // if the first leaf is solid, set startsolid
  74                                 if (t->trace->allsolid)
  75                                         t->trace->startsolid = true;
  76                                 return HULLCHECKSTATE_SOLID;
  77                         }
  78                         return HULLCHECKSTATE_EMPTY;
  79                 }
  80         }
  81
  82         // find the point distances
  83         node = t->hull->clipnodes + num;
  84
  85         plane = t->hull->planes + node->planenum;
  86         if (plane->type < 3)
  87         {
  88                 t1 = p1[plane->type] - plane->dist;
  89                 t2 = p2[plane->type] - plane->dist;
  90         }
  91         else
  92         {
  93                 t1 = DotProduct (plane->normal, p1) - plane->dist;
  94                 t2 = DotProduct (plane->normal, p2) - plane->dist;
  95         }
  96
  97         if (t1 < 0)
  98         {
  99                 if (t2 < 0)
 100                 {
 101                         num = node->children[1];
 102                         goto loc0;
 103                 }
 104                 side = 1;
 105         }
 106         else
 107         {
 108                 if (t2 >= 0)
 109                 {
 110                         num = node->children[0];
 111                         goto loc0;
 112                 }
 113                 side = 0;
 114         }
 115
 116         // the line intersects, find intersection point
 117         // LordHavoc: this uses the original trace for maximum accuracy
 118         if (plane->type < 3)
 119         {
 120                 t1 = t->start[plane->type] - plane->dist;
 121                 t2 = t->end[plane->type] - plane->dist;
 122         }
 123         else
 124         {
 125                 t1 = DotProduct (plane->normal, t->start) - plane->dist;
 126                 t2 = DotProduct (plane->normal, t->end) - plane->dist;
 127         }
 128
 129         midf = t1 / (t1 - t2);
 130         midf = bound(p1f, midf, p2f);
 131         VectorMA(t->start, midf, t->dist, mid);
 132
 133         // recurse both sides, front side first
 134         ret = RecursiveHullCheck (t, node->children[side], p1f, midf, p1, mid);
 135         // if this side is not empty, return what it is (solid or done)
 136         if (ret != HULLCHECKSTATE_EMPTY)
 137                 return ret;
 138
 139         ret = RecursiveHullCheck (t, node->children[side ^ 1], midf, p2f, mid, p2);
 140         // if other side is not solid, return what it is (empty or done)
 141         if (ret != HULLCHECKSTATE_SOLID)
 142                 return ret;
 143
 144         // front is air and back is solid, this is the impact point...
 145         if (side)
 146         {
 147                 t->trace->plane.dist = -plane->dist;
 148                 VectorNegate (plane->normal, t->trace->plane.normal);
 149         }
 150         else
 151         {
 152                 t->trace->plane.dist = plane->dist;
 153                 VectorCopy (plane->normal, t->trace->plane.normal);
 154         }
 155
 156         // bias away from surface a bit
 157         t1 = DotProduct(t->trace->plane.normal, t->start) - (t->trace->plane.dist + DIST_EPSILON);
 158         t2 = DotProduct(t->trace->plane.normal, t->end) - (t->trace->plane.dist + DIST_EPSILON);
 159
 160         midf = t1 / (t1 - t2);
 161         t->trace->fraction = bound(0.0f, midf, 1.0);
 162
 163         VectorMA(t->start, t->trace->fraction, t->dist, t->trace->endpos);
 164
 165         return HULLCHECKSTATE_DONE;
 166 }
 167
 168 #if 0
 169 // used if start and end are the same
 170 static void RecursiveHullCheckPoint (RecursiveHullCheckTraceInfo_t *t, int num)
 171 {
 172         // If you can read this, you understand BSP trees
 173         while (num >= 0)
 174                 num = t->hull->clipnodes[num].children[((t->hull->planes[t->hull->clipnodes[num].planenum].type < 3) ? (t->start[t->hull->planes[t->hull->clipnodes[num].planenum].type]) : (DotProduct(t->hull->planes[t->hull->clipnodes[num].planenum].normal, t->start))) < t->hull->planes[t->hull->clipnodes[num].planenum].dist];
 175
 176         // check for empty
 177         t->trace->endcontents = num;
 178         if (t->trace->thiscontents)
 179         {
 180                 if (num == t->trace->thiscontents)
 181                         t->trace->allsolid = false;
 182                 else
 183                 {
 184                         // if the first leaf is solid, set startsolid
 185                         if (t->trace->allsolid)
 186                                 t->trace->startsolid = true;
 187                 }
 188         }
 189         else
 190         {
 191                 if (num != CONTENTS_SOLID)
 192                 {
 193                         t->trace->allsolid = false;
 194                         if (num == CONTENTS_EMPTY)
 195                                 t->trace->inopen = true;
 196                         else
 197                                 t->trace->inwater = true;
 198                 }
 199                 else
 200                 {
 201                         // if the first leaf is solid, set startsolid
 202                         if (t->trace->allsolid)
 203                                 t->trace->startsolid = true;
 204                 }
 205         }
 206 }
 207 #endif
 208
 209 static hull_t box_hull;
 210 static dclipnode_t box_clipnodes[6];
 211 static mplane_t box_planes[6];
 212
 213 void Collision_Init (void)
 214 {
 215         int             i;
 216         int             side;
 217
 218         //Set up the planes and clipnodes so that the six floats of a bounding box
 219         //can just be stored out and get a proper hull_t structure.
 220
 221         box_hull.clipnodes = box_clipnodes;
 222         box_hull.planes = box_planes;
 223         box_hull.firstclipnode = 0;
 224         box_hull.lastclipnode = 5;
 225
 226         for (i = 0;i < 6;i++)
 227         {
 228                 box_clipnodes[i].planenum = i;
 229
 230                 side = i&1;
 231
 232                 box_clipnodes[i].children[side] = CONTENTS_EMPTY;
 233                 if (i != 5)
 234                         box_clipnodes[i].children[side^1] = i + 1;
 235                 else
 236                         box_clipnodes[i].children[side^1] = CONTENTS_SOLID;
 237
 238                 box_planes[i].type = i>>1;
 239                 box_planes[i].normal[i>>1] = 1;
 240         }
 241 }
 242
 243 void Collision_ClipTrace_Box(trace_t *trace, const vec3_t cmins, const vec3_t cmaxs, const vec3_t start, const vec3_t mins, const vec3_t maxs, const vec3_t end)
 244 {
 245         RecursiveHullCheckTraceInfo_t rhc;
 246         // fill in a default trace
 247         memset(&rhc, 0, sizeof(rhc));
 248         memset(trace, 0, sizeof(trace_t));
 249         //To keep everything totally uniform, bounding boxes are turned into small
 250         //BSP trees instead of being compared directly.
 251         // create a temp hull from bounding box sizes
 252         box_planes[0].dist = cmaxs[0] - mins[0];
 253         box_planes[1].dist = cmins[0] - maxs[0];
 254         box_planes[2].dist = cmaxs[1] - mins[1];
 255         box_planes[3].dist = cmins[1] - maxs[1];
 256         box_planes[4].dist = cmaxs[2] - mins[2];
 257         box_planes[5].dist = cmins[2] - maxs[2];
 258         // trace a line through the generated clipping hull
 259         rhc.hull = &box_hull;
 260         rhc.trace = trace;
 261         rhc.trace->fraction = 1;
 262         rhc.trace->allsolid = true;
 263         VectorCopy(start, rhc.start);
 264         VectorCopy(end, rhc.end);
 265         VectorSubtract(rhc.end, rhc.start, rhc.dist);
 266         RecursiveHullCheck(&rhc, rhc.hull->firstclipnode, 0, 1, rhc.start, rhc.end);
 267 }
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283 void Collision_PrintBrushAsQHull(colbrushf_t *brush, const char *name)
 284 {
 285         int i;
 286         Con_Printf("3 %s\n%i\n", name, brush->numpoints);
 287         for (i = 0;i < brush->numpoints;i++)
 288                 Con_Printf("%g %g %g\n", brush->points[i].v[0], brush->points[i].v[1], brush->points[i].v[2]);
 289         // FIXME: optimize!
 290         Con_Printf("4\n%i\n", brush->numplanes);
 291         for (i = 0;i < brush->numplanes;i++)
 292                 Con_Printf("%g %g %g %g\n", brush->planes[i].normal[0], brush->planes[i].normal[1], brush->planes[i].normal[2], brush->planes[i].dist);
 293 }
 294
 295
 296 colbrushf_t *Collision_AllocBrushFloat(mempool_t *mempool, int numpoints, int numplanes)
 297 {
 298         colbrushf_t *brush;
 299         brush = Mem_Alloc(mempool, sizeof(colbrushf_t) + sizeof(colpointf_t) * numpoints + sizeof(colplanef_t) * numplanes);
 300         brush->numpoints = numpoints;
 301         brush->numplanes = numplanes;
 302         brush->planes = (void *)(brush + 1);
 303         brush->points = (void *)(brush->planes + brush->numplanes);
 304         return brush;
 305 }
 306
 307 void Collision_CalcPlanesForPolygonBrushFloat(colbrushf_t *brush)
 308 {
 309         int i;
 310         float edge0[3], edge1[3], normal[3], dist, bestdist;
 311         colpointf_t *p, *p2;
 312
 313         // choose best surface normal for polygon's plane
 314         bestdist = 0;
 315         for (i = 0, p = brush->points + 1;i < brush->numpoints - 2;i++, p++)
 316         {
 317                 VectorSubtract(p[-1].v, p[0].v, edge0);
 318                 VectorSubtract(p[1].v, p[0].v, edge1);
 319                 CrossProduct(edge0, edge1, normal);
 320                 dist = DotProduct(normal, normal);
 321                 if (i == 0 || bestdist < dist)
 322                 {
 323                         bestdist = dist;
 324                         VectorCopy(normal, brush->planes->normal);
 325                 }
 326         }
 327
 328         VectorNormalize(brush->planes->normal);
 329         brush->planes->dist = DotProduct(brush->points->v, brush->planes->normal);
 330
 331         // negate plane to create other side
 332         VectorNegate(brush->planes[0].normal, brush->planes[1].normal);
 333         brush->planes[1].dist = -brush->planes[0].dist;
 334         for (i = 0, p = brush->points + (brush->numpoints - 1), p2 = brush->points;i < brush->numpoints;i++, p = p2, p2++)
 335         {
 336                 VectorSubtract(p->v, p2->v, edge0);
 337                 CrossProduct(edge0, brush->planes->normal, brush->planes[i + 2].normal);
 338                 VectorNormalize(brush->planes[i + 2].normal);
 339                 brush->planes[i + 2].dist = DotProduct(p->v, brush->planes[i + 2].normal);
 340         }
 341
 342 #if 1
 343         // validity check - will be disabled later
 344         for (i = 0;i < brush->numplanes;i++)
 345         {
 346                 int j;
 347                 for (j = 0, p = brush->points;j < brush->numpoints;j++, p++)
 348                         if (DotProduct(p->v, brush->planes[i].normal) > brush->planes[i].dist + (1.0 / 32.0))
 349                                 Con_Printf("Error in brush plane generation, plane %i\n", i);
 350         }
 351 #endif
 352 }
 353
 354 colbrushf_t *Collision_AllocBrushFromPermanentPolygonFloat(mempool_t *mempool, int numpoints, float *points)
 355 {
 356         colbrushf_t *brush;
 357         brush = Mem_Alloc(mempool, sizeof(colbrushf_t) + sizeof(colplanef_t) * (numpoints + 2));
 358         brush->numpoints = numpoints;
 359         brush->numplanes = numpoints + 2;
 360         brush->planes = (void *)(brush + 1);
 361         brush->points = (colpointf_t *)points;
 362         return brush;
 363 }
 364
 365 float nearestplanedist_float(const float *normal, const colpointf_t *points, int numpoints)
 366 {
 367         float dist, bestdist;
 368         bestdist = DotProduct(points->v, normal);
 369         points++;
 370         while(--numpoints)
 371         {
 372                 dist = DotProduct(points->v, normal);
 373                 if (bestdist > dist)
 374                         bestdist = dist;
 375                 points++;
 376         }
 377         return bestdist;
 378 }
 379
 380 float furthestplanedist_float(const float *normal, const colpointf_t *points, int numpoints)
 381 {
 382         float dist, bestdist;
 383         bestdist = DotProduct(points->v, normal);
 384         points++;
 385         while(--numpoints)
 386         {
 387                 dist = DotProduct(points->v, normal);
 388                 if (bestdist < dist)
 389                         bestdist = dist;
 390                 points++;
 391         }
 392         return bestdist;
 393 }
 394
 395 #define COLLISIONEPSILON (1.0f / 32.0f)
 396 #define COLLISIONEPSILON2 0//(1.0f / 32.0f)
 397
 398 // NOTE: start and end of each brush pair must have same numplanes/numpoints
 399 void Collision_TraceBrushBrushFloat(trace_t *trace, const colbrushf_t *thisbrush_start, const colbrushf_t *thisbrush_end, const colbrushf_t *thatbrush_start, const colbrushf_t *thatbrush_end)
 400 {
 401         int nplane, nplane2, fstartsolid, fendsolid;
 402         float enterfrac, leavefrac, d1, d2, f, newimpactnormal[3];
 403         const colplanef_t *startplane, *endplane;
 404
 405         enterfrac = -1;
 406         leavefrac = 1;
 407         fstartsolid = true;
 408         fendsolid = true;
 409
 410         for (nplane = 0;nplane < thatbrush_start->numplanes + thisbrush_start->numplanes;nplane++)
 411         {
 412                 nplane2 = nplane;
 413                 if (nplane2 >= thatbrush_start->numplanes)
 414                 {
 415                         nplane2 -= thatbrush_start->numplanes;
 416                         startplane = thisbrush_start->planes + nplane2;
 417                         endplane = thisbrush_end->planes + nplane2;
 418                 }
 419                 else
 420                 {
 421                         startplane = thatbrush_start->planes + nplane2;
 422                         endplane = thatbrush_end->planes + nplane2;
 423                 }
 424                 d1 = nearestplanedist_float(startplane->normal, thisbrush_start->points, thisbrush_start->numpoints) - furthestplanedist_float(startplane->normal, thatbrush_start->points, thatbrush_start->numpoints);
 425                 d2 = nearestplanedist_float(endplane->normal, thisbrush_end->points, thisbrush_end->numpoints) - furthestplanedist_float(endplane->normal, thatbrush_end->points, thatbrush_end->numpoints) - COLLISIONEPSILON2;
 426                 //Con_Printf("%c%i: d1 = %f, d2 = %f, d1 / (d1 - d2) = %f\n", nplane2 != nplane ? 'b' : 'a', nplane2, d1, d2, d1 / (d1 - d2));
 427
 428                 f = d1 - d2;
 429                 if (f >= 0)
 430                 {
 431                         // moving into brush
 432                         if (d2 > 0)
 433                                 return;
 434                         if (d1 < 0)
 435                                 continue;
 436                         // enter
 437                         fstartsolid = false;
 438                         f = (d1 - COLLISIONEPSILON) / f;
 439                         f = bound(0, f, 1);
 440                         if (enterfrac < f)
 441                         {
 442                                 enterfrac = f;
 443                                 VectorBlend(startplane->normal, endplane->normal, enterfrac, newimpactnormal);
 444                         }
 445                 }
 446                 else if (f < 0)
 447                 {
 448                         // moving out of brush
 449                         if (d1 > 0)
 450                                 return;
 451                         if (d2 < 0)
 452                                 continue;
 453                         // leave
 454                         fendsolid = false;
 455                         f = (d1 + COLLISIONEPSILON) / f;
 456                         f = bound(0, f, 1);
 457                         if (leavefrac > f)
 458                                 leavefrac = f;
 459                 }
 460         }
 461
 462         if (fstartsolid)
 463         {
 464                 trace->startsolid = true;
 465                 if (fendsolid)
 466                         trace->allsolid = true;
 467         }
 468
 469         // LordHavoc: we need an epsilon nudge here because for a point trace the
 470         // penetrating line segment is normally zero length if this brush was
 471         // generated from a polygon (infinitely thin), and could even be slightly
 472         // positive or negative due to rounding errors in that case.
 473         if (enterfrac > -1 && enterfrac < trace->fraction && enterfrac - (1.0f / 1024.0f) <= leavefrac)
 474         {
 475                 trace->fraction = bound(0, enterfrac, 1);
 476                 VectorCopy(newimpactnormal, trace->plane.normal);
 477         }
 478 }
 479
 480 static colplanef_t polyf_planes[256 + 2];
 481 static colbrushf_t polyf_brush;
 482
 483 void Collision_TraceBrushPolygonFloat(trace_t *trace, const colbrushf_t *thisbrush_start, const colbrushf_t *thisbrush_end, int numpoints, const float *points)
 484 {
 485         if (numpoints > 256)
 486         {
 487                 Con_Printf("Polygon with more than 256 points not supported yet (fixme!)\n");
 488                 return;
 489         }
 490         polyf_brush.numpoints = numpoints;
 491         polyf_brush.numplanes = numpoints + 2;
 492         polyf_brush.points = (colpointf_t *)points;
 493         polyf_brush.planes = polyf_planes;
 494         Collision_CalcPlanesForPolygonBrushFloat(&polyf_brush);
 495         //Collision_PrintBrushAsQHull(&polyf_brush, "polyf_brush");
 496         Collision_TraceBrushBrushFloat(trace, thisbrush_start, thisbrush_end, &polyf_brush, &polyf_brush);
 497 }
 498
 499 static colpointf_t polyf_pointsstart[256], polyf_pointsend[256];
 500 static colplanef_t polyf_planesstart[256 + 2], polyf_planesend[256 + 2];
 501 static colbrushf_t polyf_brushstart, polyf_brushend;
 502
 503 void Collision_TraceBrushPolygonTransformFloat(trace_t *trace, const colbrushf_t *thisbrush_start, const colbrushf_t *thisbrush_end, int numpoints, const float *points, const matrix4x4_t *polygonmatrixstart, const matrix4x4_t *polygonmatrixend)
 504 {
 505         int i;
 506         if (numpoints > 256)
 507         {
 508                 Con_Printf("Polygon with more than 256 points not supported yet (fixme!)\n");
 509                 return;
 510         }
 511         polyf_brushstart.numpoints = numpoints;
 512         polyf_brushstart.numplanes = numpoints + 2;
 513         polyf_brushstart.points = polyf_pointsstart;//(colpointf_t *)points;
 514         polyf_brushstart.planes = polyf_planesstart;
 515         for (i = 0;i < numpoints;i++)
 516                 Matrix4x4_Transform(polygonmatrixstart, points + i * 3, polyf_brushstart.points[i].v);
 517         polyf_brushend.numpoints = numpoints;
 518         polyf_brushend.numplanes = numpoints + 2;
 519         polyf_brushend.points = polyf_pointsend;//(colpointf_t *)points;
 520         polyf_brushend.planes = polyf_planesend;
 521         for (i = 0;i < numpoints;i++)
 522                 Matrix4x4_Transform(polygonmatrixend, points + i * 3, polyf_brushend.points[i].v);
 523         Collision_CalcPlanesForPolygonBrushFloat(&polyf_brushstart);
 524         Collision_CalcPlanesForPolygonBrushFloat(&polyf_brushend);
 525
 526         //Collision_PrintBrushAsQHull(&polyf_brushstart, "polyf_brushstart");
 527         //Collision_PrintBrushAsQHull(&polyf_brushend, "polyf_brushend");
 528
 529         Collision_TraceBrushBrushFloat(trace, thisbrush_start, thisbrush_end, &polyf_brushstart, &polyf_brushend);
 530 }
 531
 532
 533
 534 #define MAX_BRUSHFORBOX 16
 535 static int brushforbox_index = 0;
 536 static colpointf_t brushforbox_point[MAX_BRUSHFORBOX*8];
 537 static colplanef_t brushforbox_plane[MAX_BRUSHFORBOX*6];
 538 static colbrushf_t brushforbox_brush[MAX_BRUSHFORBOX];
 539
 540 void Collision_InitBrushForBox(void)
 541 {
 542         int i;
 543         for (i = 0;i < MAX_BRUSHFORBOX;i++)
 544         {
 545                 brushforbox_brush[i].numpoints = 8;
 546                 brushforbox_brush[i].numplanes = 6;
 547                 brushforbox_brush[i].points = brushforbox_point + i * 8;
 548                 brushforbox_brush[i].planes = brushforbox_plane + i * 6;
 549         }
 550 }
 551
 552 colbrushf_t *Collision_BrushForBox(const matrix4x4_t *matrix, const vec3_t mins, const vec3_t maxs)
 553 {
 554         int i;
 555         vec3_t v;
 556         colbrushf_t *brush;
 557         if (brushforbox_brush[0].numpoints == 0)
 558                 Collision_InitBrushForBox();
 559         brush = brushforbox_brush + ((brushforbox_index++) % MAX_BRUSHFORBOX);
 560         // FIXME: optimize
 561         for (i = 0;i < 8;i++)
 562         {
 563                 v[0] = i & 1 ? maxs[0] : mins[0];
 564                 v[1] = i & 2 ? maxs[1] : mins[1];
 565                 v[2] = i & 4 ? maxs[2] : mins[2];
 566                 Matrix4x4_Transform(matrix, v, brush->points[i].v);
 567         }
 568         // FIXME: optimize!
 569         for (i = 0;i < 6;i++)
 570         {
 571                 VectorClear(v);
 572                 v[i >> 1] = i & 1 ? 1 : -1;
 573                 Matrix4x4_Transform3x3(matrix, v, brush->planes[i].normal);
 574                 VectorNormalize(brush->planes[i].normal);
 575                 brush->planes[i].dist = furthestplanedist_float(brush->planes[i].normal, brush->points, brush->numpoints);
 576         }
 577         return brush;
 578 }
 579
 580 // LordHavoc: currently unused and not yet tested
 581 // note: this can be used for tracing a moving sphere vs a stationary sphere,
 582 // by simply adding the moving sphere's radius to the sphereradius parameter,
 583 // all the results are correct (impactpoint, impactnormal, and fraction)
 584 float Collision_ClipTrace_Line_Sphere(double *linestart, double *lineend, double *sphereorigin, double sphereradius, double *impactpoint, double *impactnormal)
 585 {
 586         double dir[3], scale, v[3], deviationdist, impactdist, linelength;
 587         // make sure the impactpoint and impactnormal are valid even if there is
 588         // no collision
 589         impactpoint[0] = lineend[0];
 590         impactpoint[1] = lineend[1];
 591         impactpoint[2] = lineend[2];
 592         impactnormal[0] = 0;
 593         impactnormal[1] = 0;
 594         impactnormal[2] = 0;
 595         // calculate line direction
 596         dir[0] = lineend[0] - linestart[0];
 597         dir[1] = lineend[1] - linestart[1];
 598         dir[2] = lineend[2] - linestart[2];
 599         // normalize direction
 600         linelength = sqrt(dir[0] * dir[0] + dir[1] * dir[1] + dir[2] * dir[2]);
 601         if (linelength)
 602         {
 603                 scale = 1.0 / linelength;
 604                 dir[0] *= scale;
 605                 dir[1] *= scale;
 606                 dir[2] *= scale;
 607         }
 608         // this dotproduct calculates the distance along the line at which the
 609         // sphere origin is (nearest point to the sphere origin on the line)
 610         impactdist = dir[0] * (sphereorigin[0] - linestart[0]) + dir[1] * (sphereorigin[1] - linestart[1]) + dir[2] * (sphereorigin[2] - linestart[2]);
 611         // calculate point on line at that distance, and subtract the
 612         // sphereorigin from it, so we have a vector to measure for the distance
 613         // of the line from the sphereorigin (deviation, how off-center it is)
 614         v[0] = linestart[0] + impactdist * dir[0] - sphereorigin[0];
 615         v[1] = linestart[1] + impactdist * dir[1] - sphereorigin[1];
 616         v[2] = linestart[2] + impactdist * dir[2] - sphereorigin[2];
 617         deviationdist = v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
 618         // if outside the radius, it's a miss for sure
 619         // (we do this comparison using squared radius to avoid a sqrt)
 620         if (deviationdist > sphereradius*sphereradius)
 621                 return 1; // miss (off to the side)
 622         // nudge back to find the correct impact distance
 623         impactdist += (sqrt(deviationdist) - sphereradius);
 624         if (impactdist >= linelength)
 625                 return 1; // miss (not close enough)
 626         if (impactdist < 0)
 627                 return 1; // miss (linestart is past or inside sphere)
 628         // calculate new impactpoint
 629         impactpoint[0] = linestart[0] + impactdist * dir[0];
 630         impactpoint[1] = linestart[1] + impactdist * dir[1];
 631         impactpoint[2] = linestart[2] + impactdist * dir[2];
 632         // calculate impactnormal (surface normal at point of impact)
 633         impactnormal[0] = impactpoint[0] - sphereorigin[0];
 634         impactnormal[1] = impactpoint[1] - sphereorigin[1];
 635         impactnormal[2] = impactpoint[2] - sphereorigin[2];
 636         // normalize impactnormal
 637         scale = impactnormal[0] * impactnormal[0] + impactnormal[1] * impactnormal[1] + impactnormal[2] * impactnormal[2];
 638         if (scale)
 639         {
 640                 scale = 1.0 / sqrt(scale);
 641                 impactnormal[0] *= scale;
 642                 impactnormal[1] *= scale;
 643                 impactnormal[2] *= scale;
 644         }
 645         // return fraction of movement distance
 646         return impactdist / linelength;
 647 }
 648