| 1 | /* |
| 2 | * tkTrig.c -- |
| 3 | * |
| 4 | * This file contains a collection of trigonometry utility |
| 5 | * routines that are used by Tk and in particular by the |
| 6 | * canvas code. It also has miscellaneous geometry functions |
| 7 | * used by canvases. |
| 8 | * |
| 9 | * Copyright 1992 Regents of the University of California. |
| 10 | * Permission to use, copy, modify, and distribute this |
| 11 | * software and its documentation for any purpose and without |
| 12 | * fee is hereby granted, provided that the above copyright |
| 13 | * notice appear in all copies. The University of California |
| 14 | * makes no representations about the suitability of this |
| 15 | * software for any purpose. It is provided "as is" without |
| 16 | * express or implied warranty. |
| 17 | */ |
| 18 | |
| 19 | #ifndef lint |
| 20 | static char rcsid[] = "$Header: /user6/ouster/wish/RCS/tkTrig.c,v 1.8 92/08/24 09:24:14 ouster Exp $ SPRITE (Berkeley)"; |
| 21 | #endif |
| 22 | |
| 23 | #include <stdio.h> |
| 24 | #include <math.h> |
| 25 | #include "tkconfig.h" |
| 26 | #include "tkcanvas.h" |
| 27 | |
| 28 | #undef MIN |
| 29 | #define MIN(a,b) (((a) < (b)) ? (a) : (b)) |
| 30 | #undef MAX |
| 31 | #define MAX(a,b) (((a) > (b)) ? (a) : (b)) |
| 32 | #define PI 3.14159265358979323846 |
| 33 | \f |
| 34 | /* |
| 35 | *-------------------------------------------------------------- |
| 36 | * |
| 37 | * TkLineToPoint -- |
| 38 | * |
| 39 | * Compute the distance from a point to a finite line segment. |
| 40 | * |
| 41 | * Results: |
| 42 | * The return value is the distance from the line segment |
| 43 | * whose end-points are *end1Ptr and *end2Ptr to the point |
| 44 | * given by *pointPtr. |
| 45 | * |
| 46 | * Side effects: |
| 47 | * None. |
| 48 | * |
| 49 | *-------------------------------------------------------------- |
| 50 | */ |
| 51 | |
| 52 | double |
| 53 | TkLineToPoint(end1Ptr, end2Ptr, pointPtr) |
| 54 | double end1Ptr[2]; /* Coordinates of first end-point of line. */ |
| 55 | double end2Ptr[2]; /* Coordinates of second end-point of line. */ |
| 56 | double pointPtr[2]; /* Points to coords for point. */ |
| 57 | { |
| 58 | double x, y; |
| 59 | |
| 60 | /* |
| 61 | * Compute the point on the line that is closest to the |
| 62 | * point. This must be done separately for vertical edges, |
| 63 | * horizontal edges, and other edges. |
| 64 | */ |
| 65 | |
| 66 | if (end1Ptr[0] == end2Ptr[0]) { |
| 67 | |
| 68 | /* |
| 69 | * Vertical edge. |
| 70 | */ |
| 71 | |
| 72 | x = end1Ptr[0]; |
| 73 | if (end1Ptr[1] >= end2Ptr[1]) { |
| 74 | y = MIN(end1Ptr[1], pointPtr[1]); |
| 75 | y = MAX(y, end2Ptr[1]); |
| 76 | } else { |
| 77 | y = MIN(end2Ptr[1], pointPtr[1]); |
| 78 | y = MAX(y, end1Ptr[1]); |
| 79 | } |
| 80 | } else if (end1Ptr[1] == end2Ptr[1]) { |
| 81 | |
| 82 | /* |
| 83 | * Horizontal edge. |
| 84 | */ |
| 85 | |
| 86 | y = end1Ptr[1]; |
| 87 | if (end1Ptr[0] >= end2Ptr[0]) { |
| 88 | x = MIN(end1Ptr[0], pointPtr[0]); |
| 89 | x = MAX(x, end2Ptr[0]); |
| 90 | } else { |
| 91 | x = MIN(end2Ptr[0], pointPtr[0]); |
| 92 | x = MAX(x, end1Ptr[0]); |
| 93 | } |
| 94 | } else { |
| 95 | double m1, b1, m2, b2; |
| 96 | |
| 97 | /* |
| 98 | * The edge is neither horizontal nor vertical. Convert the |
| 99 | * edge to a line equation of the form y = m1*x + b1. Then |
| 100 | * compute a line perpendicular to this edge but passing |
| 101 | * through the point, also in the form y = m2*x + b2. |
| 102 | */ |
| 103 | |
| 104 | m1 = (end2Ptr[1] - end1Ptr[1])/(end2Ptr[0] - end1Ptr[0]); |
| 105 | b1 = end1Ptr[1] - m1*end1Ptr[0]; |
| 106 | m2 = -1.0/m1; |
| 107 | b2 = pointPtr[1] - m2*pointPtr[0]; |
| 108 | x = (b2 - b1)/(m1 - m2); |
| 109 | y = m1*x + b1; |
| 110 | if (end1Ptr[0] > end2Ptr[0]) { |
| 111 | if (x > end1Ptr[0]) { |
| 112 | x = end1Ptr[0]; |
| 113 | y = end1Ptr[1]; |
| 114 | } else if (x < end2Ptr[0]) { |
| 115 | x = end2Ptr[0]; |
| 116 | y = end2Ptr[1]; |
| 117 | } |
| 118 | } else { |
| 119 | if (x > end2Ptr[0]) { |
| 120 | x = end2Ptr[0]; |
| 121 | y = end2Ptr[1]; |
| 122 | } else if (x < end1Ptr[0]) { |
| 123 | x = end1Ptr[0]; |
| 124 | y = end1Ptr[1]; |
| 125 | } |
| 126 | } |
| 127 | } |
| 128 | |
| 129 | /* |
| 130 | * Compute the distance to the closest point. |
| 131 | */ |
| 132 | |
| 133 | return hypot(pointPtr[0] - x, pointPtr[1] - y); |
| 134 | } |
| 135 | \f |
| 136 | /* |
| 137 | *-------------------------------------------------------------- |
| 138 | * |
| 139 | * TkLineToArea -- |
| 140 | * |
| 141 | * Determine whether a line lies entirely inside, entirely |
| 142 | * outside, or overlapping a given rectangular area. |
| 143 | * |
| 144 | * Results: |
| 145 | * -1 is returned if the line given by end1Ptr and end2Ptr |
| 146 | * is entirely outside the rectangle given by rectPtr. 0 is |
| 147 | * returned if the polygon overlaps the rectangle, and 1 is |
| 148 | * returned if the polygon is entirely inside the rectangle. |
| 149 | * |
| 150 | * Side effects: |
| 151 | * None. |
| 152 | * |
| 153 | *-------------------------------------------------------------- |
| 154 | */ |
| 155 | |
| 156 | int |
| 157 | TkLineToArea(end1Ptr, end2Ptr, rectPtr) |
| 158 | double end1Ptr[2]; /* X and y coordinates for one endpoint |
| 159 | * of line. */ |
| 160 | double end2Ptr[2]; /* X and y coordinates for other endpoint |
| 161 | * of line. */ |
| 162 | double rectPtr[4]; /* Points to coords for rectangle, in the |
| 163 | * order x1, y1, x2, y2. X1 must be no |
| 164 | * larger than x2, and y1 no larger than y2. */ |
| 165 | { |
| 166 | int inside1, inside2; |
| 167 | |
| 168 | /* |
| 169 | * First check the two points individually to see whether they |
| 170 | * are inside the rectangle or not. |
| 171 | */ |
| 172 | |
| 173 | inside1 = (end1Ptr[0] >= rectPtr[0]) && (end1Ptr[0] <= rectPtr[2]) |
| 174 | && (end1Ptr[1] >= rectPtr[1]) && (end1Ptr[1] <= rectPtr[3]); |
| 175 | inside2 = (end2Ptr[0] >= rectPtr[0]) && (end2Ptr[0] <= rectPtr[2]) |
| 176 | && (end2Ptr[1] >= rectPtr[1]) && (end2Ptr[1] <= rectPtr[3]); |
| 177 | if (inside1 != inside2) { |
| 178 | return 0; |
| 179 | } |
| 180 | if (inside1 & inside2) { |
| 181 | return 1; |
| 182 | } |
| 183 | |
| 184 | /* |
| 185 | * Both points are outside the rectangle, but still need to check |
| 186 | * for intersections between the line and the rectangle. Horizontal |
| 187 | * and vertical lines are particularly easy, so handle them |
| 188 | * separately. |
| 189 | */ |
| 190 | |
| 191 | if (end1Ptr[0] == end2Ptr[0]) { |
| 192 | /* |
| 193 | * Vertical line. |
| 194 | */ |
| 195 | |
| 196 | if (((end1Ptr[1] >= rectPtr[1]) ^ (end2Ptr[1] >= rectPtr[1])) |
| 197 | && (end1Ptr[0] >= rectPtr[0]) |
| 198 | && (end1Ptr[0] <= rectPtr[2])) { |
| 199 | return 0; |
| 200 | } |
| 201 | } else if (end1Ptr[1] == end2Ptr[1]) { |
| 202 | /* |
| 203 | * Horizontal line. |
| 204 | */ |
| 205 | |
| 206 | if (((end1Ptr[0] >= rectPtr[0]) ^ (end2Ptr[0] >= rectPtr[0])) |
| 207 | && (end1Ptr[1] >= rectPtr[1]) |
| 208 | && (end1Ptr[1] <= rectPtr[3])) { |
| 209 | return 0; |
| 210 | } |
| 211 | } else { |
| 212 | double m, x, y, low, high; |
| 213 | |
| 214 | /* |
| 215 | * Diagonal line. Compute slope of line and use |
| 216 | * for intersection checks against each of the |
| 217 | * sides of the rectangle: left, right, bottom, top. |
| 218 | */ |
| 219 | |
| 220 | m = (end2Ptr[1] - end1Ptr[1])/(end2Ptr[0] - end1Ptr[0]); |
| 221 | if (end1Ptr[0] < end2Ptr[0]) { |
| 222 | low = end1Ptr[0]; high = end2Ptr[0]; |
| 223 | } else { |
| 224 | low = end2Ptr[0]; high = end1Ptr[0]; |
| 225 | } |
| 226 | |
| 227 | /* |
| 228 | * Left edge. |
| 229 | */ |
| 230 | |
| 231 | y = end1Ptr[1] + (rectPtr[0] - end1Ptr[0])*m; |
| 232 | if ((rectPtr[0] >= low) && (rectPtr[0] <= high) |
| 233 | && (y >= rectPtr[1]) && (y <= rectPtr[3])) { |
| 234 | return 0; |
| 235 | } |
| 236 | |
| 237 | /* |
| 238 | * Right edge. |
| 239 | */ |
| 240 | |
| 241 | y += (rectPtr[2] - rectPtr[0])*m; |
| 242 | if ((y >= rectPtr[1]) && (y <= rectPtr[3]) |
| 243 | && (rectPtr[2] >= low) && (rectPtr[2] <= high)) { |
| 244 | return 0; |
| 245 | } |
| 246 | |
| 247 | /* |
| 248 | * Bottom edge. |
| 249 | */ |
| 250 | |
| 251 | if (end1Ptr[1] < end2Ptr[1]) { |
| 252 | low = end1Ptr[1]; high = end2Ptr[1]; |
| 253 | } else { |
| 254 | low = end2Ptr[1]; high = end1Ptr[1]; |
| 255 | } |
| 256 | x = end1Ptr[0] + (rectPtr[1] - end1Ptr[1])/m; |
| 257 | if ((x >= rectPtr[0]) && (x <= rectPtr[2]) |
| 258 | && (rectPtr[1] >= low) && (rectPtr[1] <= high)) { |
| 259 | return 0; |
| 260 | } |
| 261 | |
| 262 | /* |
| 263 | * Top edge. |
| 264 | */ |
| 265 | |
| 266 | x += (rectPtr[3] - rectPtr[1])/m; |
| 267 | if ((x >= rectPtr[0]) && (x <= rectPtr[2]) |
| 268 | && (rectPtr[3] >= low) && (rectPtr[3] <= high)) { |
| 269 | return 0; |
| 270 | } |
| 271 | } |
| 272 | return -1; |
| 273 | } |
| 274 | \f |
| 275 | /* |
| 276 | *-------------------------------------------------------------- |
| 277 | * |
| 278 | * TkPolygonToPoint -- |
| 279 | * |
| 280 | * Compute the distance from a point to a polygon. |
| 281 | * |
| 282 | * Results: |
| 283 | * The return value is 0.0 if the point referred to by |
| 284 | * pointPtr is within the polygon referred to by polyPtr |
| 285 | * and numPoints. Otherwise the return value is the |
| 286 | * distance of the point from the polygon. |
| 287 | * |
| 288 | * Side effects: |
| 289 | * None. |
| 290 | * |
| 291 | *-------------------------------------------------------------- |
| 292 | */ |
| 293 | |
| 294 | double |
| 295 | TkPolygonToPoint(polyPtr, numPoints, pointPtr) |
| 296 | double *polyPtr; /* Points to an array coordinates for |
| 297 | * closed polygon: x0, y0, x1, y1, ... |
| 298 | * The polygon may be self-intersecting. */ |
| 299 | int numPoints; /* Total number of points at *polyPtr. */ |
| 300 | double *pointPtr; /* Points to coords for point. */ |
| 301 | { |
| 302 | double bestDist; /* Closest distance between point and |
| 303 | * any edge in polygon. */ |
| 304 | int intersections; /* Number of edges in the polygon that |
| 305 | * intersect a ray extending vertically |
| 306 | * upwards from the point to infinity. */ |
| 307 | int count; |
| 308 | register double *pPtr; |
| 309 | |
| 310 | /* |
| 311 | * Iterate through all of the edges in the polygon, updating |
| 312 | * bestDist and intersections. |
| 313 | * |
| 314 | * TRICKY POINT: when computing intersections, include left |
| 315 | * x-coordinate of line within its range, but not y-coordinate. |
| 316 | * Otherwise if the point lies exactly below a vertex we'll |
| 317 | * count it as two intersections. |
| 318 | */ |
| 319 | |
| 320 | bestDist = 1.0e40; |
| 321 | intersections = 0; |
| 322 | |
| 323 | for (count = numPoints, pPtr = polyPtr; count > 1; count--, pPtr += 2) { |
| 324 | double x, y, dist; |
| 325 | |
| 326 | /* |
| 327 | * Compute the point on the current edge closest to the point |
| 328 | * and update the intersection count. This must be done |
| 329 | * separately for vertical edges, horizontal edges, and |
| 330 | * other edges. |
| 331 | */ |
| 332 | |
| 333 | if (pPtr[2] == pPtr[0]) { |
| 334 | |
| 335 | /* |
| 336 | * Vertical edge. |
| 337 | */ |
| 338 | |
| 339 | x = pPtr[0]; |
| 340 | if (pPtr[1] >= pPtr[3]) { |
| 341 | y = MIN(pPtr[1], pointPtr[1]); |
| 342 | y = MAX(y, pPtr[3]); |
| 343 | } else { |
| 344 | y = MIN(pPtr[3], pointPtr[1]); |
| 345 | y = MAX(y, pPtr[1]); |
| 346 | } |
| 347 | } else if (pPtr[3] == pPtr[1]) { |
| 348 | |
| 349 | /* |
| 350 | * Horizontal edge. |
| 351 | */ |
| 352 | |
| 353 | y = pPtr[1]; |
| 354 | if (pPtr[0] >= pPtr[2]) { |
| 355 | x = MIN(pPtr[0], pointPtr[0]); |
| 356 | x = MAX(x, pPtr[2]); |
| 357 | if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[0]) |
| 358 | && (pointPtr[0] >= pPtr[2])) { |
| 359 | intersections++; |
| 360 | } |
| 361 | } else { |
| 362 | x = MIN(pPtr[2], pointPtr[0]); |
| 363 | x = MAX(x, pPtr[0]); |
| 364 | if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[2]) |
| 365 | && (pointPtr[0] >= pPtr[0])) { |
| 366 | intersections++; |
| 367 | } |
| 368 | } |
| 369 | } else { |
| 370 | double m1, b1, m2, b2; |
| 371 | int lower; /* Non-zero means point below line. */ |
| 372 | |
| 373 | /* |
| 374 | * The edge is neither horizontal nor vertical. Convert the |
| 375 | * edge to a line equation of the form y = m1*x + b1. Then |
| 376 | * compute a line perpendicular to this edge but passing |
| 377 | * through the point, also in the form y = m2*x + b2. |
| 378 | */ |
| 379 | |
| 380 | m1 = (pPtr[3] - pPtr[1])/(pPtr[2] - pPtr[0]); |
| 381 | b1 = pPtr[1] - m1*pPtr[0]; |
| 382 | m2 = -1.0/m1; |
| 383 | b2 = pointPtr[1] - m2*pointPtr[0]; |
| 384 | x = (b2 - b1)/(m1 - m2); |
| 385 | y = m1*x + b1; |
| 386 | if (pPtr[0] > pPtr[2]) { |
| 387 | if (x > pPtr[0]) { |
| 388 | x = pPtr[0]; |
| 389 | y = pPtr[1]; |
| 390 | } else if (x < pPtr[2]) { |
| 391 | x = pPtr[2]; |
| 392 | y = pPtr[3]; |
| 393 | } |
| 394 | } else { |
| 395 | if (x > pPtr[2]) { |
| 396 | x = pPtr[2]; |
| 397 | y = pPtr[3]; |
| 398 | } else if (x < pPtr[0]) { |
| 399 | x = pPtr[0]; |
| 400 | y = pPtr[1]; |
| 401 | } |
| 402 | } |
| 403 | lower = (m1*pointPtr[0] + b1) > pointPtr[1]; |
| 404 | if (lower && (pointPtr[0] >= MIN(pPtr[0], pPtr[2])) |
| 405 | && (pointPtr[0] < MAX(pPtr[0], pPtr[2]))) { |
| 406 | intersections++; |
| 407 | } |
| 408 | } |
| 409 | |
| 410 | /* |
| 411 | * Compute the distance to the closest point, and see if that |
| 412 | * is the best distance seen so far. |
| 413 | */ |
| 414 | |
| 415 | dist = hypot(pointPtr[0] - x, pointPtr[1] - y); |
| 416 | if (dist < bestDist) { |
| 417 | bestDist = dist; |
| 418 | } |
| 419 | } |
| 420 | |
| 421 | /* |
| 422 | * We've processed all of the points. If the number of intersections |
| 423 | * is odd, the point is inside the polygon. |
| 424 | */ |
| 425 | |
| 426 | if (intersections & 0x1) { |
| 427 | return 0.0; |
| 428 | } |
| 429 | return bestDist; |
| 430 | } |
| 431 | \f |
| 432 | /* |
| 433 | *-------------------------------------------------------------- |
| 434 | * |
| 435 | * TkPolygonToArea -- |
| 436 | * |
| 437 | * Determine whether a polygon lies entirely inside, entirely |
| 438 | * outside, or overlapping a given rectangular area. |
| 439 | * |
| 440 | * Results: |
| 441 | * -1 is returned if the polygon given by polyPtr and numPoints |
| 442 | * is entirely outside the rectangle given by rectPtr. 0 is |
| 443 | * returned if the polygon overlaps the rectangle, and 1 is |
| 444 | * returned if the polygon is entirely inside the rectangle. |
| 445 | * |
| 446 | * Side effects: |
| 447 | * None. |
| 448 | * |
| 449 | *-------------------------------------------------------------- |
| 450 | */ |
| 451 | |
| 452 | int |
| 453 | TkPolygonToArea(polyPtr, numPoints, rectPtr) |
| 454 | double *polyPtr; /* Points to an array coordinates for |
| 455 | * closed polygon: x0, y0, x1, y1, ... |
| 456 | * The polygon may be self-intersecting. */ |
| 457 | int numPoints; /* Total number of points at *polyPtr. */ |
| 458 | register double *rectPtr; /* Points to coords for rectangle, in the |
| 459 | * order x1, y1, x2, y2. X1 and y1 must |
| 460 | * be lower-left corner. */ |
| 461 | { |
| 462 | int state; /* State of all edges seen so far (-1 means |
| 463 | * outside, 1 means inside, won't ever be |
| 464 | * 0). */ |
| 465 | int count; |
| 466 | register double *pPtr; |
| 467 | |
| 468 | /* |
| 469 | * Iterate over all of the edges of the polygon and test them |
| 470 | * against the rectangle. Can quit as soon as the state becomes |
| 471 | * "intersecting". |
| 472 | */ |
| 473 | |
| 474 | state = TkLineToArea(polyPtr, polyPtr+2, rectPtr); |
| 475 | if (state == 0) { |
| 476 | return 0; |
| 477 | } |
| 478 | for (pPtr = polyPtr+2, count = numPoints-1; count >= 2; |
| 479 | pPtr += 2, count--) { |
| 480 | if (TkLineToArea(pPtr, pPtr+2, rectPtr) != state) { |
| 481 | return 0; |
| 482 | } |
| 483 | } |
| 484 | |
| 485 | /* |
| 486 | * If all of the edges were inside the rectangle we're done. |
| 487 | * If all of the edges were outside, then the rectangle could |
| 488 | * still intersect the polygon (if it's entirely enclosed). |
| 489 | * Call TkPolygonToPoint to figure this out. |
| 490 | */ |
| 491 | |
| 492 | if (state == 1) { |
| 493 | return 1; |
| 494 | } |
| 495 | if (TkPolygonToPoint(polyPtr, numPoints, rectPtr) == 0.0) { |
| 496 | return 0; |
| 497 | } |
| 498 | return -1; |
| 499 | } |
| 500 | \f |
| 501 | /* |
| 502 | *-------------------------------------------------------------- |
| 503 | * |
| 504 | * TkOvalToPoint -- |
| 505 | * |
| 506 | * Computes the distance from a given point to a given |
| 507 | * oval, in canvas units. |
| 508 | * |
| 509 | * Results: |
| 510 | * The return value is 0 if the point given by *pointPtr is |
| 511 | * inside the oval. If the point isn't inside the |
| 512 | * oval then the return value is approximately the distance |
| 513 | * from the point to the oval. If the oval is filled, then |
| 514 | * anywhere in the interior is considered "inside"; if |
| 515 | * the oval isn't filled, then "inside" means only the area |
| 516 | * occupied by the outline. |
| 517 | * |
| 518 | * Side effects: |
| 519 | * None. |
| 520 | * |
| 521 | *-------------------------------------------------------------- |
| 522 | */ |
| 523 | |
| 524 | /* ARGSUSED */ |
| 525 | double |
| 526 | TkOvalToPoint(ovalPtr, width, filled, pointPtr) |
| 527 | double ovalPtr[4]; /* Pointer to array of four coordinates |
| 528 | * (x1, y1, x2, y2) defining oval's bounding |
| 529 | * box. */ |
| 530 | double width; /* Width of outline for oval. */ |
| 531 | int filled; /* Non-zero means oval should be treated as |
| 532 | * filled; zero means only consider outline. */ |
| 533 | double pointPtr[2]; /* Coordinates of point. */ |
| 534 | { |
| 535 | double xDelta, yDelta, scaledDistance, distToOutline, distToCenter; |
| 536 | |
| 537 | /* |
| 538 | * Compute the distance between the center of the oval and the |
| 539 | * point in question, using a coordinate system where the oval |
| 540 | * has been transformed to a circle with unit radius. |
| 541 | */ |
| 542 | |
| 543 | xDelta = (pointPtr[0] - (ovalPtr[0] + ovalPtr[2])/2.0); |
| 544 | yDelta = (pointPtr[1] - (ovalPtr[1] + ovalPtr[3])/2.0); |
| 545 | distToCenter = hypot(xDelta, yDelta); |
| 546 | scaledDistance = hypot(xDelta / ((ovalPtr[2] + width - ovalPtr[0])/2.0), |
| 547 | yDelta / ((ovalPtr[3] + width - ovalPtr[1])/2.0)); |
| 548 | |
| 549 | |
| 550 | /* |
| 551 | * If the scaled distance is greater than 1 then it means no |
| 552 | * hit. Compute the distance from the point to the edge of |
| 553 | * the circle, then scale this distance back to the original |
| 554 | * coordinate system. |
| 555 | * |
| 556 | * Note: this distance isn't completely accurate. It's only |
| 557 | * an approximation, and it can overestimate the correct |
| 558 | * distance when the oval is eccentric. |
| 559 | */ |
| 560 | |
| 561 | if (scaledDistance > 1.0) { |
| 562 | return (distToCenter/scaledDistance) * (scaledDistance - 1.0); |
| 563 | } |
| 564 | |
| 565 | /* |
| 566 | * Scaled distance less than 1 means the point is inside the |
| 567 | * outer edge of the oval. If this is a filled oval, then we |
| 568 | * have a hit. Otherwise, do the same computation as above |
| 569 | * (scale back to original coordinate system), but also check |
| 570 | * to see if the point is within the width of the outline. |
| 571 | */ |
| 572 | |
| 573 | if (filled) { |
| 574 | return 0.0; |
| 575 | } |
| 576 | distToOutline = (distToCenter/scaledDistance) * (1.0 - scaledDistance) |
| 577 | - width; |
| 578 | if (distToOutline < 0.0) { |
| 579 | return 0.0; |
| 580 | } |
| 581 | return distToOutline; |
| 582 | } |
| 583 | \f |
| 584 | /* |
| 585 | *-------------------------------------------------------------- |
| 586 | * |
| 587 | * TkOvalToArea -- |
| 588 | * |
| 589 | * Determine whether an oval lies entirely inside, entirely |
| 590 | * outside, or overlapping a given rectangular area. |
| 591 | * |
| 592 | * Results: |
| 593 | * -1 is returned if the oval described by ovalPtr is entirely |
| 594 | * outside the rectangle given by rectPtr. 0 is returned if the |
| 595 | * oval overlaps the rectangle, and 1 is returned if the oval |
| 596 | * is entirely inside the rectangle. |
| 597 | * |
| 598 | * Side effects: |
| 599 | * None. |
| 600 | * |
| 601 | *-------------------------------------------------------------- |
| 602 | */ |
| 603 | |
| 604 | int |
| 605 | TkOvalToArea(ovalPtr, rectPtr) |
| 606 | register double *ovalPtr; /* Points to coordinates definining the |
| 607 | * bounding rectangle for the oval: x1, y1, |
| 608 | * x2, y2. X1 must be less than x2 and y1 |
| 609 | * less than y2. */ |
| 610 | register double *rectPtr; /* Points to coords for rectangle, in the |
| 611 | * order x1, y1, x2, y2. X1 and y1 must |
| 612 | * be lower-left corner. */ |
| 613 | { |
| 614 | double centerX, centerY, radX, radY, deltaX, deltaY; |
| 615 | |
| 616 | /* |
| 617 | * First, see if oval is entirely inside rectangle or entirely |
| 618 | * outside rectangle. |
| 619 | */ |
| 620 | |
| 621 | if ((rectPtr[0] <= ovalPtr[0]) && (rectPtr[2] >= ovalPtr[2]) |
| 622 | && (rectPtr[1] <= ovalPtr[1]) && (rectPtr[3] >= ovalPtr[3])) { |
| 623 | return 1; |
| 624 | } |
| 625 | if ((rectPtr[2] < ovalPtr[0]) || (rectPtr[0] > ovalPtr[2]) |
| 626 | || (rectPtr[3] < ovalPtr[1]) || (rectPtr[1] > ovalPtr[3])) { |
| 627 | return -1; |
| 628 | } |
| 629 | |
| 630 | /* |
| 631 | * Next, go through the rectangle side by side. For each side |
| 632 | * of the rectangle, find the point on the side that is closest |
| 633 | * to the oval's center, and see if that point is inside the |
| 634 | * oval. If at least one such point is inside the oval, then |
| 635 | * the rectangle intersects the oval. |
| 636 | */ |
| 637 | |
| 638 | centerX = (ovalPtr[0] + ovalPtr[2])/2; |
| 639 | centerY = (ovalPtr[1] + ovalPtr[3])/2; |
| 640 | radX = (ovalPtr[2] - ovalPtr[0])/2; |
| 641 | radY = (ovalPtr[3] - ovalPtr[1])/2; |
| 642 | |
| 643 | deltaY = rectPtr[1] - centerY; |
| 644 | if (deltaY < 0.0) { |
| 645 | deltaY = centerY - rectPtr[3]; |
| 646 | if (deltaY < 0.0) { |
| 647 | deltaY = 0; |
| 648 | } |
| 649 | } |
| 650 | deltaY /= radY; |
| 651 | deltaY *= deltaY; |
| 652 | |
| 653 | /* |
| 654 | * Left side: |
| 655 | */ |
| 656 | |
| 657 | deltaX = (rectPtr[0] - centerX)/radX; |
| 658 | deltaX *= deltaX; |
| 659 | if ((deltaX + deltaY) <= 1.0) { |
| 660 | return 0; |
| 661 | } |
| 662 | |
| 663 | /* |
| 664 | * Right side: |
| 665 | */ |
| 666 | |
| 667 | deltaX = (rectPtr[2] - centerX)/radX; |
| 668 | deltaX *= deltaX; |
| 669 | if ((deltaX + deltaY) <= 1.0) { |
| 670 | return 0; |
| 671 | } |
| 672 | |
| 673 | deltaX = rectPtr[0] - centerX; |
| 674 | if (deltaX < 0.0) { |
| 675 | deltaX = centerX - rectPtr[2]; |
| 676 | if (deltaX < 0.0) { |
| 677 | deltaX = 0; |
| 678 | } |
| 679 | } |
| 680 | deltaX /= radX; |
| 681 | deltaX *= deltaX; |
| 682 | |
| 683 | /* |
| 684 | * Bottom side: |
| 685 | */ |
| 686 | |
| 687 | deltaY = (rectPtr[1] - centerY)/radY; |
| 688 | deltaY *= deltaY; |
| 689 | if ((deltaX + deltaY) < 1.0) { |
| 690 | return 0; |
| 691 | } |
| 692 | |
| 693 | /* |
| 694 | * Top side: |
| 695 | */ |
| 696 | |
| 697 | deltaY = (rectPtr[3] - centerY)/radY; |
| 698 | deltaY *= deltaY; |
| 699 | if ((deltaX + deltaY) < 1.0) { |
| 700 | return 0; |
| 701 | } |
| 702 | |
| 703 | return -1; |
| 704 | } |
| 705 | \f |
| 706 | /* |
| 707 | *-------------------------------------------------------------- |
| 708 | * |
| 709 | * TkIncludePoint -- |
| 710 | * |
| 711 | * Given a point and a generic canvas item header, expand |
| 712 | * the item's bounding box if needed to include the point. |
| 713 | * |
| 714 | * Results: |
| 715 | * None. |
| 716 | * |
| 717 | * Side effects: |
| 718 | * The boudn. |
| 719 | * |
| 720 | *-------------------------------------------------------------- |
| 721 | */ |
| 722 | |
| 723 | /* ARGSUSED */ |
| 724 | void |
| 725 | TkIncludePoint(canvasPtr, itemPtr, pointPtr) |
| 726 | Tk_Canvas *canvasPtr; /* Canvas containing item. */ |
| 727 | register Tk_Item *itemPtr; /* Item whose bounding box is |
| 728 | * being calculated. */ |
| 729 | double *pointPtr; /* Address of two doubles giving |
| 730 | * x and y coordinates of point. */ |
| 731 | { |
| 732 | int tmp; |
| 733 | |
| 734 | tmp = pointPtr[0] + 0.5; |
| 735 | if (tmp < itemPtr->x1) { |
| 736 | itemPtr->x1 = tmp; |
| 737 | } |
| 738 | if (tmp > itemPtr->x2) { |
| 739 | itemPtr->x2 = tmp; |
| 740 | } |
| 741 | tmp = pointPtr[1] + 0.5; |
| 742 | if (tmp < itemPtr->y1) { |
| 743 | itemPtr->y1 = tmp; |
| 744 | } |
| 745 | if (tmp > itemPtr->y2) { |
| 746 | itemPtr->y2 = tmp; |
| 747 | } |
| 748 | } |
| 749 | \f |
| 750 | /* |
| 751 | *-------------------------------------------------------------- |
| 752 | * |
| 753 | * TkBezierScreenPoints -- |
| 754 | * |
| 755 | * Given four control points, create a larger set of XPoints |
| 756 | * for a Bezier spline based on the points. |
| 757 | * |
| 758 | * Results: |
| 759 | * The array at *xPointPtr gets filled in with numSteps XPoints |
| 760 | * corresponding to the Bezier spline defined by the four |
| 761 | * control points. Note: no output point is generated for the |
| 762 | * first input point, but an output point *is* generated for |
| 763 | * the last input point. |
| 764 | * |
| 765 | * Side effects: |
| 766 | * None. |
| 767 | * |
| 768 | *-------------------------------------------------------------- |
| 769 | */ |
| 770 | |
| 771 | void |
| 772 | TkBezierScreenPoints(canvasPtr, control, numSteps, xPointPtr) |
| 773 | Tk_Canvas *canvasPtr; /* Canvas in which curve is to be |
| 774 | * drawn. */ |
| 775 | double control[]; /* Array of coordinates for four |
| 776 | * control points: x0, y0, x1, y1, |
| 777 | * ... x3 y3. */ |
| 778 | int numSteps; /* Number of curve points to |
| 779 | * generate. */ |
| 780 | register XPoint *xPointPtr; /* Where to put new points. */ |
| 781 | { |
| 782 | int i; |
| 783 | double u, u2, u3, t, t2, t3; |
| 784 | |
| 785 | for (i = 1; i <= numSteps; i++, xPointPtr++) { |
| 786 | t = ((double) i)/((double) numSteps); |
| 787 | t2 = t*t; |
| 788 | t3 = t2*t; |
| 789 | u = 1.0 - t; |
| 790 | u2 = u*u; |
| 791 | u3 = u2*u; |
| 792 | xPointPtr->x = SCREEN_X(canvasPtr, (control[0]*u3 |
| 793 | + 3.0 * (control[2]*t*u2 + control[4]*t2*u) + control[6]*t3)); |
| 794 | xPointPtr->y = SCREEN_Y(canvasPtr, (control[1]*u3 |
| 795 | + 3.0 * (control[3]*t*u2 + control[5]*t2*u) + control[7]*t3)); |
| 796 | } |
| 797 | } |
| 798 | \f |
| 799 | /* |
| 800 | *-------------------------------------------------------------- |
| 801 | * |
| 802 | * TkBezierPoints -- |
| 803 | * |
| 804 | * Given four control points, create a larger set of points |
| 805 | * for a Bezier spline based on the points. |
| 806 | * |
| 807 | * Results: |
| 808 | * The array at *coordPtr gets filled in with 2*numSteps |
| 809 | * coordinates, which correspond to the Bezier spline defined |
| 810 | * by the four control points. Note: no output point is |
| 811 | * generated for the first input point, but an output point |
| 812 | * *is* generated for the last input point. |
| 813 | * |
| 814 | * Side effects: |
| 815 | * None. |
| 816 | * |
| 817 | *-------------------------------------------------------------- |
| 818 | */ |
| 819 | |
| 820 | void |
| 821 | TkBezierPoints(control, numSteps, coordPtr) |
| 822 | double control[]; /* Array of coordinates for four |
| 823 | * control points: x0, y0, x1, y1, |
| 824 | * ... x3 y3. */ |
| 825 | int numSteps; /* Number of curve points to |
| 826 | * generate. */ |
| 827 | register double *coordPtr; /* Where to put new points. */ |
| 828 | { |
| 829 | int i; |
| 830 | double u, u2, u3, t, t2, t3; |
| 831 | |
| 832 | for (i = 1; i <= numSteps; i++, coordPtr += 2) { |
| 833 | t = ((double) i)/((double) numSteps); |
| 834 | t2 = t*t; |
| 835 | t3 = t2*t; |
| 836 | u = 1.0 - t; |
| 837 | u2 = u*u; |
| 838 | u3 = u2*u; |
| 839 | coordPtr[0] = control[0]*u3 |
| 840 | + 3.0 * (control[2]*t*u2 + control[4]*t2*u) + control[6]*t3; |
| 841 | coordPtr[1] = control[1]*u3 |
| 842 | + 3.0 * (control[3]*t*u2 + control[5]*t2*u) + control[7]*t3; |
| 843 | } |
| 844 | } |
| 845 | \f |
| 846 | /* |
| 847 | *-------------------------------------------------------------- |
| 848 | * |
| 849 | * TkMakeBezierCurve -- |
| 850 | * |
| 851 | * Given a set of points, create a new set of points that |
| 852 | * fit Bezier splines to the line segments connecting the |
| 853 | * original points. Produces output points in either of two |
| 854 | * forms. |
| 855 | * |
| 856 | * Results: |
| 857 | * Either or both of the xPoints or dblPoints arrays are filled |
| 858 | * in. The return value is the number of points placed in the |
| 859 | * arrays. Note: if the first and last points are the same, then |
| 860 | * a closed curve is generated. |
| 861 | * |
| 862 | * Side effects: |
| 863 | * None. |
| 864 | * |
| 865 | *-------------------------------------------------------------- |
| 866 | */ |
| 867 | |
| 868 | int |
| 869 | TkMakeBezierCurve(canvasPtr, pointPtr, numPoints, numSteps, xPoints, dblPoints) |
| 870 | Tk_Canvas *canvasPtr; /* Canvas in which curve is to be |
| 871 | * drawn. */ |
| 872 | double *pointPtr; /* Array of input coordinates: x0, |
| 873 | * y0, x1, y1, etc.. */ |
| 874 | int numPoints; /* Number of points at pointPtr. */ |
| 875 | int numSteps; /* Number of steps to use for each |
| 876 | * spline segments (determines |
| 877 | * smoothness of curve). */ |
| 878 | XPoint xPoints[]; /* Array of XPoints to fill in (e.g. |
| 879 | * for display. NULL means don't |
| 880 | * fill in any XPoints. */ |
| 881 | double dblPoints[]; /* Array of points to fill in as |
| 882 | * doubles, in the form x0, y0, |
| 883 | * x1, y1, .... NULL means don't |
| 884 | * fill in anything in this form. |
| 885 | * Caller must make sure that this |
| 886 | * array has enough space. */ |
| 887 | { |
| 888 | int closed, outputPoints, i; |
| 889 | int numCoords = numPoints*2; |
| 890 | double control[8]; |
| 891 | |
| 892 | /* |
| 893 | * If the curve is a closed one then generate a special spline |
| 894 | * that spans the last points and the first ones. Otherwise |
| 895 | * just put the first point into the output. |
| 896 | */ |
| 897 | |
| 898 | outputPoints = 0; |
| 899 | if ((pointPtr[0] == pointPtr[numCoords-2]) |
| 900 | && (pointPtr[1] == pointPtr[numCoords-1])) { |
| 901 | closed = 1; |
| 902 | control[0] = 0.5*pointPtr[numCoords-4] + 0.5*pointPtr[0]; |
| 903 | control[1] = 0.5*pointPtr[numCoords-3] + 0.5*pointPtr[1]; |
| 904 | control[2] = 0.167*pointPtr[numCoords-4] + 0.833*pointPtr[0]; |
| 905 | control[3] = 0.167*pointPtr[numCoords-3] + 0.833*pointPtr[1]; |
| 906 | control[4] = 0.833*pointPtr[0] + 0.167*pointPtr[2]; |
| 907 | control[5] = 0.833*pointPtr[1] + 0.167*pointPtr[3]; |
| 908 | control[6] = 0.5*pointPtr[0] + 0.5*pointPtr[2]; |
| 909 | control[7] = 0.5*pointPtr[1] + 0.5*pointPtr[3]; |
| 910 | if (xPoints != NULL) { |
| 911 | xPoints->x = SCREEN_X(canvasPtr, control[0]); |
| 912 | xPoints->y = SCREEN_Y(canvasPtr, control[1]); |
| 913 | TkBezierScreenPoints(canvasPtr, control, numSteps, xPoints+1); |
| 914 | xPoints += numSteps+1; |
| 915 | } |
| 916 | if (dblPoints != NULL) { |
| 917 | dblPoints[0] = control[0]; |
| 918 | dblPoints[1] = control[1]; |
| 919 | TkBezierPoints(control, numSteps, dblPoints+2); |
| 920 | dblPoints += 2*(numSteps+1); |
| 921 | } |
| 922 | outputPoints += numSteps+1; |
| 923 | } else { |
| 924 | closed = 0; |
| 925 | if (xPoints != NULL) { |
| 926 | xPoints->x = SCREEN_X(canvasPtr, pointPtr[0]); |
| 927 | xPoints->y = SCREEN_Y(canvasPtr, pointPtr[1]); |
| 928 | xPoints += 1; |
| 929 | } |
| 930 | if (dblPoints != NULL) { |
| 931 | dblPoints[0] = pointPtr[0]; |
| 932 | dblPoints[1] = pointPtr[1]; |
| 933 | dblPoints += 2; |
| 934 | } |
| 935 | outputPoints += 1; |
| 936 | } |
| 937 | |
| 938 | for (i = 2; i < numPoints; i++, pointPtr += 2) { |
| 939 | /* |
| 940 | * Set up the first two control points. This is done |
| 941 | * differently for the first spline of an open curve |
| 942 | * than for other cases. |
| 943 | */ |
| 944 | |
| 945 | if ((i == 2) && !closed) { |
| 946 | control[0] = pointPtr[0]; |
| 947 | control[1] = pointPtr[1]; |
| 948 | control[2] = 0.333*pointPtr[0] + 0.667*pointPtr[2]; |
| 949 | control[3] = 0.333*pointPtr[1] + 0.667*pointPtr[3]; |
| 950 | } else { |
| 951 | control[0] = 0.5*pointPtr[0] + 0.5*pointPtr[2]; |
| 952 | control[1] = 0.5*pointPtr[1] + 0.5*pointPtr[3]; |
| 953 | control[2] = 0.167*pointPtr[0] + 0.833*pointPtr[2]; |
| 954 | control[3] = 0.167*pointPtr[1] + 0.833*pointPtr[3]; |
| 955 | } |
| 956 | |
| 957 | /* |
| 958 | * Set up the last two control points. This is done |
| 959 | * differently for the last spline of an open curve |
| 960 | * than for other cases. |
| 961 | */ |
| 962 | |
| 963 | if ((i == (numPoints-1)) && !closed) { |
| 964 | control[4] = .667*pointPtr[2] + .333*pointPtr[4]; |
| 965 | control[5] = .667*pointPtr[3] + .333*pointPtr[5]; |
| 966 | control[6] = pointPtr[4]; |
| 967 | control[7] = pointPtr[5]; |
| 968 | } else { |
| 969 | control[4] = .833*pointPtr[2] + .167*pointPtr[4]; |
| 970 | control[5] = .833*pointPtr[3] + .167*pointPtr[5]; |
| 971 | control[6] = 0.5*pointPtr[2] + 0.5*pointPtr[4]; |
| 972 | control[7] = 0.5*pointPtr[3] + 0.5*pointPtr[5]; |
| 973 | } |
| 974 | |
| 975 | /* |
| 976 | * If the first two points coincide, or if the last |
| 977 | * two points coincide, then generate a single |
| 978 | * straight-line segment by outputting the last control |
| 979 | * point. |
| 980 | */ |
| 981 | |
| 982 | if (((pointPtr[0] == pointPtr[2]) && (pointPtr[1] == pointPtr[3])) |
| 983 | || ((pointPtr[2] == pointPtr[4]) |
| 984 | && (pointPtr[3] == pointPtr[5]))) { |
| 985 | if (xPoints != NULL) { |
| 986 | xPoints[0].x = SCREEN_X(canvasPtr, control[6]); |
| 987 | xPoints[0].y = SCREEN_Y(canvasPtr, control[7]); |
| 988 | xPoints++; |
| 989 | } |
| 990 | if (dblPoints != NULL) { |
| 991 | dblPoints[0] = control[6]; |
| 992 | dblPoints[1] = control[7]; |
| 993 | dblPoints += 2; |
| 994 | } |
| 995 | outputPoints += 1; |
| 996 | continue; |
| 997 | } |
| 998 | |
| 999 | /* |
| 1000 | * Generate a Bezier spline using the control points. |
| 1001 | */ |
| 1002 | |
| 1003 | |
| 1004 | if (xPoints != NULL) { |
| 1005 | TkBezierScreenPoints(canvasPtr, control, numSteps, xPoints); |
| 1006 | xPoints += numSteps; |
| 1007 | } |
| 1008 | if (dblPoints != NULL) { |
| 1009 | TkBezierPoints(control, numSteps, dblPoints); |
| 1010 | dblPoints += 2*numSteps; |
| 1011 | } |
| 1012 | outputPoints += numSteps; |
| 1013 | } |
| 1014 | return outputPoints; |
| 1015 | } |
| 1016 | \f |
| 1017 | /* |
| 1018 | *-------------------------------------------------------------- |
| 1019 | * |
| 1020 | * TkGetMiterPoints -- |
| 1021 | * |
| 1022 | * Given three points forming an angle, compute the |
| 1023 | * coordinates of the inside and outside points of |
| 1024 | * the mitered corner formed by a line of a given |
| 1025 | * width at that angle. |
| 1026 | * |
| 1027 | * Results: |
| 1028 | * If the angle formed by the three points is less than |
| 1029 | * 11 degrees then 0 is returned and m1 and m2 aren't |
| 1030 | * modified. Otherwise 1 is returned and the points at |
| 1031 | * m1 and m2 are filled in with the positions of the points |
| 1032 | * of the mitered corner. |
| 1033 | * |
| 1034 | * Side effects: |
| 1035 | * None. |
| 1036 | * |
| 1037 | *-------------------------------------------------------------- |
| 1038 | */ |
| 1039 | |
| 1040 | int |
| 1041 | TkGetMiterPoints(p1, p2, p3, width, m1, m2) |
| 1042 | double p1[]; /* Points to x- and y-coordinates of point |
| 1043 | * before vertex. */ |
| 1044 | double p2[]; /* Points to x- and y-coordinates of vertex |
| 1045 | * for mitered joint. */ |
| 1046 | double p3[]; /* Points to x- and y-coordinates of point |
| 1047 | * after vertex. */ |
| 1048 | double width; /* Width of line. */ |
| 1049 | double m1[]; /* Points to place to put "left" vertex |
| 1050 | * point (see as you face from p1 to p2). */ |
| 1051 | double m2[]; /* Points to place to put "right" vertex |
| 1052 | * point. */ |
| 1053 | { |
| 1054 | double theta1; /* Angle of segment p2-p1. */ |
| 1055 | double theta2; /* Angle of segment p2-p3. */ |
| 1056 | double theta; /* Angle between line segments (angle |
| 1057 | * of joint). */ |
| 1058 | double theta3; /* Angle that bisects theta1 and |
| 1059 | * theta2 and points to m1. */ |
| 1060 | double dist; /* Distance of miter points from p2. */ |
| 1061 | double deltaX, deltaY; /* X and y offsets cooresponding to |
| 1062 | * dist (fudge factors for bounding |
| 1063 | * box). */ |
| 1064 | static float elevenDegrees = (11.0*2.0*PI)/360.0; |
| 1065 | |
| 1066 | if (p2[1] == p1[1]) { |
| 1067 | theta1 = (p2[0] < p1[0]) ? 0 : PI; |
| 1068 | } else if (p2[0] == p1[0]) { |
| 1069 | theta1 = (p2[1] < p1[1]) ? PI/2.0 : -PI/2.0; |
| 1070 | } else { |
| 1071 | theta1 = atan2(p1[1] - p2[1], p1[0] - p2[0]); |
| 1072 | } |
| 1073 | if (p3[1] == p2[1]) { |
| 1074 | theta2 = (p3[0] > p2[0]) ? 0 : PI; |
| 1075 | } else if (p3[0] == p2[0]) { |
| 1076 | theta2 = (p3[1] > p2[1]) ? PI/2.0 : -PI/2.0; |
| 1077 | } else { |
| 1078 | theta2 = atan2(p3[1] - p2[1], p3[0] - p2[0]); |
| 1079 | } |
| 1080 | theta = theta1 - theta2; |
| 1081 | if (theta > PI) { |
| 1082 | theta -= 2*PI; |
| 1083 | } else if (theta < -PI) { |
| 1084 | theta += 2*PI; |
| 1085 | } |
| 1086 | if ((theta < elevenDegrees) && (theta > -elevenDegrees)) { |
| 1087 | return 0; |
| 1088 | } |
| 1089 | dist = 0.5*width/sin(0.5*theta); |
| 1090 | if (dist < 0.0) { |
| 1091 | dist = -dist; |
| 1092 | } |
| 1093 | |
| 1094 | /* |
| 1095 | * Compute theta3 (make sure that it points to the left when |
| 1096 | * looking from p1 to p2). |
| 1097 | */ |
| 1098 | |
| 1099 | theta3 = (theta1 + theta2)/2.0; |
| 1100 | if (sin(theta3 - (theta1 + PI)) < 0.0) { |
| 1101 | theta3 += PI; |
| 1102 | } |
| 1103 | deltaX = dist*cos(theta3); |
| 1104 | m1[0] = p2[0] + deltaX; |
| 1105 | m2[0] = p2[0] - deltaX; |
| 1106 | deltaY = dist*sin(theta3); |
| 1107 | m1[1] = p2[1] + deltaY; |
| 1108 | m2[1] = p2[1] - deltaY; |
| 1109 | return 1; |
| 1110 | } |
| 1111 | \f |
| 1112 | /* |
| 1113 | *-------------------------------------------------------------- |
| 1114 | * |
| 1115 | * TkGetButtPoints -- |
| 1116 | * |
| 1117 | * Given two points forming a line segment, compute the |
| 1118 | * coordinates of two endpoints of a rectangle formed by |
| 1119 | * bloating the line segment until it is width units wide. |
| 1120 | * |
| 1121 | * Results: |
| 1122 | * There is no return value. M1 and m2 are filled in to |
| 1123 | * correspond to m1 and m2 in the diagram below: |
| 1124 | * |
| 1125 | * ----------------* m1 |
| 1126 | * | |
| 1127 | * p1 *---------------* p2 |
| 1128 | * | |
| 1129 | * ----------------* m2 |
| 1130 | * |
| 1131 | * M1 and m2 will be W units apart, with p2 centered between |
| 1132 | * them and m1-m2 perpendicular to p1-p2. However, if |
| 1133 | * "project" is true then m1 and m2 will be as follows: |
| 1134 | * |
| 1135 | * -------------------* m1 |
| 1136 | * p2 | |
| 1137 | * p1 *---------------* | |
| 1138 | * | |
| 1139 | * -------------------* m2 |
| 1140 | * |
| 1141 | * In this case p2 will be width/2 units from the segment m1-m2. |
| 1142 | * |
| 1143 | * Side effects: |
| 1144 | * None. |
| 1145 | * |
| 1146 | *-------------------------------------------------------------- |
| 1147 | */ |
| 1148 | |
| 1149 | void |
| 1150 | TkGetButtPoints(p1, p2, width, project, m1, m2) |
| 1151 | double p1[]; /* Points to x- and y-coordinates of point |
| 1152 | * before vertex. */ |
| 1153 | double p2[]; /* Points to x- and y-coordinates of vertex |
| 1154 | * for mitered joint. */ |
| 1155 | double width; /* Width of line. */ |
| 1156 | int project; /* Non-zero means project p2 by an additional |
| 1157 | * width/2 before computing m1 and m2. */ |
| 1158 | double m1[]; /* Points to place to put "left" result |
| 1159 | * point, as you face from p1 to p2. */ |
| 1160 | double m2[]; /* Points to place to put "right" result |
| 1161 | * point. */ |
| 1162 | { |
| 1163 | double length; /* Length of p1-p2 segment. */ |
| 1164 | double deltaX, deltaY; /* Increments in coords. */ |
| 1165 | |
| 1166 | width *= 0.5; |
| 1167 | length = hypot(p2[0] - p1[0], p2[1] - p1[1]); |
| 1168 | if (length == 0.0) { |
| 1169 | m1[0] = m2[0] = p2[0]; |
| 1170 | m1[1] = m2[1] = p2[1]; |
| 1171 | } else { |
| 1172 | deltaX = -width * (p2[1] - p1[1]) / length; |
| 1173 | deltaY = width * (p2[0] - p1[0]) / length; |
| 1174 | m1[0] = p2[0] + deltaX; |
| 1175 | m2[0] = p2[0] - deltaX; |
| 1176 | m1[1] = p2[1] + deltaY; |
| 1177 | m2[1] = p2[1] - deltaY; |
| 1178 | if (project) { |
| 1179 | m1[0] += deltaY; |
| 1180 | m2[0] += deltaY; |
| 1181 | m1[1] -= deltaX; |
| 1182 | m2[1] -= deltaX; |
| 1183 | } |
| 1184 | } |
| 1185 | } |