[162] | 1 |
|
---|
| 2 | // GOLEM library
|
---|
| 3 | #include <assert.h>
|
---|
| 4 | #include <iostream>
|
---|
| 5 | using namespace std;
|
---|
| 6 | #include "AxisAlignedBox3.h"
|
---|
| 7 | #include "Ray.h"
|
---|
| 8 |
|
---|
| 9 | #define FATAL Debug
|
---|
| 10 | #define FATAL_ABORT exit(1)
|
---|
| 11 |
|
---|
| 12 |
|
---|
| 13 | // AxisAlignedBox3 implementations
|
---|
| 14 |
|
---|
| 15 | // Overload << operator for C++-style output
|
---|
| 16 | ostream&
|
---|
| 17 | operator<< (ostream &s, const AxisAlignedBox3 &A)
|
---|
| 18 | {
|
---|
| 19 | return s << '[' << A.mMin.x << ", " << A.mMin.y << ", " << A.mMin.z << "]["
|
---|
| 20 | << A.mMax.x << ", " << A.mMax.y << ", " << A.mMax.z << ']';
|
---|
| 21 | }
|
---|
| 22 |
|
---|
| 23 | // Overload >> operator for C++-style input
|
---|
| 24 | istream&
|
---|
| 25 | operator>> (istream &s, AxisAlignedBox3 &A)
|
---|
| 26 | {
|
---|
| 27 | char a;
|
---|
| 28 | // read "[min.x, min.y, min.z][mMax.x, mMax.y, mMax.z]"
|
---|
| 29 | return s >> a >> A.mMin.x >> a >> A.mMin.y >> a >> A.mMin.z >> a >> a
|
---|
| 30 | >> A.mMax.x >> a >> A.mMax.y >> a >> A.mMax.z >> a;
|
---|
| 31 | }
|
---|
| 32 |
|
---|
| 33 | bool
|
---|
| 34 | AxisAlignedBox3::Unbounded() const
|
---|
| 35 | {
|
---|
| 36 | return (mMin == Vector3(-MAXFLOAT)) ||
|
---|
| 37 | (mMax == Vector3(-MAXFLOAT));
|
---|
| 38 | }
|
---|
| 39 |
|
---|
| 40 | void
|
---|
| 41 | AxisAlignedBox3::Include(const Vector3 &newpt)
|
---|
| 42 | {
|
---|
| 43 | Minimize(mMin, newpt);
|
---|
| 44 | Maximize(mMax, newpt);
|
---|
| 45 | }
|
---|
| 46 |
|
---|
| 47 | void
|
---|
| 48 | AxisAlignedBox3::Include(const AxisAlignedBox3 &bbox)
|
---|
| 49 | {
|
---|
| 50 | Minimize(mMin, bbox.mMin);
|
---|
| 51 | Maximize(mMax, bbox.mMax);
|
---|
| 52 | }
|
---|
| 53 |
|
---|
| 54 | bool
|
---|
| 55 | AxisAlignedBox3::IsCorrect()
|
---|
| 56 | {
|
---|
| 57 | if ( (mMin.x > mMax.x) ||
|
---|
| 58 | (mMin.y > mMax.y) ||
|
---|
| 59 | (mMin.z > mMax.z) )
|
---|
| 60 | return false; // box is not formed
|
---|
| 61 | return true;
|
---|
| 62 | }
|
---|
| 63 |
|
---|
| 64 | void
|
---|
| 65 | AxisAlignedBox3::GetEdge(const int edge, Vector3 *a, Vector3 *b) const
|
---|
| 66 | {
|
---|
| 67 | switch(edge) {
|
---|
| 68 | case 0:
|
---|
| 69 | a->SetValue(mMin.x, mMin.y, mMin.z);
|
---|
| 70 | b->SetValue(mMin.x, mMin.y, mMax.z);
|
---|
| 71 | break;
|
---|
| 72 | case 1:
|
---|
| 73 | a->SetValue(mMin.x, mMin.y, mMin.z);
|
---|
| 74 | b->SetValue(mMin.x, mMax.y, mMin.z);
|
---|
| 75 | break;
|
---|
| 76 | case 2:
|
---|
| 77 | a->SetValue(mMin.x, mMin.y, mMin.z);
|
---|
| 78 | b->SetValue(mMax.x, mMin.y, mMin.z);
|
---|
| 79 | break;
|
---|
| 80 | case 3:
|
---|
| 81 | a->SetValue(mMax.x, mMax.y, mMax.z);
|
---|
| 82 | b->SetValue(mMax.x, mMax.y, mMin.z);
|
---|
| 83 | break;
|
---|
| 84 | case 4:
|
---|
| 85 | a->SetValue(mMax.x, mMax.y, mMax.z);
|
---|
| 86 | b->SetValue(mMax.x, mMin.y, mMax.z);
|
---|
| 87 | break;
|
---|
| 88 | case 5:
|
---|
| 89 | a->SetValue(mMax.x, mMax.y, mMax.z);
|
---|
| 90 | b->SetValue(mMin.x, mMax.y, mMax.z);
|
---|
| 91 | break;
|
---|
| 92 |
|
---|
| 93 | case 6:
|
---|
| 94 | a->SetValue(mMin.x, mMin.y, mMax.z);
|
---|
| 95 | b->SetValue(mMin.x, mMax.y, mMax.z);
|
---|
| 96 | break;
|
---|
| 97 | case 7:
|
---|
| 98 | a->SetValue(mMin.x, mMin.y, mMax.z);
|
---|
| 99 | b->SetValue(mMax.x, mMin.y, mMax.z);
|
---|
| 100 | break;
|
---|
| 101 | case 8:
|
---|
| 102 | a->SetValue(mMin.x, mMax.y, mMin.z);
|
---|
| 103 | b->SetValue(mMin.x, mMax.y, mMax.z);
|
---|
| 104 | break;
|
---|
| 105 | case 9:
|
---|
| 106 | a->SetValue(mMin.x, mMax.y, mMin.z);
|
---|
| 107 | b->SetValue(mMax.x, mMax.y, mMin.z);
|
---|
| 108 | break;
|
---|
| 109 | case 10:
|
---|
| 110 | a->SetValue(mMax.x, mMin.y, mMin.z);
|
---|
| 111 | b->SetValue(mMax.x, mMax.y, mMin.z);
|
---|
| 112 | break;
|
---|
| 113 | case 11:
|
---|
| 114 | a->SetValue(mMax.x, mMin.y, mMin.z);
|
---|
| 115 | b->SetValue(mMax.x, mMin.y, mMax.z);
|
---|
| 116 | break;
|
---|
| 117 | }
|
---|
| 118 | }
|
---|
| 119 |
|
---|
| 120 | void
|
---|
| 121 | AxisAlignedBox3::Include(const int &axis, const float &newBound)
|
---|
| 122 | {
|
---|
| 123 | switch (axis) {
|
---|
| 124 | case 0: { // x-axis
|
---|
| 125 | if (mMin.x > newBound)
|
---|
| 126 | mMin.x = newBound;
|
---|
| 127 | if (mMax.x < newBound)
|
---|
| 128 | mMax.x = newBound;
|
---|
| 129 | break;
|
---|
| 130 | }
|
---|
| 131 | case 1: { // y-axis
|
---|
| 132 | if (mMin.y > newBound)
|
---|
| 133 | mMin.y = newBound;
|
---|
| 134 | if (mMax.y < newBound)
|
---|
| 135 | mMax.y = newBound;
|
---|
| 136 | break;
|
---|
| 137 | }
|
---|
| 138 | case 2: { // z-axis
|
---|
| 139 | if (mMin.z > newBound)
|
---|
| 140 | mMin.z = newBound;
|
---|
| 141 | if (mMax.z < newBound)
|
---|
| 142 | mMax.z = newBound;
|
---|
| 143 | break;
|
---|
| 144 | }
|
---|
| 145 | }
|
---|
| 146 | }
|
---|
| 147 |
|
---|
| 148 | #if 0
|
---|
| 149 | // ComputeMinMaxT computes the minimum and maximum signed distances
|
---|
| 150 | // of intersection with the ray; it returns 1 if the ray hits
|
---|
| 151 | // the bounding box and 0 if it does not.
|
---|
| 152 | int
|
---|
| 153 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray,
|
---|
| 154 | float *tmin,
|
---|
| 155 | float *tmax) const
|
---|
| 156 | {
|
---|
| 157 | float minx, maxx, miny, maxy, minz, maxz;
|
---|
| 158 |
|
---|
| 159 | if (fabs(ray.dir.x) < 0.001) {
|
---|
| 160 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
|
---|
| 161 | minx = -MAXFLOAT;
|
---|
| 162 | maxx = MAXFLOAT;
|
---|
| 163 | }
|
---|
| 164 | else
|
---|
| 165 | return 0;
|
---|
| 166 | }
|
---|
| 167 | else {
|
---|
| 168 | float t1 = (mMin.x - ray.loc.x) / ray.dir.x;
|
---|
| 169 | float t2 = (mMax.x - ray.loc.x) / ray.dir.x;
|
---|
| 170 | if (t1 < t2) {
|
---|
| 171 | minx = t1;
|
---|
| 172 | maxx = t2;
|
---|
| 173 | }
|
---|
| 174 | else {
|
---|
| 175 | minx = t2;
|
---|
| 176 | maxx = t1;
|
---|
| 177 | }
|
---|
| 178 | if (maxx < 0)
|
---|
| 179 | return 0;
|
---|
| 180 | }
|
---|
| 181 |
|
---|
| 182 | if (fabs(ray.dir.y) < 0.001) {
|
---|
| 183 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
|
---|
| 184 | miny = -MAXFLOAT;
|
---|
| 185 | maxy = MAXFLOAT;
|
---|
| 186 | }
|
---|
| 187 | else
|
---|
| 188 | return 0;
|
---|
| 189 | }
|
---|
| 190 | else {
|
---|
| 191 | float t1 = (mMin.y - ray.loc.y) / ray.dir.y;
|
---|
| 192 | float t2 = (mMax.y - ray.loc.y) / ray.dir.y;
|
---|
| 193 | if (t1 < t2) {
|
---|
| 194 | miny = t1;
|
---|
| 195 | maxy = t2;
|
---|
| 196 | }
|
---|
| 197 | else {
|
---|
| 198 | miny = t2;
|
---|
| 199 | maxy = t1;
|
---|
| 200 | }
|
---|
| 201 | if (maxy < 0.0)
|
---|
| 202 | return 0;
|
---|
| 203 | }
|
---|
| 204 |
|
---|
| 205 | if (fabs(ray.dir.z) < 0.001) {
|
---|
| 206 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
|
---|
| 207 | minz = -MAXFLOAT;
|
---|
| 208 | maxz = MAXFLOAT;
|
---|
| 209 | }
|
---|
| 210 | else
|
---|
| 211 | return 0;
|
---|
| 212 | }
|
---|
| 213 | else {
|
---|
| 214 | float t1 = (mMin.z - ray.loc.z) / ray.dir.z;
|
---|
| 215 | float t2 = (mMax.z - ray.loc.z) / ray.dir.z;
|
---|
| 216 | if (t1 < t2) {
|
---|
| 217 | minz = t1;
|
---|
| 218 | maxz = t2;
|
---|
| 219 | }
|
---|
| 220 | else {
|
---|
| 221 | minz = t2;
|
---|
| 222 | maxz = t1;
|
---|
| 223 | }
|
---|
| 224 | if (maxz < 0.0)
|
---|
| 225 | return 0;
|
---|
| 226 | }
|
---|
| 227 |
|
---|
| 228 | *tmin = minx;
|
---|
| 229 | if (miny > *tmin)
|
---|
| 230 | *tmin = miny;
|
---|
| 231 | if (minz > *tmin)
|
---|
| 232 | *tmin = minz;
|
---|
| 233 |
|
---|
| 234 | *tmax = maxx;
|
---|
| 235 | if (maxy < *tmax)
|
---|
| 236 | *tmax = maxy;
|
---|
| 237 | if (maxz < *tmax)
|
---|
| 238 | *tmax = maxz;
|
---|
| 239 |
|
---|
| 240 | return 1; // yes, intersection was found
|
---|
| 241 | }
|
---|
| 242 | #else
|
---|
| 243 | // another variant of the same, with less variables
|
---|
| 244 | int
|
---|
| 245 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray,
|
---|
| 246 | float *tmin,
|
---|
| 247 | float *tmax) const
|
---|
| 248 | {
|
---|
| 249 | register float minx, maxx;
|
---|
| 250 | ray.ComputeInvertedDir();
|
---|
| 251 |
|
---|
| 252 | if (fabs(ray.dir.x) < 0.001) {
|
---|
| 253 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
|
---|
| 254 | minx = -MAXFLOAT;
|
---|
| 255 | maxx = MAXFLOAT;
|
---|
| 256 | }
|
---|
| 257 | else
|
---|
| 258 | return 0;
|
---|
| 259 | }
|
---|
| 260 | else {
|
---|
| 261 | float t1 = (mMin.x - ray.loc.x) * ray.invDir.x;
|
---|
| 262 | float t2 = (mMax.x - ray.loc.x) * ray.invDir.x;
|
---|
| 263 | if (t1 < t2) {
|
---|
| 264 | minx = t1;
|
---|
| 265 | maxx = t2;
|
---|
| 266 | }
|
---|
| 267 | else {
|
---|
| 268 | minx = t2;
|
---|
| 269 | maxx = t1;
|
---|
| 270 | }
|
---|
| 271 | if (maxx < 0.0)
|
---|
| 272 | return 0;
|
---|
| 273 | }
|
---|
| 274 |
|
---|
| 275 | *tmin = minx;
|
---|
| 276 | *tmax = maxx;
|
---|
| 277 |
|
---|
| 278 | if (fabs(ray.dir.y) < 0.001) {
|
---|
| 279 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
|
---|
| 280 | minx = -MAXFLOAT;
|
---|
| 281 | maxx = MAXFLOAT;
|
---|
| 282 | }
|
---|
| 283 | else
|
---|
| 284 | return 0;
|
---|
| 285 | }
|
---|
| 286 | else {
|
---|
| 287 | float t1 = (mMin.y - ray.loc.y) * ray.invDir.y;
|
---|
| 288 | float t2 = (mMax.y - ray.loc.y) * ray.invDir.y;
|
---|
| 289 | if (t1 < t2) {
|
---|
| 290 | minx = t1;
|
---|
| 291 | maxx = t2;
|
---|
| 292 | }
|
---|
| 293 | else {
|
---|
| 294 | minx = t2;
|
---|
| 295 | maxx = t1;
|
---|
| 296 | }
|
---|
| 297 | if (maxx < 0.0)
|
---|
| 298 | return 0;
|
---|
| 299 | }
|
---|
| 300 |
|
---|
| 301 | if (minx > *tmin)
|
---|
| 302 | *tmin = minx;
|
---|
| 303 | if (maxx < *tmax)
|
---|
| 304 | *tmax = maxx;
|
---|
| 305 |
|
---|
| 306 | if (fabs(ray.dir.z) < 0.001) {
|
---|
| 307 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
|
---|
| 308 | minx = -MAXFLOAT;
|
---|
| 309 | maxx = MAXFLOAT;
|
---|
| 310 | }
|
---|
| 311 | else
|
---|
| 312 | return 0;
|
---|
| 313 | }
|
---|
| 314 | else {
|
---|
| 315 | float t1 = (mMin.z - ray.loc.z) * ray.invDir.z;
|
---|
| 316 | float t2 = (mMax.z - ray.loc.z) * ray.invDir.z;
|
---|
| 317 | if (t1 < t2) {
|
---|
| 318 | minx = t1;
|
---|
| 319 | maxx = t2;
|
---|
| 320 | }
|
---|
| 321 | else {
|
---|
| 322 | minx = t2;
|
---|
| 323 | maxx = t1;
|
---|
| 324 | }
|
---|
| 325 | if (maxx < 0.0)
|
---|
| 326 | return 0;
|
---|
| 327 | }
|
---|
| 328 |
|
---|
| 329 | if (minx > *tmin)
|
---|
| 330 | *tmin = minx;
|
---|
| 331 | if (maxx < *tmax)
|
---|
| 332 | *tmax = maxx;
|
---|
| 333 |
|
---|
| 334 | return 1; // yes, intersection was found
|
---|
| 335 | }
|
---|
| 336 | #endif
|
---|
| 337 |
|
---|
| 338 | // ComputeMinMaxT computes the minimum and maximum parameters
|
---|
| 339 | // of intersection with the ray; it returns 1 if the ray hits
|
---|
| 340 | // the bounding box and 0 if it does not.
|
---|
| 341 | int
|
---|
| 342 | AxisAlignedBox3::ComputeMinMaxT(const Ray &ray, float *tmin, float *tmax,
|
---|
| 343 | EFaces &entryFace, EFaces &exitFace) const
|
---|
| 344 | {
|
---|
| 345 | float minx, maxx, miny, maxy, minz, maxz;
|
---|
| 346 | int swapped[3];
|
---|
| 347 |
|
---|
| 348 | if (fabs(ray.dir.x) < 0.001) {
|
---|
| 349 | if (mMin.x < ray.loc.x && mMax.x > ray.loc.x) {
|
---|
| 350 | minx = -MAXFLOAT;
|
---|
| 351 | maxx = MAXFLOAT;
|
---|
| 352 | }
|
---|
| 353 | else
|
---|
| 354 | return 0;
|
---|
| 355 | }
|
---|
| 356 | else {
|
---|
| 357 | float t1 = (mMin.x - ray.loc.x) / ray.dir.x;
|
---|
| 358 | float t2 = (mMax.x - ray.loc.x) / ray.dir.x;
|
---|
| 359 | if (t1 < t2) {
|
---|
| 360 | minx = t1;
|
---|
| 361 | maxx = t2;
|
---|
| 362 | swapped[0] = 0;
|
---|
| 363 | }
|
---|
| 364 | else {
|
---|
| 365 | minx = t2;
|
---|
| 366 | maxx = t1;
|
---|
| 367 | swapped[0] = 1;
|
---|
| 368 | }
|
---|
| 369 | if (maxx < 0)
|
---|
| 370 | return 0;
|
---|
| 371 | }
|
---|
| 372 |
|
---|
| 373 | if (fabs(ray.dir.y) < 0.001) {
|
---|
| 374 | if (mMin.y < ray.loc.y && mMax.y > ray.loc.y) {
|
---|
| 375 | miny = -MAXFLOAT;
|
---|
| 376 | maxy = MAXFLOAT;
|
---|
| 377 | }
|
---|
| 378 | else
|
---|
| 379 | return 0;
|
---|
| 380 | }
|
---|
| 381 | else {
|
---|
| 382 | float t1 = (mMin.y - ray.loc.y) / ray.dir.y;
|
---|
| 383 | float t2 = (mMax.y - ray.loc.y) / ray.dir.y;
|
---|
| 384 | if (t1 < t2) {
|
---|
| 385 | miny = t1;
|
---|
| 386 | maxy = t2;
|
---|
| 387 | swapped[1] = 0;
|
---|
| 388 | }
|
---|
| 389 | else {
|
---|
| 390 | miny = t2;
|
---|
| 391 | maxy = t1;
|
---|
| 392 | swapped[1] = 1;
|
---|
| 393 | }
|
---|
| 394 | if (maxy < 0.0)
|
---|
| 395 | return 0;
|
---|
| 396 | }
|
---|
| 397 |
|
---|
| 398 | if (fabs(ray.dir.z) < 0.001) {
|
---|
| 399 | if (mMin.z < ray.loc.z && mMax.z > ray.loc.z) {
|
---|
| 400 | minz = -MAXFLOAT;
|
---|
| 401 | maxz = MAXFLOAT;
|
---|
| 402 | }
|
---|
| 403 | else
|
---|
| 404 | return 0;
|
---|
| 405 | }
|
---|
| 406 | else {
|
---|
| 407 | float t1 = (mMin.z - ray.loc.z) / ray.dir.z;
|
---|
| 408 | float t2 = (mMax.z - ray.loc.z) / ray.dir.z;
|
---|
| 409 | if (t1 < t2) {
|
---|
| 410 | minz = t1;
|
---|
| 411 | maxz = t2;
|
---|
| 412 | swapped[2] = 0;
|
---|
| 413 | }
|
---|
| 414 | else {
|
---|
| 415 | minz = t2;
|
---|
| 416 | maxz = t1;
|
---|
| 417 | swapped[2] = 1;
|
---|
| 418 | }
|
---|
| 419 | if (maxz < 0.0)
|
---|
| 420 | return 0;
|
---|
| 421 | }
|
---|
| 422 |
|
---|
| 423 | *tmin = minx;
|
---|
| 424 | entryFace = ID_Back;
|
---|
| 425 | if (miny > *tmin) {
|
---|
| 426 | *tmin = miny;
|
---|
| 427 | entryFace = ID_Left;
|
---|
| 428 | }
|
---|
| 429 | if (minz > *tmin) {
|
---|
| 430 | *tmin = minz;
|
---|
| 431 | entryFace = ID_Bottom;
|
---|
| 432 | }
|
---|
| 433 |
|
---|
| 434 | *tmax = maxx;
|
---|
| 435 | exitFace = ID_Back;
|
---|
| 436 | if (maxy < *tmax) {
|
---|
| 437 | *tmax = maxy;
|
---|
| 438 | exitFace = ID_Left;
|
---|
| 439 | }
|
---|
| 440 | if (maxz < *tmax) {
|
---|
| 441 | *tmax = maxz;
|
---|
| 442 | exitFace = ID_Bottom;
|
---|
| 443 | }
|
---|
| 444 |
|
---|
| 445 | if (swapped[entryFace])
|
---|
| 446 | entryFace = (EFaces)(entryFace + 3);
|
---|
| 447 |
|
---|
| 448 | if (!swapped[exitFace])
|
---|
| 449 | exitFace = (EFaces)(exitFace + 3);
|
---|
| 450 |
|
---|
| 451 | return 1; // yes, intersection was found
|
---|
| 452 | }
|
---|
| 453 |
|
---|
| 454 | void
|
---|
| 455 | AxisAlignedBox3::Describe(ostream &app, int ind) const
|
---|
| 456 | {
|
---|
| 457 | indent(app, ind);
|
---|
| 458 | app << "AxisAlignedBox3: min at(" << mMin << "), max at(" << mMax << ")\n";
|
---|
| 459 | }
|
---|
| 460 |
|
---|
| 461 | // computes the passing through parameters for case tmin<tmax and tmax>0
|
---|
| 462 | int
|
---|
| 463 | AxisAlignedBox3::GetMinMaxT(const Ray &ray, float *tmin, float *tmax) const
|
---|
| 464 | {
|
---|
| 465 | if (!ComputeMinMaxT(ray, tmin, tmax))
|
---|
| 466 | return 0;
|
---|
| 467 | if ( *tmax < *tmin)
|
---|
| 468 | return 0; // the ray passes outside the box
|
---|
| 469 |
|
---|
| 470 | if ( *tmax < 0.0)
|
---|
| 471 | return 0; // the intersection is not on the positive halfline
|
---|
| 472 |
|
---|
| 473 | return 1; // ray hits the box .. origin can be outside or inside the box
|
---|
| 474 | }
|
---|
| 475 |
|
---|
| 476 | // computes the signed distances for case tmin<tmax and tmax>0
|
---|
| 477 | int
|
---|
| 478 | AxisAlignedBox3::GetMinMaxT(const Ray &ray, float *tmin, float *tmax,
|
---|
| 479 | EFaces &entryFace, EFaces &exitFace) const
|
---|
| 480 | {
|
---|
| 481 | if (!ComputeMinMaxT(ray, tmin, tmax, entryFace, exitFace))
|
---|
| 482 | return 0;
|
---|
| 483 | if ( *tmax < *tmin)
|
---|
| 484 | return 0; // the ray passes outside the box
|
---|
| 485 |
|
---|
| 486 | if ( *tmax < 0.0)
|
---|
| 487 | return 0; // the intersection is not on the positive halfline
|
---|
| 488 |
|
---|
| 489 | return 1; // ray hits the box .. origin can be outside or inside the box
|
---|
| 490 | }
|
---|
| 491 |
|
---|
| 492 | #if 0
|
---|
| 493 | int
|
---|
| 494 | AxisAlignedBox3::IsInside(const Vector3 &point) const
|
---|
| 495 | {
|
---|
| 496 | return (point.x >= mMin.x) && (point.x <= mMax.x) &&
|
---|
| 497 | (point.y >= mMin.y) && (point.y <= mMax.y) &&
|
---|
| 498 | (point.z >= mMin.z) && (point.z <= mMax.z);
|
---|
| 499 | }
|
---|
| 500 | #else
|
---|
| 501 | int
|
---|
| 502 | AxisAlignedBox3::IsInside(const Vector3 &v) const
|
---|
| 503 | {
|
---|
| 504 | return ! (v.x < mMin.x ||
|
---|
| 505 | v.x > mMax.x ||
|
---|
| 506 | v.y < mMin.y ||
|
---|
| 507 | v.y > mMax.y ||
|
---|
| 508 | v.z < mMin.z ||
|
---|
| 509 | v.z > mMax.z);
|
---|
| 510 | }
|
---|
| 511 | #endif
|
---|
| 512 |
|
---|
| 513 | bool
|
---|
| 514 | AxisAlignedBox3::Includes(const AxisAlignedBox3 &b) const
|
---|
| 515 | {
|
---|
| 516 | return (b.mMin.x >= mMin.x &&
|
---|
| 517 | b.mMin.y >= mMin.y &&
|
---|
| 518 | b.mMin.z >= mMin.z &&
|
---|
| 519 | b.mMax.x <= mMax.x &&
|
---|
| 520 | b.mMax.y <= mMax.y &&
|
---|
| 521 | b.mMax.z <= mMax.z);
|
---|
| 522 |
|
---|
| 523 | }
|
---|
| 524 |
|
---|
| 525 |
|
---|
| 526 | // compute the coordinates of one vertex of the box
|
---|
| 527 | Vector3
|
---|
| 528 | AxisAlignedBox3::GetVertex(int xAxis, int yAxis, int zAxis) const
|
---|
| 529 | {
|
---|
| 530 | Vector3 p;
|
---|
| 531 | if (xAxis)
|
---|
| 532 | p.x = mMax.x;
|
---|
| 533 | else
|
---|
| 534 | p.x = mMin.x;
|
---|
| 535 |
|
---|
| 536 | if (yAxis)
|
---|
| 537 | p.y = mMax.y;
|
---|
| 538 | else
|
---|
| 539 | p.y = mMin.y;
|
---|
| 540 |
|
---|
| 541 | if (zAxis)
|
---|
| 542 | p.z = mMax.z;
|
---|
| 543 | else
|
---|
| 544 | p.z = mMin.z;
|
---|
| 545 | return p;
|
---|
| 546 | }
|
---|
| 547 |
|
---|
| 548 | // compute the vertex for number N = <0..7>, N = 4.x + 2.y + z, where
|
---|
| 549 | // x,y,z are either 0 or 1; (0 .. min coordinate, 1 .. max coordinate)
|
---|
| 550 | void
|
---|
[191] | 551 | AxisAlignedBox3::GetVertex(const int N, Vector3 &vertex) const
|
---|
[162] | 552 | {
|
---|
| 553 | switch (N) {
|
---|
| 554 | case 0: vertex = mMin; break;
|
---|
| 555 | case 1: vertex.SetValue(mMin.x, mMin.y, mMax.z); break;
|
---|
| 556 | case 2: vertex.SetValue(mMin.x, mMax.y, mMin.z); break;
|
---|
| 557 | case 3: vertex.SetValue(mMin.x, mMax.y, mMax.z); break;
|
---|
| 558 | case 4: vertex.SetValue(mMax.x, mMin.y, mMin.z); break;
|
---|
| 559 | case 5: vertex.SetValue(mMax.x, mMin.y, mMax.z); break;
|
---|
| 560 | case 6: vertex.SetValue(mMax.x, mMax.y, mMin.z); break;
|
---|
| 561 | case 7: vertex = mMax; break;
|
---|
| 562 | default: {
|
---|
| 563 | FATAL << "ERROR in AxisAlignedBox3::GetVertex N=" << N << "\n";
|
---|
| 564 | FATAL_ABORT;
|
---|
| 565 | }
|
---|
| 566 | }
|
---|
| 567 | }
|
---|
| 568 |
|
---|
| 569 | // Returns region 0 .. 26 ; R = 9*x + 3*y + z ; (x,y,z) \in {0,1,2}
|
---|
| 570 | int
|
---|
| 571 | AxisAlignedBox3::GetRegionID(const Vector3 &point) const
|
---|
| 572 | {
|
---|
| 573 | int ID = 0;
|
---|
| 574 |
|
---|
| 575 | if (point.z >= mMin.z) {
|
---|
| 576 | if (point.z <= mMax.z)
|
---|
| 577 | ID += 1; // inside the two boundary planes
|
---|
| 578 | else
|
---|
| 579 | ID += 2; // outside
|
---|
| 580 | }
|
---|
| 581 |
|
---|
| 582 | if (point.y >= mMin.y) {
|
---|
| 583 | if (point.y <= mMax.y)
|
---|
| 584 | ID += 3; // inside the two boundary planes
|
---|
| 585 | else
|
---|
| 586 | ID += 6; // outside
|
---|
| 587 | }
|
---|
| 588 |
|
---|
| 589 | if (point.x >= mMin.x) {
|
---|
| 590 | if (point.x <= mMax.x)
|
---|
| 591 | ID += 9; // inside the two boundary planes
|
---|
| 592 | else
|
---|
| 593 | ID += 18; // outside
|
---|
| 594 | }
|
---|
| 595 | return ID;
|
---|
| 596 | }
|
---|
| 597 |
|
---|
| 598 |
|
---|
| 599 |
|
---|
| 600 | // computes if a given box (smaller) lies at least in one
|
---|
| 601 | // projection whole in the box (larger) = this encompasses given
|
---|
| 602 | // ;-----;
|
---|
| 603 | // | ;-; |
|
---|
| 604 | // | '-' |
|
---|
| 605 | // '-----'
|
---|
| 606 | int
|
---|
| 607 | AxisAlignedBox3::IsPiercedByBox(const AxisAlignedBox3 &box, int &axis) const
|
---|
| 608 | {
|
---|
| 609 | // test on x-axis
|
---|
| 610 | if ( (mMax.x < box.mMin.x) ||
|
---|
| 611 | (mMin.x > box.mMax.x) )
|
---|
| 612 | return 0; // the boxes do not overlap at all at x-axis
|
---|
| 613 | if ( (box.mMin.y > mMin.y) &&
|
---|
| 614 | (box.mMax.y < mMax.y) &&
|
---|
| 615 | (box.mMin.z > mMin.z) &&
|
---|
| 616 | (box.mMax.z < mMax.z) ) {
|
---|
| 617 | axis = 0;
|
---|
| 618 | return 1; // the boxes overlap in x-axis
|
---|
| 619 | }
|
---|
| 620 | // test on y-axis
|
---|
| 621 | if ( (mMax.y < box.mMin.y) ||
|
---|
| 622 | (mMin.y > box.mMax.y) )
|
---|
| 623 | return 0; // the boxes do not overlap at all at y-axis
|
---|
| 624 | if ( (box.mMin.x > mMin.x) &&
|
---|
| 625 | (box.mMax.x < mMax.x) &&
|
---|
| 626 | (box.mMin.z > mMin.z) &&
|
---|
| 627 | (box.mMax.z < mMax.z) ) {
|
---|
| 628 | axis = 1;
|
---|
| 629 | return 1; // the boxes overlap in y-axis
|
---|
| 630 | }
|
---|
| 631 | // test on z-axis
|
---|
| 632 | if ( (mMax.z < box.mMin.z) ||
|
---|
| 633 | (mMin.z > box.mMax.z) )
|
---|
| 634 | return 0; // the boxes do not overlap at all at y-axis
|
---|
| 635 | if ( (box.mMin.x > mMin.x) &&
|
---|
| 636 | (box.mMax.x < mMax.x) &&
|
---|
| 637 | (box.mMin.y > mMin.y) &&
|
---|
| 638 | (box.mMax.y < mMax.y) ) {
|
---|
| 639 | axis = 2;
|
---|
| 640 | return 1; // the boxes overlap in z-axis
|
---|
| 641 | }
|
---|
| 642 | return 0;
|
---|
| 643 | }
|
---|
| 644 |
|
---|
| 645 | float
|
---|
| 646 | AxisAlignedBox3::SurfaceArea() const
|
---|
| 647 | {
|
---|
| 648 | Vector3 ext = mMax - mMin;
|
---|
| 649 | return 2.0 * (ext.x * ext.y +
|
---|
| 650 | ext.x * ext.z +
|
---|
| 651 | ext.y * ext.z);
|
---|
| 652 | }
|
---|
| 653 |
|
---|
| 654 | const int AxisAlignedBox3::bvertices[27][9] =
|
---|
| 655 | { // region number.. position
|
---|
| 656 | {5,1,3,2,6,4,-1,-1,-1}, // 0 .. x=0 y=0 z=0
|
---|
| 657 | {4,5,1,3,2,0,-1,-1,-1}, // 1 .. x=0 y=0 z=1
|
---|
| 658 | {4,5,7,3,2,0,-1,-1,-1}, // 2 .. x=0 y=0 z=2
|
---|
| 659 |
|
---|
| 660 | {0,1,3,2,6,4,-1,-1,-1}, // 3 .. x=0 y=1 z=0
|
---|
| 661 | {0,1,3,2,-1,-1,-1,-1,-1}, // 4 .. x=0 y=1 z=1
|
---|
| 662 | {1,5,7,3,2,0,-1,-1,-1}, // 5 .. x=0 y=1 z=2
|
---|
| 663 |
|
---|
| 664 | {0,1,3,7,6,4,-1,-1,-1}, // 6 .. x=0 y=2 z=0
|
---|
| 665 | {0,1,3,7,6,2,-1,-1,-1}, // 7 .. x=0 y=2 z=1
|
---|
| 666 | {1,5,7,6,2,0,-1,-1,-1}, // 8 .. x=0 y=2 z=2
|
---|
| 667 |
|
---|
| 668 | // the regions number <9,17>
|
---|
| 669 | {5,1,0,2,6,4,-1,-1,-1}, // 9 .. x=1 y=0 z=0
|
---|
| 670 | {5,1,0,4,-1,-1,-1,-1,-1}, // 10 .. x=1 y=0 z=1
|
---|
| 671 | {7,3,1,0,4,5,-1,-1,-1}, // 11 .. x=1 y=0 z=2
|
---|
| 672 |
|
---|
| 673 | {4,0,2,6,-1,-1,-1,-1,-1}, // 12 .. x=1 y=1 z=0
|
---|
| 674 | {0,2,3,1,5,4,6,7,-1}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 675 | {1,5,7,3,-1,-1,-1,-1,-1}, // 14 .. x=1 y=1 z=2
|
---|
| 676 |
|
---|
| 677 | {4,0,2,3,7,6,-1,-1,-1}, // 15 .. x=1 y=2 z=0
|
---|
| 678 | {6,2,3,7,-1,-1,-1,-1,-1}, // 16 .. x=1 y=2 z=1
|
---|
| 679 | {1,5,7,6,2,3,-1,-1,-1}, // 17 .. x=1 y=2 z=2
|
---|
| 680 |
|
---|
| 681 | // the regions number <18,26>
|
---|
| 682 | {1,0,2,6,7,5,-1,-1,-1}, // 18 .. x=2 y=0 z=0
|
---|
| 683 | {1,0,4,6,7,5,-1,-1,-1}, // 19 .. x=2 y=0 z=1
|
---|
| 684 | {0,4,6,7,3,1,-1,-1,-1}, // 20 .. x=2 y=0 z=2
|
---|
| 685 |
|
---|
| 686 | {4,0,2,6,7,5,-1,-1,-1}, // 21 .. x=2 y=1 z=0
|
---|
| 687 | {5,4,6,7,-1,-1,-1,-1,-1}, // 22 .. x=2 y=1 z=1
|
---|
| 688 | {5,4,6,7,3,1,-1,-1,-1}, // 23 .. x=2 y=1 z=2
|
---|
| 689 |
|
---|
| 690 | {4,0,2,3,7,5,-1,-1,-1}, // 24 .. x=2 y=2 z=0
|
---|
| 691 | {5,4,6,2,3,7,-1,-1,-1}, // 25 .. x=2 y=2 z=1
|
---|
| 692 | {5,4,6,2,3,1,-1,-1,-1}, // 26 .. x=2 y=2 z=2
|
---|
| 693 | };
|
---|
| 694 |
|
---|
| 695 | // the visibility of boundary faces from a given region
|
---|
| 696 | // one to three triples: (axis, min_vertex, max_vertex), axis==-1(terminator)
|
---|
| 697 | const int AxisAlignedBox3::bfaces[27][10] =
|
---|
| 698 | { // region number .. position
|
---|
| 699 | {0,0,3,1,0,5,2,0,6,-1}, // 0 .. x=0 y=0 z=0
|
---|
| 700 | {0,0,3,1,0,5,-1,-1,-1,-1}, // 1 .. x=0 y=0 z=1
|
---|
| 701 | {0,0,3,1,0,5,2,1,7,-1}, // 2 .. x=0 y=0 z=2
|
---|
| 702 |
|
---|
| 703 | {0,0,3,2,0,6,-1,-1,-1,-1}, // 3 .. x=0 y=1 z=0
|
---|
| 704 | {0,0,3,-1,-1,-1,-1,-1,-1,-1},// 4 .. x=0 y=1 z=1
|
---|
| 705 | {0,0,3,2,1,7,-1,-1,-1,-1}, // 5 .. x=0 y=1 z=2
|
---|
| 706 |
|
---|
| 707 | {0,0,3,1,2,7,2,0,6,-1}, // 6 .. x=0 y=2 z=0
|
---|
| 708 | {0,0,3,1,2,7,-1,-1,-1,-1}, // 7 .. x=0 y=2 z=1
|
---|
| 709 | {0,0,3,1,2,7,2,1,7,-1}, // 8 .. x=0 y=2 z=2
|
---|
| 710 |
|
---|
| 711 | // the regions number <9,17>
|
---|
| 712 | {1,0,5,2,0,6,-1,-1,-1,-1}, // 9 .. x=1 y=0 z=0
|
---|
| 713 | {1,0,5,-1,-1,-1,-1,-1,-1,-1},// 10 .. x=1 y=0 z=1
|
---|
| 714 | {1,0,5,2,1,7,-1,-1,-1,-1}, // 11 .. x=1 y=0 z=2
|
---|
| 715 |
|
---|
| 716 | {2,0,6,-1,-1,-1,-1,-1,-1,-1},// 12 .. x=1 y=1 z=0
|
---|
| 717 | {-1,-1,-1,-1,-1,-1,-1,-1,-1,-1},// 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 718 | {2,1,7,-1,-1,-1,-1,-1,-1,-1},// 14 .. x=1 y=1 z=2
|
---|
| 719 |
|
---|
| 720 | {1,2,7,2,0,6,-1,-1,-1,-1}, // 15 .. x=1 y=2 z=0
|
---|
| 721 | {1,2,7,-1,-1,-1,-1,-1,-1,-1},// 16 .. x=1 y=2 z=1
|
---|
| 722 | {1,2,7,2,1,7,-1,-1,-1,-1}, // 17 .. x=1 y=2 z=2
|
---|
| 723 |
|
---|
| 724 | // the region number <18,26>
|
---|
| 725 | {0,4,7,1,0,5,2,0,6,-1}, // 18 .. x=2 y=0 z=0
|
---|
| 726 | {0,4,7,1,0,5,-1,-1,-1,-1}, // 19 .. x=2 y=0 z=1
|
---|
| 727 | {0,4,7,1,0,5,2,1,7,-1}, // 20 .. x=2 y=0 z=2
|
---|
| 728 |
|
---|
| 729 | {0,4,7,2,0,6,-1,-1,-1,-1}, // 21 .. x=2 y=1 z=0
|
---|
| 730 | {0,4,7,-1,-1,-1,-1,-1,-1,-1},// 22 .. x=2 y=1 z=1
|
---|
| 731 | {0,4,7,2,1,7,-1,-1,-1,-1}, // 23 .. x=2 y=1 z=2
|
---|
| 732 |
|
---|
| 733 | {0,4,7,1,2,7,2,0,6,-1}, // 24 .. x=2 y=2 z=0
|
---|
| 734 | {0,4,7,1,2,7,-1,-1,-1,-1}, // 25 .. x=2 y=2 z=1
|
---|
| 735 | {0,4,7,1,2,7,2,1,7,-1}, // 26 .. x=2 y=2 z=2
|
---|
| 736 | };
|
---|
| 737 |
|
---|
| 738 | // the correct corners indexing from entry face to exit face
|
---|
| 739 | // first index determines entry face, second index exit face, and
|
---|
| 740 | // the two numbers (indx, inc) determines: ind = the index on the exit
|
---|
| 741 | // face, when starting from the vertex 0 on entry face, 'inc' is
|
---|
| 742 | // the increment when we go on entry face in order 0,1,2,3 to create
|
---|
| 743 | // convex shaft with the rectangle on exit face. That is, inc = -1 or 1.
|
---|
| 744 | const int AxisAlignedBox3::pairFaceRects[6][6][2] = {
|
---|
| 745 | { // entry face = 0
|
---|
| 746 | {-1,0}, // exit face 0 .. no meaning
|
---|
| 747 | {0,-1}, // 1
|
---|
| 748 | {0,-1}, // 2
|
---|
| 749 | {0,1}, // 3 .. opposite face
|
---|
| 750 | {3,1}, // 4
|
---|
| 751 | {1,1} // 5
|
---|
| 752 | },
|
---|
| 753 | { // entry face = 1
|
---|
| 754 | {0,-1}, // exit face 0
|
---|
| 755 | {-1,0}, // 1 .. no meaning
|
---|
| 756 | {0,-1}, // 2
|
---|
| 757 | {1,1}, // 3
|
---|
| 758 | {0,1}, // 4 .. opposite face
|
---|
| 759 | {3,1} // 5
|
---|
| 760 | },
|
---|
| 761 | { // entry face = 2
|
---|
| 762 | {0,-1}, // 0
|
---|
| 763 | {0,-1}, // 1
|
---|
| 764 | {-1,0}, // 2 .. no meaning
|
---|
| 765 | {3,1}, // 3
|
---|
| 766 | {1,1}, // 4
|
---|
| 767 | {0,1} // 5 .. opposite face
|
---|
| 768 | },
|
---|
| 769 | { // entry face = 3
|
---|
| 770 | {0,1}, // 0 .. opposite face
|
---|
| 771 | {3,-1}, // 1
|
---|
| 772 | {1,1}, // 2
|
---|
| 773 | {-1,0}, // 3 .. no meaning
|
---|
| 774 | {0,-1}, // 4
|
---|
| 775 | {0,-1} // 5
|
---|
| 776 | },
|
---|
| 777 | { // entry face = 4
|
---|
| 778 | {1,1}, // 0
|
---|
| 779 | {0,1}, // 1 .. opposite face
|
---|
| 780 | {3,1}, // 2
|
---|
| 781 | {0,-1}, // 3
|
---|
| 782 | {-1,0}, // 4 .. no meaning
|
---|
| 783 | {0,-1} // 5
|
---|
| 784 | },
|
---|
| 785 | { // entry face = 5
|
---|
| 786 | {3,-1}, // 0
|
---|
| 787 | {1,1}, // 1
|
---|
| 788 | {0,1}, // 2 .. opposite face
|
---|
| 789 | {0,-1}, // 3
|
---|
| 790 | {0,-1}, // 4
|
---|
| 791 | {-1,0} // 5 .. no meaning
|
---|
| 792 | }
|
---|
| 793 | };
|
---|
| 794 |
|
---|
| 795 |
|
---|
| 796 | // ------------------------------------------------------------
|
---|
| 797 | // The vertices that form CLOSEST points with respect to the region
|
---|
| 798 | // for all the regions possible, number of regions is 3^3 = 27,
|
---|
| 799 | // since two parallel sides of bbox forms three disjoint spaces.
|
---|
| 800 | // The vertices are given in anti-clockwise order, stopped by value 15,
|
---|
| 801 | // at most 8 points, at least 1 point.
|
---|
| 802 | // The table includes the closest 1/2/4/8 points, followed possibly
|
---|
| 803 | // by the set of coordinates that should be used for testing for
|
---|
| 804 | // the proximity queries. The coordinates to be tested are described by
|
---|
| 805 | // the pair (a,b), when a=0, we want to test min vector of the box,
|
---|
| 806 | // when a=1, we want to test max vector of the box
|
---|
| 807 | // b=0,1,2 corresponds to the axis (0=x,1=y,2=z)
|
---|
| 808 | // The sequence is ended by 15, number -1 is used as the separator
|
---|
| 809 | // between the vertices and coordinates.
|
---|
| 810 | const int
|
---|
| 811 | AxisAlignedBox3::cvertices[27][9] =
|
---|
| 812 | { // region number.. position
|
---|
| 813 | {0,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D one vertex
|
---|
| 814 | {0,1,-1,0,0,0,1,15,15}, // 1 .. x=0 y=0 z=1 D two vertices foll. by 2
|
---|
| 815 | {1,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D one vertex
|
---|
| 816 |
|
---|
| 817 | {0,2,-1,0,0,0,2,15,15}, // 3 .. x=0 y=1 z=0 D
|
---|
| 818 | {0,1,3,2,-1,0,0,15,15}, // 4 .. x=0 y=1 z=1 D
|
---|
| 819 | {1,3,-1,0,0,1,2,15,15}, // 5 .. x=0 y=1 z=2 D
|
---|
| 820 |
|
---|
| 821 | {2,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D
|
---|
| 822 | {2,3,-1,0,0,1,1,15,15}, // 7 .. x=0 y=2 z=1 D
|
---|
| 823 | {3,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D
|
---|
| 824 |
|
---|
| 825 | // the regions number <9,17>
|
---|
| 826 | {0,4,-1,0,1,0,2,15,15}, // 9 .. x=1 y=0 z=0 D
|
---|
| 827 | {5,1,0,4,-1,0,1,15,15}, // 10 .. x=1 y=0 z=1 D
|
---|
| 828 | {1,5,-1,0,1,1,2,15,15}, // 11 .. x=1 y=0 z=2 D
|
---|
| 829 |
|
---|
| 830 | {4,0,2,6,-1,0,2,15,15}, // 12 .. x=1 y=1 z=0 D
|
---|
| 831 | {0,2,3,1,5,4,6,7,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 832 | {1,5,7,3,-1,1,2,15,15}, // 14 .. x=1 y=1 z=2 D
|
---|
| 833 |
|
---|
| 834 | {6,2,-1,0,2,1,1,15,15}, // 15 .. x=1 y=2 z=0 D
|
---|
| 835 | {6,2,3,7,-1,1,1,15,15}, // 16 .. x=1 y=2 z=1 D
|
---|
| 836 | {3,7,-1,1,1,1,2,15,15}, // 17 .. x=1 y=2 z=2 D
|
---|
| 837 |
|
---|
| 838 | // the regions number <18,26>
|
---|
| 839 | {4,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D
|
---|
| 840 | {4,5,-1,0,1,1,0,15,15}, // 19 .. x=2 y=0 z=1 D
|
---|
| 841 | {5,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D
|
---|
| 842 |
|
---|
| 843 | {4,6,-1,0,2,1,0,15,15}, // 21 .. x=2 y=1 z=0 D
|
---|
| 844 | {5,4,6,7,-1,1,0,15,15}, // 22 .. x=2 y=1 z=1 D
|
---|
| 845 | {7,5,-1,1,0,1,2,15,15}, // 23 .. x=2 y=1 z=2 D
|
---|
| 846 |
|
---|
| 847 | {6,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D
|
---|
| 848 | {6,7,-1,1,0,1,1,15,15}, // 25 .. x=2 y=2 z=1 D
|
---|
| 849 | {7,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D
|
---|
| 850 | };
|
---|
| 851 |
|
---|
| 852 | // Table for Sphere-AABB intersection based on the region knowledge
|
---|
| 853 | // Similar array to previous cvertices, but we omit the surfaces
|
---|
| 854 | // which are not necessary for testing. First are vertices,
|
---|
| 855 | // they are finished with -1. Second, there are indexes in
|
---|
| 856 | // the pair (a,b), when a=0, we want to test min vector of the box,
|
---|
| 857 | // when a=1, we want to test max vector of the box
|
---|
| 858 | // b=0,1,2 corresponds to the axis (0=x,1=y,2=z)
|
---|
| 859 | //
|
---|
| 860 | // So either we check the vertices or only the distance in specified
|
---|
| 861 | // dimensions. There are at all four possible cases:
|
---|
| 862 | //
|
---|
| 863 | // 1) we check one vertex - then sequence start with non-negative index
|
---|
| 864 | // and is finished with 15
|
---|
| 865 | // 2) we check two coordinates of min/max vector describe by the pair
|
---|
| 866 | // (a,b) .. a=min/max(0/1) b=x/y/z (0/1/2), sequence starts with 8
|
---|
| 867 | // and finishes with 15
|
---|
| 868 | // 3) we check only one coordinate of min/max, as for 2), sequence start
|
---|
| 869 | // with 9 and ends with 15
|
---|
| 870 | // 4) Position 13 - sphere is inside the box, intersection always exist
|
---|
| 871 | // the sequence start with 15 .. no further testing is necessary
|
---|
| 872 | // in this case
|
---|
| 873 | const int
|
---|
| 874 | AxisAlignedBox3::csvertices[27][6] =
|
---|
| 875 | { // region number.. position
|
---|
| 876 | {0,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D vertex only
|
---|
| 877 | {8,0,0,0,1,15}, // 1 .. x=0 y=0 z=1 D two coords.
|
---|
| 878 | {1,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D vertex only
|
---|
| 879 |
|
---|
| 880 | {8,0,0,0,2,15}, // 3 .. x=0 y=1 z=0 D two coords
|
---|
| 881 | {9,0,0,15,15,15}, // 4 .. x=0 y=1 z=1 D one coord
|
---|
| 882 | {8,0,0,1,2,15}, // 5 .. x=0 y=1 z=2 D two coords.
|
---|
| 883 |
|
---|
| 884 | {2,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D one vertex
|
---|
| 885 | {8,0,0,1,1,15}, // 7 .. x=0 y=2 z=1 D two coords
|
---|
| 886 | {3,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D one vertex
|
---|
| 887 |
|
---|
| 888 | // the regions number <9,17>
|
---|
| 889 | {8,0,1,0,2,15}, // 9 .. x=1 y=0 z=0 D two coords
|
---|
| 890 | {9,0,1,15,15,15}, // 10 .. x=1 y=0 z=1 D one coord
|
---|
| 891 | {8,0,1,1,2,15}, // 11 .. x=1 y=0 z=2 D two coords
|
---|
| 892 |
|
---|
| 893 | {9,0,2,15,15,15}, // 12 .. x=1 y=1 z=0 D one coord
|
---|
| 894 | {15,15,15,15,15,15}, // 13 .. x=1 y=1 z=1 inside the box, special case/value
|
---|
| 895 | {9,1,2,15,15,15}, // 14 .. x=1 y=1 z=2 D one corrd
|
---|
| 896 |
|
---|
| 897 | {8,0,2,1,1,15}, // 15 .. x=1 y=2 z=0 D two coords
|
---|
| 898 | {9,1,1,15,15}, // 16 .. x=1 y=2 z=1 D one coord
|
---|
| 899 | {8,1,1,1,2,15}, // 17 .. x=1 y=2 z=2 D two coords
|
---|
| 900 |
|
---|
| 901 | // the regions number <18,26>
|
---|
| 902 | {4,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D one vertex
|
---|
| 903 | {8,0,1,1,0,15}, // 19 .. x=2 y=0 z=1 D two coords
|
---|
| 904 | {5,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D one vertex
|
---|
| 905 |
|
---|
| 906 | {8,0,2,1,0,15}, // 21 .. x=2 y=1 z=0 D two coords
|
---|
| 907 | {9,1,0,15,15,15}, // 22 .. x=2 y=1 z=1 D one coord
|
---|
| 908 | {8,1,0,1,2,15}, // 23 .. x=2 y=1 z=2 D two coords
|
---|
| 909 |
|
---|
| 910 | {6,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D one vertex
|
---|
| 911 | {8,1,0,1,1,15}, // 25 .. x=2 y=2 z=1 D two coords
|
---|
| 912 | {7,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D one vertex
|
---|
| 913 | };
|
---|
| 914 |
|
---|
| 915 |
|
---|
| 916 | // The vertices that form all FARTHEST points with respect to the region
|
---|
| 917 | // for all the regions possible, number of regions is 3^3 = 27,
|
---|
| 918 | // since two parallel sides of bbox forms three disjoint spaces.
|
---|
| 919 | // The vertices are given in anti-clockwise order, stopped by value 15,
|
---|
| 920 | // at most 8 points, at least 1 point.
|
---|
| 921 | // For testing, if the AABB is whole in the sphere, it is enough
|
---|
| 922 | // to test only vertices, either 1,2,4, or 8.
|
---|
| 923 | const int
|
---|
| 924 | AxisAlignedBox3::fvertices[27][9] =
|
---|
| 925 | { // region number.. position
|
---|
| 926 | {7,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D
|
---|
| 927 | {6,7,15,15,15,15,15,15,15}, // 1 .. x=0 y=0 z=1 D
|
---|
| 928 | {6,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D
|
---|
| 929 |
|
---|
| 930 | {5,7,15,15,15,15,15,15,15}, // 3 .. x=0 y=1 z=0 D
|
---|
| 931 | {4,5,7,6,15,15,15,15,15}, // 4 .. x=0 y=1 z=1 D
|
---|
| 932 | {4,6,15,15,15,15,15,15,15}, // 5 .. x=0 y=1 z=2 D
|
---|
| 933 |
|
---|
| 934 | {5,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D
|
---|
| 935 | {4,5,15,15,15,15,15,15,15}, // 7 .. x=0 y=2 z=1 D
|
---|
| 936 | {4,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D
|
---|
| 937 |
|
---|
| 938 | // the regions number <9,17>
|
---|
| 939 | {3,7,15,15,15,15,15,15,15}, // 9 .. x=1 y=0 z=0 D
|
---|
| 940 | {7,3,2,6,15,15,15,15,15}, // 10 .. x=1 y=0 z=1 D
|
---|
| 941 | {2,6,15,15,15,15,15,15,15}, // 11 .. x=1 y=0 z=2 D
|
---|
| 942 |
|
---|
| 943 | {5,1,3,7,15,15,15,15,15}, // 12 .. x=1 y=1 z=0 D
|
---|
| 944 | {0,7,1,6,3,4,5,2,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 945 | {0,4,6,2,15,15,15,15,15}, // 14 .. x=1 y=1 z=2 D
|
---|
| 946 |
|
---|
| 947 | {5,1,15,15,15,15,15,15,15}, // 15 .. x=1 y=2 z=0 D
|
---|
| 948 | {4,0,1,5,15,15,15,15,15}, // 16 .. x=1 y=2 z=1 D
|
---|
| 949 | {4,0,15,15,15,15,15,15,15}, // 17 .. x=1 y=2 z=2 D
|
---|
| 950 |
|
---|
| 951 | // the regions number <18,26>
|
---|
| 952 | {3,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D
|
---|
| 953 | {2,3,15,15,15,15,15,15,15}, // 19 .. x=2 y=0 z=1 D
|
---|
| 954 | {2,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D
|
---|
| 955 |
|
---|
| 956 | {1,3,15,15,15,15,15,15,15}, // 21 .. x=2 y=1 z=0 D
|
---|
| 957 | {1,0,2,3,15,15,15,15,15}, // 22 .. x=2 y=1 z=1 D
|
---|
| 958 | {2,0,15,15,15,15,15,15,15}, // 23 .. x=2 y=1 z=2 D
|
---|
| 959 |
|
---|
| 960 | {1,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D
|
---|
| 961 | {0,1,15,15,15,15,15,15,15}, // 25 .. x=2 y=2 z=1 D
|
---|
| 962 | {0,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D
|
---|
| 963 | };
|
---|
| 964 |
|
---|
| 965 | // Similar table as above, farthest points, but only the ones
|
---|
| 966 | // necessary for testing the intersection problem. If we do
|
---|
| 967 | // not consider the case 13, center of the sphere is inside the
|
---|
| 968 | // box, then we can always test at most 2 box vertices to say whether
|
---|
| 969 | // the whole box is inside the sphere.
|
---|
| 970 | // The number of vertices is minimized using some assumptions
|
---|
| 971 | // about the ortogonality of vertices and sphere properties.
|
---|
| 972 | const int
|
---|
| 973 | AxisAlignedBox3::fsvertices[27][9] =
|
---|
| 974 | { // region number.. position
|
---|
| 975 | {7,15,15,15,15,15,15,15,15}, // 0 .. x=0 y=0 z=0 D 1 vertex
|
---|
| 976 | {6,7,15,15,15,15,15,15,15}, // 1 .. x=0 y=0 z=1 D 2 vertices
|
---|
| 977 | {6,15,15,15,15,15,15,15,15}, // 2 .. x=0 y=0 z=2 D 1 vertex
|
---|
| 978 |
|
---|
| 979 | {5,7,15,15,15,15,15,15,15}, // 3 .. x=0 y=1 z=0 D 2 vertices
|
---|
| 980 | {4,7,15,5,6,15,15,15,15}, // 4 .. x=0 y=1 z=1 D 4/2 vertices
|
---|
| 981 | {4,6,15,15,15,15,15,15,15}, // 5 .. x=0 y=1 z=2 D 2 vertices
|
---|
| 982 |
|
---|
| 983 | {5,15,15,15,15,15,15,15,15}, // 6 .. x=0 y=2 z=0 D 1 vertex
|
---|
| 984 | {4,5,15,15,15,15,15,15,15}, // 7 .. x=0 y=2 z=1 D 2 vertices
|
---|
| 985 | {4,15,15,15,15,15,15,15,15}, // 8 .. x=0 y=2 z=2 D 1 vertex
|
---|
| 986 |
|
---|
| 987 | // the regions number <9,17>
|
---|
| 988 | {3,7,15,15,15,15,15,15,15}, // 9 .. x=1 y=0 z=0 D 2 vertices
|
---|
| 989 | {7,2,15,3,6,15,15,15,15}, // 10 .. x=1 y=0 z=1 D 4/2 vertices
|
---|
| 990 | {2,6,15,15,15,15,15,15,15}, // 11 .. x=1 y=0 z=2 D 2 vertices
|
---|
| 991 |
|
---|
| 992 | {5,3,15,1,7,15,15,15,15}, // 12 .. x=1 y=1 z=0 D 4/2 vertices
|
---|
| 993 | {0,7,1,6,3,4,5,2,15}, // 13 .. x=1 y=1 z=1 .. inside the box
|
---|
| 994 | {0,6,15,4,2,15,15,15,15}, // 14 .. x=1 y=1 z=2 D 4/2 vertices
|
---|
| 995 |
|
---|
| 996 | {5,1,15,15,15,15,15,15,15}, // 15 .. x=1 y=2 z=0 D 2 vertices
|
---|
| 997 | {4,1,15,0,5,15,15,15,15}, // 16 .. x=1 y=2 z=1 D 4/2 vertices
|
---|
| 998 | {4,0,15,15,15,15,15,15,15}, // 17 .. x=1 y=2 z=2 D 2 vertices
|
---|
| 999 |
|
---|
| 1000 | // the regions number <18,26>
|
---|
| 1001 | {3,15,15,15,15,15,15,15,15}, // 18 .. x=2 y=0 z=0 D 1 vertex
|
---|
| 1002 | {2,3,15,15,15,15,15,15,15}, // 19 .. x=2 y=0 z=1 D 2 vertices
|
---|
| 1003 | {2,15,15,15,15,15,15,15,15}, // 20 .. x=2 y=0 z=2 D 1 vertex
|
---|
| 1004 |
|
---|
| 1005 | {1,3,15,15,15,15,15,15,15}, // 21 .. x=2 y=1 z=0 D 2 vertices
|
---|
| 1006 | {1,2,15,0,3,15,15,15,15}, // 22 .. x=2 y=1 z=1 D 4/2 vertices
|
---|
| 1007 | {2,0,15,15,15,15,15,15,15}, // 23 .. x=2 y=1 z=2 D 2 vertices
|
---|
| 1008 |
|
---|
| 1009 | {1,15,15,15,15,15,15,15,15}, // 24 .. x=2 y=2 z=0 D 1 vertex
|
---|
| 1010 | {0,1,15,15,15,15,15,15,15}, // 25 .. x=2 y=2 z=1 D 2 vertices
|
---|
| 1011 | {0,15,15,15,15,15,15,15,15}, // 26 .. x=2 y=2 z=2 D 1 vertex
|
---|
| 1012 | };
|
---|
| 1013 |
|
---|
| 1014 | // The fast computation of arctangent .. the maximal error is less
|
---|
| 1015 | // than 4.1 degrees, according to Graphics GEMSII, 1991, pages 389--391
|
---|
| 1016 | // Ron Capelli: "Fast approximation to the arctangent"
|
---|
| 1017 | float
|
---|
| 1018 | atan22(const float& y)
|
---|
| 1019 | {
|
---|
| 1020 | const float x = 1.0;
|
---|
| 1021 | const float c = (float)(M_PI * 0.25);
|
---|
| 1022 |
|
---|
| 1023 | if (y < 0.0) {
|
---|
| 1024 | if (y < -1.0)
|
---|
| 1025 | return c * (-2.0 + x / y); // for angle in <-PI/2, -PI/4)
|
---|
| 1026 | else
|
---|
| 1027 | return c * (y / x); // for angle in <-PI/4 , 0>
|
---|
| 1028 | }
|
---|
| 1029 | else {
|
---|
| 1030 | if (y > 1.0)
|
---|
| 1031 | return c * (2.0 - x / y); // for angle in <PI/4, PI/2>
|
---|
| 1032 | else
|
---|
| 1033 | return c * (y / x); // for angle in <0, PI/2>
|
---|
| 1034 | }
|
---|
| 1035 | }
|
---|
| 1036 |
|
---|
| 1037 |
|
---|
| 1038 | float
|
---|
| 1039 | AxisAlignedBox3::ProjectToSphereSA(const Vector3 &viewpoint, int *tcase) const
|
---|
| 1040 | {
|
---|
| 1041 | int id = GetRegionID(viewpoint);
|
---|
| 1042 | *tcase = id;
|
---|
| 1043 |
|
---|
| 1044 | // spherical projection .. SA represents solid angle
|
---|
| 1045 | if (id == 13) // .. inside the box
|
---|
| 1046 | return (float)(4.0*M_PI); // the whole sphere
|
---|
| 1047 | float SA = 0.0; // inital value
|
---|
| 1048 |
|
---|
| 1049 | int i = 0; // the pointer in the array of vertices
|
---|
| 1050 | while (bfaces[id][i] >= 0) {
|
---|
| 1051 | int axisO = bfaces[id][i++];
|
---|
| 1052 | int minvIdx = bfaces[id][i++];
|
---|
| 1053 | int maxvIdx = bfaces[id][i++];
|
---|
| 1054 | Vector3 vmin, vmax;
|
---|
| 1055 | GetVertex(minvIdx, vmin);
|
---|
| 1056 | GetVertex(maxvIdx, vmax);
|
---|
| 1057 | float h = fabs(vmin[axisO] - viewpoint[axisO]);
|
---|
| 1058 | int axis = (axisO + 1) % 3; // next axis
|
---|
| 1059 | float a = (vmin[axis] - viewpoint[axis]) / h; // minimum for v-range
|
---|
| 1060 | float b = (vmax[axis] - viewpoint[axis]) / h; // maximum for v-range
|
---|
| 1061 | //if (a > b) {
|
---|
| 1062 | // FATAL << "ProjectToSphereSA::Error a > b\n";
|
---|
| 1063 | // FATAL_ABORT;
|
---|
| 1064 | //}
|
---|
| 1065 | //if (vmin[axisO] != vmax[axisO]) {
|
---|
| 1066 | // FATAL << "ProjectToSphereSA::Error a-axis != b-axis\n";
|
---|
| 1067 | // FATAL_ABORT;
|
---|
| 1068 | //}
|
---|
| 1069 | axis = (axisO + 2) % 3; // next second axis
|
---|
| 1070 | float c = (vmin[axis] - viewpoint[axis]) / h; // minimum for u-range
|
---|
| 1071 | float d = (vmax[axis] - viewpoint[axis]) / h; // maximum for u-range
|
---|
| 1072 | //if (c > d) {
|
---|
| 1073 | // FATAL << "ProjectToSphereSA::Error c > d\n";
|
---|
| 1074 | // FATAL_ABORT;
|
---|
| 1075 | //}
|
---|
| 1076 | SA +=atan22(d*b/sqrt(b*b + d*d + 1.0)) - atan22(b*c/sqrt(b*b + c*c + 1.0))
|
---|
| 1077 | - atan22(d*a/sqrt(a*a + d*d + 1.0)) + atan22(a*c/sqrt(a*a + c*c + 1.0));
|
---|
| 1078 | }
|
---|
| 1079 |
|
---|
| 1080 | #if 0
|
---|
| 1081 | if ((SA > 2.0*M_PI) ||
|
---|
| 1082 | (SA < 0.0)) {
|
---|
| 1083 | FATAL << "The solid angle has strange value: ";
|
---|
| 1084 | FATAL << "SA = "<< SA << endl;
|
---|
| 1085 | FATAL_ABORT;
|
---|
| 1086 | }
|
---|
| 1087 | #endif
|
---|
| 1088 |
|
---|
| 1089 | return SA;
|
---|
| 1090 | }
|
---|
| 1091 |
|
---|
| 1092 | // Projects the box to a plane given a normal vector only and
|
---|
| 1093 | // computes the surface area of the projected silhouette
|
---|
| 1094 | // no clipping of the box is performed.
|
---|
| 1095 | float
|
---|
| 1096 | AxisAlignedBox3::ProjectToPlaneSA(const Vector3 &normal) const
|
---|
| 1097 | {
|
---|
| 1098 | Vector3 size = Size();
|
---|
| 1099 |
|
---|
| 1100 | // the surface area of the box to a yz-plane - perpendicular to x-axis
|
---|
| 1101 | float sax = size.y * size.z;
|
---|
| 1102 |
|
---|
| 1103 | // the surface area of the box to a zx-plane - perpendicular to y-axis
|
---|
| 1104 | float say = size.z * size.x;
|
---|
| 1105 |
|
---|
| 1106 | // the surface area of the box to a xy-plane - perpendicular to z-axis
|
---|
| 1107 | float saz = size.x * size.y;
|
---|
| 1108 |
|
---|
| 1109 | return sax * fabs(normal.x) + say * fabs(normal.y) + saz * fabs(normal.z);
|
---|
| 1110 | }
|
---|
| 1111 |
|
---|
| 1112 |
|
---|
| 1113 |
|
---|
| 1114 | // This definition allows to be a point when answering true
|
---|
| 1115 | bool
|
---|
| 1116 | AxisAlignedBox3::IsCorrectAndNotPoint() const
|
---|
| 1117 | {
|
---|
| 1118 | if ( (mMin.x > mMax.x) ||
|
---|
| 1119 | (mMin.y > mMax.y) ||
|
---|
| 1120 | (mMin.z > mMax.z) )
|
---|
| 1121 | return false; // box is not formed
|
---|
| 1122 |
|
---|
| 1123 | if ( (mMin.x == mMax.x) &&
|
---|
| 1124 | (mMin.y == mMax.y) &&
|
---|
| 1125 | (mMin.z == mMax.z) )
|
---|
| 1126 | return false; // degenerates to a point
|
---|
| 1127 |
|
---|
| 1128 | return true;
|
---|
| 1129 | }
|
---|
| 1130 |
|
---|
| 1131 | // This definition allows to be a point when answering true
|
---|
| 1132 | bool
|
---|
| 1133 | AxisAlignedBox3::IsPoint() const
|
---|
| 1134 | {
|
---|
| 1135 | if ( (mMin.x == mMax.x) &&
|
---|
| 1136 | (mMin.y == mMax.y) &&
|
---|
| 1137 | (mMin.z == mMax.z) )
|
---|
| 1138 | return true; // degenerates to a point
|
---|
| 1139 |
|
---|
| 1140 | return false;
|
---|
| 1141 | }
|
---|
| 1142 |
|
---|
| 1143 | // This definition requires shape of non-zero volume
|
---|
| 1144 | bool
|
---|
| 1145 | AxisAlignedBox3::IsSingularOrIncorrect() const
|
---|
| 1146 | {
|
---|
| 1147 | if ( (mMin.x >= mMax.x) ||
|
---|
| 1148 | (mMin.y >= mMax.y) ||
|
---|
| 1149 | (mMin.z >= mMax.z) )
|
---|
| 1150 | return true; // box is not formed
|
---|
| 1151 |
|
---|
| 1152 | return false; // has non-zero volume
|
---|
| 1153 | }
|
---|
| 1154 |
|
---|
| 1155 | // returns true, when the sphere specified by the origin and radius
|
---|
| 1156 | // fully contains the box
|
---|
| 1157 | bool
|
---|
| 1158 | AxisAlignedBox3::IsFullyContainedInSphere(const Vector3 ¢er, float rad) const
|
---|
| 1159 | {
|
---|
| 1160 | int region = GetRegionID(center);
|
---|
| 1161 | float rad2 = rad*rad;
|
---|
| 1162 |
|
---|
| 1163 | // vertex of the box
|
---|
| 1164 | Vector3 vertex;
|
---|
| 1165 |
|
---|
| 1166 | int i = 0;
|
---|
| 1167 | for (i = 0 ; ; i++) {
|
---|
| 1168 | int a = fsvertices[region][i];
|
---|
| 1169 | if (a == 15)
|
---|
| 1170 | return true; // if was not false untill now, it must be contained
|
---|
| 1171 |
|
---|
| 1172 | assert( (a>=0) && (a<8) );
|
---|
| 1173 |
|
---|
| 1174 | // normal vertex
|
---|
| 1175 | GetVertex(a, vertex);
|
---|
| 1176 |
|
---|
| 1177 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
| 1178 | return false;
|
---|
| 1179 | } // for
|
---|
| 1180 |
|
---|
| 1181 | }
|
---|
| 1182 |
|
---|
| 1183 | // returns true, when the volume of the sphere and volume of the
|
---|
| 1184 | // axis aligned box has no intersection
|
---|
| 1185 | bool
|
---|
| 1186 | AxisAlignedBox3::HasNoIntersectionWithSphere(const Vector3 ¢er, float rad) const
|
---|
| 1187 | {
|
---|
| 1188 | int region = GetRegionID(center);
|
---|
| 1189 | float rad2 = rad*rad;
|
---|
| 1190 |
|
---|
| 1191 | // vertex of the box
|
---|
| 1192 | Vector3 vertex;
|
---|
| 1193 |
|
---|
| 1194 | switch (csvertices[region][0]) {
|
---|
| 1195 | case 8: {
|
---|
| 1196 | // test two coordinates described within the field
|
---|
| 1197 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
| 1198 | float dist = GetExtent(face) - center[csvertices[region][2]];
|
---|
| 1199 | dist *= dist;
|
---|
| 1200 | face = 3 * (csvertices[region][3]) + csvertices[region][4];
|
---|
| 1201 | float dist2 = GetExtent(face) - center[csvertices[region][4]];
|
---|
| 1202 | dist += (dist2 * dist2);
|
---|
| 1203 | if (dist > rad2)
|
---|
| 1204 | return true; // no intersection is possible
|
---|
| 1205 | }
|
---|
| 1206 | case 9: {
|
---|
| 1207 | // test one coordinate described within the field
|
---|
| 1208 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
| 1209 | float dist = fabs(GetExtent(face) - center[csvertices[region][2]]);
|
---|
| 1210 | if (dist > rad)
|
---|
| 1211 | return true; // no intersection is possible
|
---|
| 1212 | }
|
---|
| 1213 | case 15:
|
---|
| 1214 | return false; // box and sphere surely has intersection
|
---|
| 1215 | default: {
|
---|
| 1216 | // test using normal vertices
|
---|
| 1217 | assert( (csvertices[region][0]>=0) && (csvertices[region][0]<8) );
|
---|
| 1218 |
|
---|
| 1219 | // normal vertex
|
---|
| 1220 | GetVertex(csvertices[region][0], vertex);
|
---|
| 1221 |
|
---|
| 1222 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
| 1223 | return true; // no intersectino is possible
|
---|
| 1224 | }
|
---|
| 1225 | } // switch
|
---|
| 1226 |
|
---|
| 1227 | return false; // partial or full containtment
|
---|
| 1228 | }
|
---|
| 1229 |
|
---|
| 1230 | #if 0
|
---|
| 1231 | // Given the sphere, determine the mutual position between the
|
---|
| 1232 | // sphere and box
|
---|
| 1233 |
|
---|
| 1234 | // SOME BUG IS INSIDE !!!! V.H. 25/4/2001
|
---|
| 1235 | int
|
---|
| 1236 | AxisAlignedBox3::MutualPositionWithSphere(const Vector3 ¢er, float rad) const
|
---|
| 1237 | {
|
---|
| 1238 | int region = GetRegionID(center);
|
---|
| 1239 | float rad2 = rad*rad;
|
---|
| 1240 |
|
---|
| 1241 | // vertex of the box
|
---|
| 1242 | Vector3 vertex;
|
---|
| 1243 |
|
---|
| 1244 | // first testing for full containtment - whether sphere fully
|
---|
| 1245 | // contains the box
|
---|
| 1246 | int countInside = 0; // how many points were found inside
|
---|
| 1247 |
|
---|
| 1248 | int i = 0;
|
---|
| 1249 | for (i = 0 ; ; i++) {
|
---|
| 1250 | int a = fsvertices[region][i];
|
---|
| 1251 | if (a == 15)
|
---|
| 1252 | return 1; // the sphere fully contain the box
|
---|
| 1253 |
|
---|
| 1254 | assert( (a>=0) && (a<8) );
|
---|
| 1255 |
|
---|
| 1256 | // normal vertex
|
---|
| 1257 | GetVertex(a, vertex);
|
---|
| 1258 |
|
---|
| 1259 | if (SqrMagnitude(vertex - center) <= rad2)
|
---|
| 1260 | countInside++; // the number of vertices inside the sphere
|
---|
| 1261 | else {
|
---|
| 1262 | if (countInside)
|
---|
| 1263 | return 0; // partiall overlap has been found
|
---|
| 1264 | // the sphere does not fully contain the box .. only way to break
|
---|
| 1265 | // this loop and go for other testing
|
---|
| 1266 | break;
|
---|
| 1267 | }
|
---|
| 1268 | } // for
|
---|
| 1269 |
|
---|
| 1270 | // now only box and sphere can partially overlap or no intersection
|
---|
| 1271 | switch (csvertices[region][0]) {
|
---|
| 1272 | case 8: {
|
---|
| 1273 | // test two coordinates described within the field
|
---|
| 1274 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
| 1275 | float dist = GetExtent(face) - center[csvertices[region][2]];
|
---|
| 1276 | dist *= dist;
|
---|
| 1277 | face = 3 * (csvertices[region][3]) + csvertices[region][4];
|
---|
| 1278 | float dist2 = GetExtent(face) - center[csvertices[region][4]];
|
---|
| 1279 | dist += (dist2 * dist2);
|
---|
| 1280 | if (dist > rad2 )
|
---|
| 1281 | return -1; // no intersection is possible
|
---|
| 1282 | }
|
---|
| 1283 | case 9: {
|
---|
| 1284 | // test one coordinate described within the field
|
---|
| 1285 | int face = 3*csvertices[region][1] + csvertices[region][2];
|
---|
| 1286 | float dist = fabs(GetExtent(face) - center[csvertices[region][2]]);
|
---|
| 1287 | if (dist > rad)
|
---|
| 1288 | return -1; // no intersection is possible
|
---|
| 1289 | }
|
---|
| 1290 | case 15:
|
---|
| 1291 | return 0 ; // partial overlap is now guaranteed
|
---|
| 1292 | default: {
|
---|
| 1293 | // test using normal vertices
|
---|
| 1294 | assert( (csvertices[region][0]>=0) && (csvertices[region][0]<8) );
|
---|
| 1295 |
|
---|
| 1296 | // normal vertex
|
---|
| 1297 | GetVertex(csvertices[region][0], vertex);
|
---|
| 1298 |
|
---|
| 1299 | if (SqrMagnitude(vertex - center) > rad2)
|
---|
| 1300 | return -1; // no intersection is possible
|
---|
| 1301 | }
|
---|
| 1302 | } // switch
|
---|
| 1303 |
|
---|
| 1304 | return 0; // partial intersection is guaranteed
|
---|
| 1305 | }
|
---|
| 1306 | #else
|
---|
| 1307 |
|
---|
| 1308 | // Some maybe smarter version, extendible easily to d-dimensional
|
---|
| 1309 | // space!
|
---|
| 1310 | // Given a sphere described by the center and radius,
|
---|
| 1311 | // the fullowing function returns:
|
---|
| 1312 | // -1 ... the sphere and the box are completely separate
|
---|
| 1313 | // 0 ... the sphere and the box only partially overlap
|
---|
| 1314 | // 1 ... the sphere contains fully the box
|
---|
| 1315 | // Note: the case when box fully contains the sphere is not reported
|
---|
| 1316 | // since it was not required.
|
---|
| 1317 | int
|
---|
| 1318 | AxisAlignedBox3::MutualPositionWithSphere(const Vector3 ¢er, float rad) const
|
---|
| 1319 | {
|
---|
| 1320 | //#define SPEED_UP
|
---|
| 1321 |
|
---|
| 1322 | #ifndef SPEED_UP
|
---|
| 1323 | // slow version, instructively written
|
---|
| 1324 | #if 0
|
---|
| 1325 | // does it make sense to test
|
---|
| 1326 | // checking the sides of the box for possible non-intersection
|
---|
| 1327 | if ( ((center.x + rad) < mMin.x) ||
|
---|
| 1328 | ((center.x - rad) > mMax.x) ||
|
---|
| 1329 | ((center.y + rad) < mMin.y) ||
|
---|
| 1330 | ((center.y - rad) > mMax.y) ||
|
---|
| 1331 | ((center.z + rad) < mMin.z) ||
|
---|
| 1332 | ((center.z - rad) > mMax.z) ) {
|
---|
| 1333 | // cout << "r ";
|
---|
| 1334 | return -1; // no overlap is possible
|
---|
| 1335 | }
|
---|
| 1336 | #endif
|
---|
| 1337 |
|
---|
| 1338 | // someoverlap is possible, check the distance of vertices
|
---|
| 1339 | rad = rad*rad;
|
---|
| 1340 | float sumMin = 0;
|
---|
| 1341 | // Try to minimize the function of a distance
|
---|
| 1342 | // from the sphere center
|
---|
| 1343 |
|
---|
| 1344 | // for x-axis
|
---|
| 1345 | float minSqrX = sqr(mMin.x - center.x);
|
---|
| 1346 | float maxSqrX = sqr(mMax.x - center.x);
|
---|
| 1347 | if (center.x < mMin.x)
|
---|
| 1348 | sumMin = minSqrX;
|
---|
| 1349 | else
|
---|
| 1350 | if (center.x > mMax.x)
|
---|
| 1351 | sumMin = maxSqrX;
|
---|
| 1352 |
|
---|
| 1353 | // for y-axis
|
---|
| 1354 | float minSqrY = sqr(mMin.y - center.y);
|
---|
| 1355 | float maxSqrY = sqr(mMax.y - center.y);
|
---|
| 1356 | if (center.y < mMin.y)
|
---|
| 1357 | sumMin += minSqrY;
|
---|
| 1358 | else
|
---|
| 1359 | if (center.y > mMax.y)
|
---|
| 1360 | sumMin += maxSqrY;
|
---|
| 1361 |
|
---|
| 1362 | // for z-axis
|
---|
| 1363 | float minSqrZ = sqr(mMin.z - center.z);
|
---|
| 1364 | float maxSqrZ = sqr(mMax.z - center.z);
|
---|
| 1365 | if (center.z < mMin.z)
|
---|
| 1366 | sumMin += minSqrZ;
|
---|
| 1367 | else
|
---|
| 1368 | if (center.z > mMax.z)
|
---|
| 1369 | sumMin += maxSqrZ;
|
---|
| 1370 |
|
---|
| 1371 | if (sumMin > rad)
|
---|
| 1372 | return -1; // no intersection between sphere and box
|
---|
| 1373 |
|
---|
| 1374 | // try to find out the maximum distance between the
|
---|
| 1375 | // sphere center and vertices
|
---|
| 1376 | float sumMax = 0;
|
---|
| 1377 |
|
---|
| 1378 | if (minSqrX > maxSqrX)
|
---|
| 1379 | sumMax = minSqrX;
|
---|
| 1380 | else
|
---|
| 1381 | sumMax = maxSqrX;
|
---|
| 1382 |
|
---|
| 1383 | if (minSqrY > maxSqrY)
|
---|
| 1384 | sumMax += minSqrY;
|
---|
| 1385 | else
|
---|
| 1386 | sumMax += maxSqrY;
|
---|
| 1387 |
|
---|
| 1388 | if (minSqrZ > maxSqrZ)
|
---|
| 1389 | sumMax += minSqrZ;
|
---|
| 1390 | else
|
---|
| 1391 | sumMax += maxSqrZ;
|
---|
| 1392 |
|
---|
| 1393 | // sumMin < rad
|
---|
| 1394 | if (sumMax < rad)
|
---|
| 1395 | return 1; // the sphere contains the box completely
|
---|
| 1396 |
|
---|
| 1397 | // partial intersection, part of the box is outside the sphere
|
---|
| 1398 | return 0;
|
---|
| 1399 | #else
|
---|
| 1400 |
|
---|
| 1401 | // Optimized version of the test
|
---|
| 1402 |
|
---|
| 1403 | #ifndef __VECTOR_HACK
|
---|
| 1404 | #error "__VECTOR_HACK for Vector3 was not defined"
|
---|
| 1405 | #endif
|
---|
| 1406 |
|
---|
| 1407 | // some overlap is possible, check the distance of vertices
|
---|
| 1408 | rad = rad*rad;
|
---|
| 1409 | float sumMin = 0;
|
---|
| 1410 | float sumMax = 0;
|
---|
| 1411 | // Try to minimize the function of a distance
|
---|
| 1412 | // from the sphere center
|
---|
| 1413 |
|
---|
| 1414 | const float *minp = &(min[0]);
|
---|
| 1415 | const float *maxp = &(max[0]);
|
---|
| 1416 | const float *pcenter = &(center[0]);
|
---|
| 1417 |
|
---|
| 1418 | // for x-axis
|
---|
| 1419 | for (int i = 0; i < 3; i++, minp++, maxp++, pcenter++) {
|
---|
| 1420 | float minsqr = sqr(*minp - *pcenter);
|
---|
| 1421 | float maxsqr = sqr(*maxp - *pcenter);
|
---|
| 1422 | if (*pcenter < *minp)
|
---|
| 1423 | sumMin += minsqr;
|
---|
| 1424 | else
|
---|
| 1425 | if (*pcenter > *maxp)
|
---|
| 1426 | sumMin += maxsqr;
|
---|
| 1427 | sumMax += (minsqr > maxsqr) ? minsqr : maxsqr;
|
---|
| 1428 | }
|
---|
| 1429 |
|
---|
| 1430 | if (sumMin > rad)
|
---|
| 1431 | return -1; // no intersection between sphere and box
|
---|
| 1432 |
|
---|
| 1433 | // sumMin < rad
|
---|
| 1434 | if (sumMax < rad)
|
---|
| 1435 | return 1; // the sphere contains the box completely
|
---|
| 1436 |
|
---|
| 1437 | // partial intersection, part of the box is outside the sphere
|
---|
| 1438 | return 0;
|
---|
| 1439 | #endif
|
---|
| 1440 | }
|
---|
| 1441 | #endif
|
---|
| 1442 |
|
---|
| 1443 | // Given the cube describe by the center and the half-sie,
|
---|
| 1444 | // determine the mutual position between the cube and the box
|
---|
| 1445 | int
|
---|
| 1446 | AxisAlignedBox3::MutualPositionWithCube(const Vector3 ¢er, float radius) const
|
---|
| 1447 | {
|
---|
| 1448 | // the cube is described by the center and the distance to the any face
|
---|
| 1449 | // along the axes
|
---|
| 1450 |
|
---|
| 1451 | // Note on efficiency!
|
---|
| 1452 | // Can be quite optimized using tables, but I do not have time
|
---|
| 1453 | // V.H. 18/11/2001
|
---|
| 1454 |
|
---|
| 1455 | AxisAlignedBox3 a =
|
---|
| 1456 | AxisAlignedBox3(Vector3(center.x - radius, center.y - radius, center.z - radius),
|
---|
| 1457 | Vector3(center.x + radius, center.y + radius, center.z + radius));
|
---|
| 1458 |
|
---|
| 1459 | if (a.Includes(*this))
|
---|
| 1460 | return 1; // cube contains the box
|
---|
| 1461 |
|
---|
| 1462 | if (OverlapS(a,*this))
|
---|
| 1463 | return 0; // cube partially overlap the box
|
---|
| 1464 |
|
---|
| 1465 | return -1; // completely separate
|
---|
| 1466 | }
|
---|
| 1467 |
|
---|
| 1468 | void
|
---|
| 1469 | AxisAlignedBox3::GetSqrDistances(const Vector3 &point,
|
---|
| 1470 | float &minDistance,
|
---|
| 1471 | float &maxDistance
|
---|
| 1472 | ) const
|
---|
| 1473 | {
|
---|
| 1474 |
|
---|
| 1475 |
|
---|
| 1476 | #ifndef __VECTOR_HACK
|
---|
| 1477 | #error "__VECTOR_HACK for Vector3 was not defined"
|
---|
| 1478 | #endif
|
---|
| 1479 |
|
---|
| 1480 | // some overlap is possible, check the distance of vertices
|
---|
| 1481 | float sumMin = 0;
|
---|
| 1482 | float sumMax = 0;
|
---|
| 1483 |
|
---|
| 1484 | // Try to minimize the function of a distance
|
---|
| 1485 | // from the sphere center
|
---|
| 1486 |
|
---|
| 1487 | const float *minp = &(mMin[0]);
|
---|
| 1488 | const float *maxp = &(mMax[0]);
|
---|
| 1489 | const float *pcenter = &(point[0]);
|
---|
| 1490 |
|
---|
| 1491 | // for x-axis
|
---|
| 1492 | for (int i = 0; i < 3; i++, minp++, maxp++, pcenter++) {
|
---|
| 1493 | float minsqr = sqr(*minp - *pcenter);
|
---|
| 1494 | float maxsqr = sqr(*maxp - *pcenter);
|
---|
| 1495 | if (*pcenter < *minp)
|
---|
| 1496 | sumMin += minsqr;
|
---|
| 1497 | else
|
---|
| 1498 | if (*pcenter > *maxp)
|
---|
| 1499 | sumMin += maxsqr;
|
---|
| 1500 | sumMax += (minsqr > maxsqr) ? minsqr : maxsqr;
|
---|
| 1501 | }
|
---|
| 1502 |
|
---|
| 1503 | minDistance = sumMin;
|
---|
| 1504 | maxDistance = sumMax;
|
---|
| 1505 |
|
---|
| 1506 |
|
---|
| 1507 | }
|
---|
| 1508 |
|
---|
| 1509 |
|
---|
[177] | 1510 | int
|
---|
| 1511 | AxisAlignedBox3::Side(const Plane3 &plane) const
|
---|
| 1512 | {
|
---|
| 1513 | Vector3 v;
|
---|
| 1514 | int i, m=3, M=-3, s;
|
---|
| 1515 |
|
---|
| 1516 | for (i=0;i<8;i++) {
|
---|
| 1517 | GetVertex(i, v);
|
---|
| 1518 | if((s = plane.Side(v)) < m)
|
---|
| 1519 | m=s;
|
---|
| 1520 | if(s > M)
|
---|
| 1521 | M=s;
|
---|
| 1522 | if (m && m==-M)
|
---|
| 1523 | return 0;
|
---|
| 1524 | }
|
---|
| 1525 |
|
---|
| 1526 | return (m == M) ? m : m + M;
|
---|
| 1527 | }
|
---|
[191] | 1528 |
|
---|
| 1529 | int
|
---|
| 1530 | AxisAlignedBox3::GetFaceVisibilityMask(const Rectangle3 &rectangle) const
|
---|
| 1531 | {
|
---|
| 1532 | int mask = 0;
|
---|
| 1533 | for (int i=0; i < 4; i++)
|
---|
| 1534 | mask |= GetFaceVisibilityMask(rectangle.mVertices[i]);
|
---|
| 1535 | return mask;
|
---|
| 1536 | }
|
---|
| 1537 |
|
---|
| 1538 | int
|
---|
| 1539 | AxisAlignedBox3::GetFaceVisibilityMask(const Vector3 &position) const {
|
---|
| 1540 |
|
---|
| 1541 | // assume that we are not inside the box
|
---|
| 1542 | int c=0;
|
---|
| 1543 |
|
---|
| 1544 | if (position.x<(mMin.x-Limits::Small))
|
---|
| 1545 | c|=1;
|
---|
| 1546 | else
|
---|
| 1547 | if (position.x>(mMax.x+Limits::Small))
|
---|
| 1548 | c|=2;
|
---|
| 1549 |
|
---|
| 1550 | if (position.y<(mMin.y-Limits::Small))
|
---|
| 1551 | c|=4;
|
---|
| 1552 | else
|
---|
| 1553 | if (position.y>(mMax.y+Limits::Small))
|
---|
| 1554 | c|=8;
|
---|
| 1555 |
|
---|
| 1556 | if (position.z<(mMin.z-Limits::Small))
|
---|
| 1557 | c|=16;
|
---|
| 1558 | else
|
---|
| 1559 | if (position.z>(mMax.z+Limits::Small))
|
---|
| 1560 | c|=32;
|
---|
| 1561 |
|
---|
| 1562 | return c;
|
---|
| 1563 | }
|
---|
| 1564 |
|
---|
| 1565 |
|
---|
| 1566 | Rectangle3
|
---|
| 1567 | AxisAlignedBox3::GetFace(const int face) const
|
---|
| 1568 | {
|
---|
| 1569 | Vector3 v[4];
|
---|
| 1570 | switch (face) {
|
---|
| 1571 |
|
---|
| 1572 | case 0:
|
---|
| 1573 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
| 1574 | v[2].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
| 1575 | v[1].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
| 1576 | v[0].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
| 1577 | break;
|
---|
| 1578 |
|
---|
| 1579 | case 1:
|
---|
| 1580 | v[0].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
| 1581 | v[1].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
| 1582 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
| 1583 | v[3].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
| 1584 | break;
|
---|
| 1585 |
|
---|
| 1586 | case 2:
|
---|
| 1587 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
| 1588 | v[2].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
| 1589 | v[1].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
| 1590 | v[0].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
| 1591 | break;
|
---|
| 1592 |
|
---|
| 1593 | case 3:
|
---|
| 1594 | v[0].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
| 1595 | v[1].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
| 1596 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
| 1597 | v[3].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
| 1598 | break;
|
---|
| 1599 |
|
---|
| 1600 | case 4:
|
---|
| 1601 | v[3].SetValue(mMin.x,mMin.y,mMin.z);
|
---|
| 1602 | v[2].SetValue(mMax.x,mMin.y,mMin.z);
|
---|
| 1603 | v[1].SetValue(mMax.x,mMax.y,mMin.z);
|
---|
| 1604 | v[0].SetValue(mMin.x,mMax.y,mMin.z);
|
---|
| 1605 | break;
|
---|
| 1606 |
|
---|
| 1607 | case 5:
|
---|
| 1608 | v[0].SetValue(mMin.x,mMin.y,mMax.z);
|
---|
| 1609 | v[1].SetValue(mMax.x,mMin.y,mMax.z);
|
---|
| 1610 | v[2].SetValue(mMax.x,mMax.y,mMax.z);
|
---|
| 1611 | v[3].SetValue(mMin.x,mMax.y,mMax.z);
|
---|
| 1612 | break;
|
---|
| 1613 | }
|
---|
| 1614 |
|
---|
| 1615 | return Rectangle3(v[0], v[1], v[2], v[3]);
|
---|
| 1616 | }
|
---|