| 1 | /* $Id$ $Revision$ */ |
| 2 | /* vim:set shiftwidth=4 ts=8: */ |
| 3 | |
| 4 | /************************************************************************* |
| 5 | * Copyright (c) 2011 AT&T Intellectual Property |
| 6 | * All rights reserved. This program and the accompanying materials |
| 7 | * are made available under the terms of the Eclipse Public License v1.0 |
| 8 | * which accompanies this distribution, and is available at |
| 9 | * http://www.eclipse.org/legal/epl-v10.html |
| 10 | * |
| 11 | * Contributors: See CVS logs. Details at http://www.graphviz.org/ |
| 12 | *************************************************************************/ |
| 13 | |
| 14 | /* geometric functions (e.g. on points and boxes) with application to, but |
| 15 | * no specific dependence on graphs */ |
| 16 | |
| 17 | #include "config.h" |
| 18 | |
| 19 | #include "geom.h" |
| 20 | #include "geomprocs.h" |
| 21 | #ifdef _WIN32 |
| 22 | #define inline |
| 23 | #endif |
| 24 | |
| 25 | box mkbox(point p, point q) |
| 26 | { |
| 27 | box r; |
| 28 | |
| 29 | if (p.x < q.x) { |
| 30 | r.LL.x = p.x; |
| 31 | r.UR.x = q.x; |
| 32 | } else { |
| 33 | r.LL.x = q.x; |
| 34 | r.UR.x = p.x; |
| 35 | } |
| 36 | if (p.y < q.y) { |
| 37 | r.LL.y = p.y; |
| 38 | r.UR.y = q.y; |
| 39 | } else { |
| 40 | r.LL.y = q.y; |
| 41 | r.UR.y = p.y; |
| 42 | } |
| 43 | return r; |
| 44 | } |
| 45 | |
| 46 | boxf mkboxf(pointf p, pointf q) |
| 47 | { |
| 48 | boxf r; |
| 49 | |
| 50 | if (p.x < q.x) { |
| 51 | r.LL.x = p.x; |
| 52 | r.UR.x = q.x; |
| 53 | } else { |
| 54 | r.LL.x = q.x; |
| 55 | r.UR.x = p.x; |
| 56 | } |
| 57 | if (p.y < q.y) { |
| 58 | r.LL.y = p.y; |
| 59 | r.UR.y = q.y; |
| 60 | } else { |
| 61 | r.LL.y = q.y; |
| 62 | r.UR.y = p.y; |
| 63 | } |
| 64 | return r; |
| 65 | } |
| 66 | |
| 67 | /* |
| 68 | *-------------------------------------------------------------- |
| 69 | * |
| 70 | * lineToBox -- |
| 71 | * |
| 72 | * Determine whether a line lies entirely inside, entirely |
| 73 | * outside, or overlapping a given rectangular area. |
| 74 | * |
| 75 | * Results: |
| 76 | * -1 is returned if the line given by p and q |
| 77 | * is entirely outside the rectangle given by b. |
| 78 | * 0 is returned if the polygon overlaps the rectangle, and |
| 79 | * 1 is returned if the polygon is entirely inside the rectangle. |
| 80 | * |
| 81 | * Side effects: |
| 82 | * None. |
| 83 | * |
| 84 | *-------------------------------------------------------------- |
| 85 | */ |
| 86 | |
| 87 | /* This code steals liberally from algorithms in tk/generic/tkTrig.c -- jce */ |
| 88 | |
| 89 | int lineToBox(pointf p, pointf q, boxf b) |
| 90 | { |
| 91 | int inside1, inside2; |
| 92 | |
| 93 | /* |
| 94 | * First check the two points individually to see whether they |
| 95 | * are inside the rectangle or not. |
| 96 | */ |
| 97 | |
| 98 | inside1 = (p.x >= b.LL.x) && (p.x <= b.UR.x) |
| 99 | && (p.y >= b.LL.y) && (p.y <= b.UR.y); |
| 100 | inside2 = (q.x >= b.LL.x) && (q.x <= b.UR.x) |
| 101 | && (q.y >= b.LL.y) && (q.y <= b.UR.y); |
| 102 | if (inside1 != inside2) { |
| 103 | return 0; |
| 104 | } |
| 105 | if (inside1 & inside2) { |
| 106 | return 1; |
| 107 | } |
| 108 | |
| 109 | /* |
| 110 | * Both points are outside the rectangle, but still need to check |
| 111 | * for intersections between the line and the rectangle. Horizontal |
| 112 | * and vertical lines are particularly easy, so handle them |
| 113 | * separately. |
| 114 | */ |
| 115 | |
| 116 | if (p.x == q.x) { |
| 117 | /* |
| 118 | * Vertical line. |
| 119 | */ |
| 120 | |
| 121 | if (((p.y >= b.LL.y) ^ (q.y >= b.LL.y)) |
| 122 | && (p.x >= b.LL.x) |
| 123 | && (p.x <= b.UR.x)) { |
| 124 | return 0; |
| 125 | } |
| 126 | } else if (p.y == q.y) { |
| 127 | /* |
| 128 | * Horizontal line. |
| 129 | */ |
| 130 | if (((p.x >= b.LL.x) ^ (q.x >= b.LL.x)) |
| 131 | && (p.y >= b.LL.y) |
| 132 | && (p.y <= b.UR.y)) { |
| 133 | return 0; |
| 134 | } |
| 135 | } else { |
| 136 | double m, x, y, low, high; |
| 137 | |
| 138 | /* |
| 139 | * Diagonal line. Compute slope of line and use |
| 140 | * for intersection checks against each of the |
| 141 | * sides of the rectangle: left, right, bottom, top. |
| 142 | */ |
| 143 | |
| 144 | m = (q.y - p.y)/(q.x - p.x); |
| 145 | if (p.x < q.x) { |
| 146 | low = p.x; high = q.x; |
| 147 | } else { |
| 148 | low = q.x; high = p.x; |
| 149 | } |
| 150 | |
| 151 | /* |
| 152 | * Left edge. |
| 153 | */ |
| 154 | |
| 155 | y = p.y + (b.LL.x - p.x)*m; |
| 156 | if ((b.LL.x >= low) && (b.LL.x <= high) |
| 157 | && (y >= b.LL.y) && (y <= b.UR.y)) { |
| 158 | return 0; |
| 159 | } |
| 160 | |
| 161 | /* |
| 162 | * Right edge. |
| 163 | */ |
| 164 | |
| 165 | y += (b.UR.x - b.LL.x)*m; |
| 166 | if ((y >= b.LL.y) && (y <= b.UR.y) |
| 167 | && (b.UR.x >= low) && (b.UR.x <= high)) { |
| 168 | return 0; |
| 169 | } |
| 170 | |
| 171 | /* |
| 172 | * Bottom edge. |
| 173 | */ |
| 174 | |
| 175 | if (p.y < q.y) { |
| 176 | low = p.y; high = q.y; |
| 177 | } else { |
| 178 | low = q.y; high = p.y; |
| 179 | } |
| 180 | x = p.x + (b.LL.y - p.y)/m; |
| 181 | if ((x >= b.LL.x) && (x <= b.UR.x) |
| 182 | && (b.LL.y >= low) && (b.LL.y <= high)) { |
| 183 | return 0; |
| 184 | } |
| 185 | |
| 186 | /* |
| 187 | * Top edge. |
| 188 | */ |
| 189 | |
| 190 | x += (b.UR.y - b.LL.y)/m; |
| 191 | if ((x >= b.LL.x) && (x <= b.UR.x) |
| 192 | && (b.UR.y >= low) && (b.UR.y <= high)) { |
| 193 | return 0; |
| 194 | } |
| 195 | } |
| 196 | return -1; |
| 197 | } |
| 198 | #ifdef WIN32_STATIC |
| 199 | #define inline |
| 200 | #endif |
| 201 | void rect2poly(pointf *p) |
| 202 | { |
| 203 | p[3].x = p[2].x = p[1].x; |
| 204 | p[2].y = p[1].y; |
| 205 | p[3].y = p[0].y; |
| 206 | p[1].x = p[0].x; |
| 207 | } |
| 208 | |
| 209 | static pointf rotatepf(pointf p, int cwrot) |
| 210 | { |
| 211 | static double sina, cosa; |
| 212 | static int last_cwrot; |
| 213 | pointf P; |
| 214 | |
| 215 | /* cosa is initially wrong for a cwrot of 0 |
| 216 | * this caching only works because we are never called for 0 rotations */ |
| 217 | if (cwrot != last_cwrot) { |
| 218 | sincos(cwrot / (2 * M_PI), &sina, &cosa); |
| 219 | last_cwrot = cwrot; |
| 220 | } |
| 221 | P.x = p.x * cosa - p.y * sina; |
| 222 | P.y = p.y * cosa + p.x * sina; |
| 223 | return P; |
| 224 | } |
| 225 | |
| 226 | static point rotatep(point p, int cwrot) |
| 227 | { |
| 228 | pointf pf; |
| 229 | |
| 230 | P2PF(p, pf); |
| 231 | pf = rotatepf(pf, cwrot); |
| 232 | PF2P(pf, p); |
| 233 | return p; |
| 234 | } |
| 235 | |
| 236 | point cwrotatep(point p, int cwrot) |
| 237 | { |
| 238 | int x = p.x, y = p.y; |
| 239 | switch (cwrot) { |
| 240 | case 0: |
| 241 | break; |
| 242 | case 90: |
| 243 | p.x = y; |
| 244 | p.y = -x; |
| 245 | break; |
| 246 | case 180: |
| 247 | p.x = x; |
| 248 | p.y = -y; |
| 249 | break; |
| 250 | case 270: |
| 251 | p.x = y; |
| 252 | p.y = x; |
| 253 | break; |
| 254 | default: |
| 255 | if (cwrot < 0) |
| 256 | return ccwrotatep(p, -cwrot); |
| 257 | if (cwrot > 360) |
| 258 | return cwrotatep(p, cwrot%360); |
| 259 | return rotatep(p, cwrot); |
| 260 | } |
| 261 | return p; |
| 262 | } |
| 263 | |
| 264 | pointf cwrotatepf(pointf p, int cwrot) |
| 265 | { |
| 266 | double x = p.x, y = p.y; |
| 267 | switch (cwrot) { |
| 268 | case 0: |
| 269 | break; |
| 270 | case 90: |
| 271 | p.x = y; |
| 272 | p.y = -x; |
| 273 | break; |
| 274 | case 180: |
| 275 | p.x = x; |
| 276 | p.y = -y; |
| 277 | break; |
| 278 | case 270: |
| 279 | p.x = y; |
| 280 | p.y = x; |
| 281 | break; |
| 282 | default: |
| 283 | if (cwrot < 0) |
| 284 | return ccwrotatepf(p, -cwrot); |
| 285 | if (cwrot > 360) |
| 286 | return cwrotatepf(p, cwrot%360); |
| 287 | return rotatepf(p, cwrot); |
| 288 | } |
| 289 | return p; |
| 290 | } |
| 291 | |
| 292 | point ccwrotatep(point p, int ccwrot) |
| 293 | { |
| 294 | int x = p.x, y = p.y; |
| 295 | switch (ccwrot) { |
| 296 | case 0: |
| 297 | break; |
| 298 | case 90: |
| 299 | p.x = -y; |
| 300 | p.y = x; |
| 301 | break; |
| 302 | case 180: |
| 303 | p.x = x; |
| 304 | p.y = -y; |
| 305 | break; |
| 306 | case 270: |
| 307 | p.x = y; |
| 308 | p.y = x; |
| 309 | break; |
| 310 | default: |
| 311 | if (ccwrot < 0) |
| 312 | return cwrotatep(p, -ccwrot); |
| 313 | if (ccwrot > 360) |
| 314 | return ccwrotatep(p, ccwrot%360); |
| 315 | return rotatep(p, 360-ccwrot); |
| 316 | } |
| 317 | return p; |
| 318 | } |
| 319 | |
| 320 | pointf ccwrotatepf(pointf p, int ccwrot) |
| 321 | { |
| 322 | double x = p.x, y = p.y; |
| 323 | switch (ccwrot) { |
| 324 | case 0: |
| 325 | break; |
| 326 | case 90: |
| 327 | p.x = -y; |
| 328 | p.y = x; |
| 329 | break; |
| 330 | case 180: |
| 331 | p.x = x; |
| 332 | p.y = -y; |
| 333 | break; |
| 334 | case 270: |
| 335 | p.x = y; |
| 336 | p.y = x; |
| 337 | break; |
| 338 | default: |
| 339 | if (ccwrot < 0) |
| 340 | return cwrotatepf(p, -ccwrot); |
| 341 | if (ccwrot > 360) |
| 342 | return ccwrotatepf(p, ccwrot%360); |
| 343 | return rotatepf(p, 360-ccwrot); |
| 344 | } |
| 345 | return p; |
| 346 | } |
| 347 | |
| 348 | inline box flip_rec_box(box b, point p) |
| 349 | { |
| 350 | box r; |
| 351 | /* flip box */ |
| 352 | r.UR.x = b.UR.y; |
| 353 | r.UR.y = b.UR.x; |
| 354 | r.LL.x = b.LL.y; |
| 355 | r.LL.y = b.LL.x; |
| 356 | /* move box */ |
| 357 | r.LL.x += p.x; |
| 358 | r.LL.y += p.y; |
| 359 | r.UR.x += p.x; |
| 360 | r.UR.y += p.y; |
| 361 | return r; |
| 362 | } |
| 363 | |
| 364 | boxf flip_rec_boxf(boxf b, pointf p) |
| 365 | { |
| 366 | boxf r; |
| 367 | /* flip box */ |
| 368 | r.UR.x = b.UR.y; |
| 369 | r.UR.y = b.UR.x; |
| 370 | r.LL.x = b.LL.y; |
| 371 | r.LL.y = b.LL.x; |
| 372 | /* move box */ |
| 373 | r.LL.x += p.x; |
| 374 | r.LL.y += p.y; |
| 375 | r.UR.x += p.x; |
| 376 | r.UR.y += p.y; |
| 377 | return r; |
| 378 | } |
| 379 | |
| 380 | #ifdef WIN32_STATIC |
| 381 | #undef inline |
| 382 | #endif |
| 383 | |
| 384 | |
| 385 | #define SMALL 0.0000000001 |
| 386 | |
| 387 | /* ptToLine2: |
| 388 | * Return distance from point p to line a-b squared. |
| 389 | */ |
| 390 | double ptToLine2 (pointf a, pointf b, pointf p) |
| 391 | { |
| 392 | double dx = b.x-a.x; |
| 393 | double dy = b.y-a.y; |
| 394 | double a2 = (p.y-a.y)*dx - (p.x-a.x)*dy; |
| 395 | a2 *= a2; /* square - ensures that it is positive */ |
| 396 | if (a2 < SMALL) return 0.; /* avoid 0/0 problems */ |
| 397 | return a2 / (dx*dx + dy*dy); |
| 398 | } |
| 399 | |
| 400 | #define dot(v,w) (v.x*w.x+v.y*w.y) |
| 401 | |
| 402 | /* line_intersect: |
| 403 | * Computes intersection of lines a-b and c-d, returning intersection |
| 404 | * point in *p. |
| 405 | * Returns 0 if no intersection (lines parallel), 1 otherwise. |
| 406 | */ |
| 407 | int line_intersect (pointf a, pointf b, pointf c, pointf d, pointf* p) |
| 408 | { |
| 409 | |
| 410 | pointf mv = sub_pointf(b,a); |
| 411 | pointf lv = sub_pointf(d,c); |
| 412 | pointf ln = perp (lv); |
| 413 | double lc = -dot(ln,c); |
| 414 | double dt = dot(ln,mv); |
| 415 | |
| 416 | if (fabs(dt) < SMALL) return 0; |
| 417 | |
| 418 | *p = sub_pointf(a,scale((dot(ln,a)+lc)/dt,mv)); |
| 419 | return 1; |
| 420 | } |
| 421 | |
| 422 | |