├── .github └── FUNDING.yml ├── .gitignore ├── Delaunator.py ├── LICENSE ├── README.md └── Test.py /.github/FUNDING.yml: -------------------------------------------------------------------------------- 1 | # These are supported funding model platforms 2 | 3 | github: # Replace with up to 4 GitHub Sponsors-enabled usernames e.g., [user1, user2] 4 | patreon: HakanSeven12 5 | open_collective: # Replace with a single Open Collective username 6 | ko_fi: # Replace with a single Ko-fi username 7 | tidelift: # Replace with a single Tidelift platform-name/package-name e.g., npm/babel 8 | community_bridge: # Replace with a single Community Bridge project-name e.g., cloud-foundry 9 | liberapay: # Replace with a single Liberapay username 10 | issuehunt: # Replace with a single IssueHunt username 11 | otechie: # Replace with a single Otechie username 12 | custom: # Replace with up to 4 custom sponsorship URLs e.g., ['link1', 'link2'] 13 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | pip-wheel-metadata/ 24 | share/python-wheels/ 25 | *.egg-info/ 26 | .installed.cfg 27 | *.egg 28 | MANIFEST 29 | 30 | # PyInstaller 31 | # Usually these files are written by a python script from a template 32 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 33 | *.manifest 34 | *.spec 35 | 36 | # Installer logs 37 | pip-log.txt 38 | pip-delete-this-directory.txt 39 | 40 | # Unit test / coverage reports 41 | htmlcov/ 42 | .tox/ 43 | .nox/ 44 | .coverage 45 | .coverage.* 46 | .cache 47 | nosetests.xml 48 | coverage.xml 49 | *.cover 50 | *.py,cover 51 | .hypothesis/ 52 | .pytest_cache/ 53 | 54 | # Translations 55 | *.mo 56 | *.pot 57 | 58 | # Django stuff: 59 | *.log 60 | local_settings.py 61 | db.sqlite3 62 | db.sqlite3-journal 63 | 64 | # Flask stuff: 65 | instance/ 66 | .webassets-cache 67 | 68 | # Scrapy stuff: 69 | .scrapy 70 | 71 | # Sphinx documentation 72 | docs/_build/ 73 | 74 | # PyBuilder 75 | target/ 76 | 77 | # Jupyter Notebook 78 | .ipynb_checkpoints 79 | 80 | # IPython 81 | profile_default/ 82 | ipython_config.py 83 | 84 | # pyenv 85 | .python-version 86 | 87 | # pipenv 88 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. 89 | # However, in case of collaboration, if having platform-specific dependencies or dependencies 90 | # having no cross-platform support, pipenv may install dependencies that don't work, or not 91 | # install all needed dependencies. 92 | #Pipfile.lock 93 | 94 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow 95 | __pypackages__/ 96 | 97 | # Celery stuff 98 | celerybeat-schedule 99 | celerybeat.pid 100 | 101 | # SageMath parsed files 102 | *.sage.py 103 | 104 | # Environments 105 | .env 106 | .venv 107 | env/ 108 | venv/ 109 | ENV/ 110 | env.bak/ 111 | venv.bak/ 112 | 113 | # Spyder project settings 114 | .spyderproject 115 | .spyproject 116 | 117 | # Rope project settings 118 | .ropeproject 119 | 120 | # mkdocs documentation 121 | /site 122 | 123 | # mypy 124 | .mypy_cache/ 125 | .dmypy.json 126 | dmypy.json 127 | 128 | # Pyre type checker 129 | .pyre/ 130 | -------------------------------------------------------------------------------- /Delaunator.py: -------------------------------------------------------------------------------- 1 | import math 2 | 3 | EPSILON = math.pow(2,-52) 4 | EDGE_STACK =[None] * 512 5 | 6 | class Delaunator: 7 | 8 | def __init__(self,points): 9 | n = len(points) 10 | 11 | if (len(points) < 3): 12 | raise ValueError("Need at least 3 points") 13 | coords = [None] * n * 2 14 | 15 | for i in range(0,n): 16 | p = points[i] 17 | coords[2 * i] = (p[0]) 18 | coords[2 * i+1] = (p[1]) 19 | triangles = self.constructor(coords) 20 | 21 | def constructor(self, coords): 22 | n = len(coords) >> 1 23 | 24 | self.coords = coords 25 | 26 | # arrays that will store the triangulation graph 27 | maxTriangles = max(2 * n - 5, 0) 28 | self._triangles = [None] * maxTriangles * 3 29 | self._halfedges = [None] * maxTriangles * 3 30 | 31 | # temporary arrays for tracking the edges of the advancing convex hull 32 | self.hashSize = math.ceil(math.sqrt(n)) 33 | self.hullPrev = [None] * n # edge to prev edge 34 | self.hullNext = [None] * n # edge to next edge 35 | self.hullTri = [None] * n # edge to adjacent triangle 36 | self.hullHash = [-1] * self.hashSize # angular edge hash 37 | 38 | # temporary arrays for sorting points 39 | self._ids = [None] * n 40 | self._dists = [None] * n 41 | triangles = self.update(coords) 42 | 43 | return triangles 44 | 45 | def update(self,coords): 46 | n = len(coords) >> 1 47 | 48 | # populate an array of point indices; calculate input data bbox 49 | minX = math.inf 50 | minY = math.inf 51 | maxX = -math.inf 52 | maxY = -math.inf 53 | 54 | for i in range(0,n): 55 | x = coords[2 * i] 56 | y = coords[2 * i + 1] 57 | if (x < minX): minX = x 58 | if (y < minY): minY = y 59 | if (x > maxX): maxX = x 60 | if (y > maxY): maxY = y 61 | self._ids[i] = i 62 | 63 | cx = (minX + maxX) / 2 64 | cy = (minY + maxY) / 2 65 | 66 | minDist = math.inf 67 | i0 = 0 68 | i1 = 0 69 | i2 = 0 70 | 71 | # pick a seed point close to the center 72 | for i in range(0,n): 73 | d = dist(cx, cy, coords[2 * i], coords[2 * i + 1]) 74 | 75 | if (d < minDist): 76 | i0 = i 77 | minDist = d 78 | 79 | i0x = coords[2 * i0] 80 | i0y = coords[2 * i0 + 1] 81 | minDist = math.inf 82 | 83 | # find the point closest to the seed 84 | for i in range(0,n): 85 | if (i == i0): continue 86 | d = dist(i0x, i0y, coords[2 * i], coords[2 * i + 1]) 87 | 88 | if (d < minDist and d > 0): 89 | i1 = i 90 | minDist = d 91 | 92 | i1x = coords[2 * i1] 93 | i1y = coords[2 * i1 + 1] 94 | 95 | minRadius = math.inf 96 | 97 | # find the third point which forms the smallest circumcircle with the first two 98 | for i in range(0,n): 99 | if (i == i0 or i == i1): continue 100 | r = circumradius(i0x, i0y, i1x, i1y, coords[2 * i], coords[2 * i + 1]) 101 | 102 | if (r < minRadius): 103 | i2 = i 104 | minRadius = r 105 | 106 | i2x = coords[2 * i2] 107 | i2y = coords[2 * i2 + 1] 108 | 109 | if (minRadius == math.inf): 110 | # order collinear points by dx (or dy if all x are identical) 111 | # and return the list as a hull 112 | for i in range(0,n): 113 | self._dists[i] = (coords[2 * i] - coords[0]) or (coords[2 * i + 1] - coords[1]) 114 | 115 | quicksort(self._ids, self._dists, 0, n - 1) 116 | hull = [None] * n 117 | j = 0 118 | d0 = -math.inf 119 | 120 | for i in range(0,n): 121 | id = self._ids[i] 122 | 123 | if (self._dists[id] > d0): 124 | hull[j] = id 125 | j+=1 126 | d0 = self._dists[id] 127 | 128 | self.hull = hull[0:j] 129 | self.triangles = [] 130 | self.halfedges = [] 131 | 132 | # swap the order of the seed points for counter-clockwise orientation 133 | if (orient(i0x, i0y, i1x, i1y, i2x, i2y)): 134 | i = i1 135 | x = i1x 136 | y = i1y 137 | i1 = i2 138 | i1x = i2x 139 | i1y = i2y 140 | i2 = i 141 | i2x = x 142 | i2y = y 143 | 144 | center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y) 145 | self._cx = center[0] 146 | self._cy = center[1] 147 | 148 | for i in range(0,n): 149 | self._dists[i] = dist(coords[2 * i], coords[2 * i + 1], center[0], center[1]) 150 | 151 | # sort the points by distance from the seed triangle circumcenter 152 | quicksort(self._ids, self._dists, 0, n - 1) 153 | 154 | # set up the seed triangle as the starting hull 155 | self._hullStart = i0 156 | hullSize = 3 157 | 158 | self.hullNext[i0] = self.hullPrev[i2] = i1 159 | self.hullNext[i1] = self.hullPrev[i0] = i2 160 | self.hullNext[i2] = self.hullPrev[i1] = i0 161 | 162 | self.hullTri[i0] = 0 163 | self.hullTri[i1] = 1 164 | self.hullTri[i2] = 2 165 | 166 | self.hullHash[self._hashKey(i0x, i0y)] = i0 167 | self.hullHash[self._hashKey(i1x, i1y)] = i1 168 | self.hullHash[self._hashKey(i2x, i2y)] = i2 169 | 170 | self.trianglesLen = 0 171 | self._addTriangle(i0, i1, i2, -1, -1, -1) 172 | 173 | xp=0 174 | yp=0 175 | 176 | for k in range(0,len(self._ids)): 177 | i = self._ids[k] 178 | x = coords[2 * i] 179 | y = coords[2 * i + 1] 180 | 181 | # skip near-duplicate points 182 | if (k > 0 and abs(x - xp) <= EPSILON and abs(y - yp) <= EPSILON): continue 183 | 184 | xp = x 185 | yp = y 186 | 187 | # skip seed triangle points 188 | if (i == i0 or i == i1 or i == i2): continue 189 | 190 | # find a visible edge on the convex hull using edge hash 191 | start = 0 192 | key = self._hashKey(x, y) 193 | 194 | for j in range(0,self.hashSize): 195 | start = self.hullHash[(key + j) % self.hashSize] 196 | if (start != -1 and start != self.hullNext[start]): break 197 | 198 | start = self.hullPrev[start] 199 | e = start 200 | 201 | while True: 202 | q = self.hullNext[e] 203 | if orient(x, y, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1]): break 204 | e = q 205 | 206 | if (e == start): 207 | e = -1 208 | break 209 | 210 | if (e == -1): continue # likely a near-duplicate point; skip it 211 | 212 | # add the first triangle from the point 213 | t = self._addTriangle(e, i, self.hullNext[e], -1, -1, self.hullTri[e]) 214 | 215 | # recursively flip triangles from the point until they satisfy the Delaunay condition 216 | self.hullTri[i] = self._legalize(t + 2,coords) 217 | self.hullTri[e] = t # keep track of boundary triangles on the hull 218 | hullSize+=1 219 | 220 | # walk forward through the hull, adding more triangles and flipping recursively 221 | n = self.hullNext[e] 222 | 223 | while True: 224 | q = self.hullNext[n] 225 | if not (orient(x, y, coords[2 * n], coords[2 * n + 1], coords[2 * q], coords[2 * q + 1])): break 226 | t = self._addTriangle(n, i, q, self.hullTri[i], -1, self.hullTri[n]) 227 | self.hullTri[i] = self._legalize(t + 2,coords) 228 | self.hullNext[n] = n # mark as removed 229 | hullSize-=1 230 | n = q 231 | 232 | # walk backward from the other side, adding more triangles and flipping 233 | if (e == start): 234 | while True: 235 | q = self.hullPrev[e] 236 | if not (orient(x, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1])): break 237 | t = self._addTriangle(q, i, e, -1, self.hullTri[e], self.hullTri[q]) 238 | self._legalize(t + 2,coords) 239 | self.hullTri[q] = t 240 | self.hullNext[e] = e # mark as removed 241 | hullSize-=1 242 | e = q 243 | 244 | # update the hull indices 245 | self._hullStart = self.hullPrev[i] = e 246 | self.hullNext[e] = self.hullPrev[n] = i 247 | self.hullNext[i] = n 248 | 249 | # save the two new edges in the hash table 250 | self.hullHash[self._hashKey(x, y)] = i 251 | self.hullHash[self._hashKey(coords[2 * e], coords[2 * e + 1])] = e 252 | 253 | self.hull = [None] * hullSize 254 | e = self._hullStart 255 | for i in range(0,hullSize): 256 | self.hull[i] = e 257 | e = self.hullNext[e] 258 | 259 | # trim typed triangle mesh arrays 260 | self.triangles = self._triangles[0:self.trianglesLen] 261 | self.halfedges = self._halfedges[0:self.trianglesLen] 262 | 263 | return self.triangles 264 | 265 | def _hashKey(self,x, y): 266 | return math.floor(pseudoAngle(x - self._cx, y - self._cy) * self.hashSize) % self.hashSize 267 | 268 | def _legalize(self,a,coords): 269 | i = 0 270 | ar = 0 271 | 272 | # recursion eliminated with a fixed-size stack 273 | while True: 274 | b = self._halfedges[a] 275 | """ 276 | if the pair of triangles doesn't satisfy the Delaunay condition 277 | (p1 is inside the circumcircle of [p0, pl, pr]), flip them, 278 | then do the same check/flip recursively for the new pair of triangles 279 | """ 280 | 281 | # pl pl 282 | # /||\ / \ 283 | # al/ || \bl al/ \a 284 | # / || \ / \ 285 | # / a||b \ flip /___ar___\ 286 | # p0\ || /p1 => p0\---bl---/p1 287 | # \ || / \ / 288 | # ar\ || /br b\ /br 289 | # \||/ \ / 290 | # pr pr 291 | 292 | a0 = a - a % 3 293 | ar = a0 + (a + 2) % 3 294 | 295 | if (b == -1): # convex hull edge 296 | if (i == 0): break 297 | i-=1 298 | a = EDGE_STACK[i] 299 | continue 300 | 301 | b0 = b - b % 3 302 | al = a0 + (a + 1) % 3 303 | bl = b0 + (b + 2) % 3 304 | 305 | p0 = self._triangles[ar] 306 | pr = self._triangles[a] 307 | pl = self._triangles[al] 308 | p1 = self._triangles[bl] 309 | 310 | illegal = inCircle( 311 | coords[2 * p0], coords[2 * p0 + 1], 312 | coords[2 * pr], coords[2 * pr + 1], 313 | coords[2 * pl], coords[2 * pl + 1], 314 | coords[2 * p1], coords[2 * p1 + 1]) 315 | 316 | if (illegal): 317 | self._triangles[a] = p1 318 | self._triangles[b] = p0 319 | 320 | hbl = self._halfedges[bl] 321 | 322 | # edge swapped on the other side of the hull (rare); fix the halfedge reference 323 | if (hbl == -1): 324 | e = self._hullStart 325 | 326 | while True: 327 | if (self.hullTri[e] == bl): 328 | self.hullTri[e] = a 329 | break 330 | 331 | e = self.hullPrev[e] 332 | if (e == self._hullStart): break 333 | 334 | self._link(a, hbl) 335 | self._link(b, self._halfedges[ar]) 336 | self._link(ar, bl) 337 | 338 | br = b0 + (b + 1) % 3 339 | 340 | # don't worry about hitting the cap: it can only happen on extremely degenerate input 341 | if (i < len(EDGE_STACK)): 342 | EDGE_STACK[i] = br 343 | i+=1 344 | 345 | else: 346 | if (i == 0): break 347 | i-=1 348 | a = EDGE_STACK[i] 349 | 350 | return ar 351 | 352 | def _link(self,a, b): 353 | self._halfedges[a] = b 354 | if (b != -1): 355 | self._halfedges[b] = a 356 | 357 | # add a new triangle given vertex indices and adjacent half-edge ids 358 | def _addTriangle(self,i0, i1, i2, a, b, c): 359 | t = self.trianglesLen 360 | 361 | self._triangles[t] = i0 362 | self._triangles[t + 1] = i1 363 | self._triangles[t + 2] = i2 364 | 365 | self._link(t, a) 366 | self._link(t + 1, b) 367 | self._link(t + 2, c) 368 | 369 | self.trianglesLen += 3 370 | 371 | return t 372 | 373 | # monotonically increases with real angle, but doesn't need expensive trigonometry 374 | def pseudoAngle(dx, dy): 375 | p = dx / (abs(dx) + abs(dy)) 376 | 377 | if (dy > 0): 378 | return (3 - p) / 4 # [0..1] 379 | else: 380 | return (1 + p) / 4 # [0..1] 381 | 382 | def dist(ax, ay, bx, by): 383 | dx = ax - bx 384 | dy = ay - by 385 | return dx * dx + dy * dy 386 | 387 | # return 2d orientation sign if we're confident in it through J. Shewchuk's error bound check 388 | def orientIfSure(px, py, rx, ry, qx, qy): 389 | l = (ry - py) * (qx - px) 390 | r = (rx - px) * (qy - py) 391 | 392 | if (abs(l - r) >= 3.3306690738754716e-16 * abs(l + r)): 393 | return l - r 394 | else: 395 | return 0 396 | 397 | # a more robust orientation test that's stable in a given triangle (to fix robustness issues) 398 | def orient(rx, ry, qx, qy, px, py): 399 | return (orientIfSure(px, py, rx, ry, qx, qy) or\ 400 | orientIfSure(rx, ry, qx, qy, px, py) or\ 401 | orientIfSure(qx, qy, px, py, rx, ry)) < 0 402 | 403 | def inCircle(ax, ay, bx, by, cx, cy, px, py): 404 | dx = ax - px 405 | dy = ay - py 406 | ex = bx - px 407 | ey = by - py 408 | fx = cx - px 409 | fy = cy - py 410 | 411 | ap = dx * dx + dy * dy 412 | bp = ex * ex + ey * ey 413 | cp = fx * fx + fy * fy 414 | 415 | return dx * (ey * cp - bp * fy) -\ 416 | dy * (ex * cp - bp * fx) +\ 417 | ap * (ex * fy - ey * fx) < 0 418 | 419 | def circumradius(ax, ay, bx, by, cx, cy): 420 | dx = bx - ax 421 | dy = by - ay 422 | ex = cx - ax 423 | ey = cy - ay 424 | 425 | bl = dx * dx + dy * dy 426 | cl = ex * ex + ey * ey 427 | try: 428 | d = 0.5/(dx * ey - dy * ex) 429 | except ZeroDivisionError: 430 | d = float('inf') 431 | 432 | x = (ey * bl - dy * cl) * d 433 | y = (dx * cl - ex * bl) * d 434 | 435 | return x*x + y*y 436 | 437 | def circumcenter(ax, ay, bx, by, cx, cy): 438 | dx = bx - ax 439 | dy = by - ay 440 | ex = cx - ax 441 | ey = cy - ay 442 | 443 | bl = dx * dx + dy * dy 444 | cl = ex * ex + ey * ey 445 | try: 446 | d = 0.5/(dx * ey - dy * ex) 447 | except ZeroDivisionError: 448 | d = float('inf') 449 | 450 | x = ax + (ey * bl - dy * cl) * d 451 | y = ay + (dx * cl - ex * bl) * d 452 | 453 | return x, y 454 | 455 | def quicksort(ids, dists, left, right): 456 | if (right - left <= 20): 457 | for i in range(left + 1,right+1): 458 | temp = ids[i] 459 | tempDist = dists[temp] 460 | j = i-1 461 | while (j >= left and dists[ids[j]] > tempDist): 462 | ids[j + 1] = ids[j] 463 | j-=1 464 | ids[j + 1] = temp; 465 | 466 | else: 467 | median = (left + right) >> 1 468 | i = left + 1 469 | j = right 470 | swap(ids, median, i) 471 | 472 | if (dists[ids[left]] > dists[ids[right]]): 473 | swap(ids, left, right) 474 | 475 | if (dists[ids[i]] > dists[ids[right]]): 476 | swap(ids, i, right) 477 | 478 | if (dists[ids[left]] > dists[ids[i]]): 479 | swap(ids, left, i) 480 | 481 | temp = ids[i] 482 | tempDist = dists[temp] 483 | 484 | while True: 485 | while True: 486 | i+=1 487 | if (dists[ids[i]] >= tempDist): break 488 | 489 | while True: 490 | j-=1 491 | if (dists[ids[j]] <= tempDist): break 492 | 493 | if (j < i): break 494 | swap(ids, i, j); 495 | 496 | ids[left + 1] = ids[j]; 497 | ids[j] = temp; 498 | 499 | if (right - i + 1 >= j - left): 500 | quicksort(ids, dists, i, right) 501 | quicksort(ids, dists, left, j - 1) 502 | 503 | else: 504 | quicksort(ids, dists, left, j - 1) 505 | quicksort(ids, dists, i, right) 506 | 507 | def swap(arr, i, j): 508 | tmp = arr[i] 509 | arr[i] = arr[j] 510 | arr[j] = tmp 511 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU LESSER GENERAL PUBLIC LICENSE 2 | Version 2.1, February 1999 3 | 4 | Copyright (C) 1991, 1999 Free Software Foundation, Inc. 5 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 6 | Everyone is permitted to copy and distribute verbatim copies 7 | of this license document, but changing it is not allowed. 8 | 9 | [This is the first released version of the Lesser GPL. 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Here is a sample; alter the names: 496 | 497 | Yoyodyne, Inc., hereby disclaims all copyright interest in the 498 | library `Frob' (a library for tweaking knobs) written by James Random 499 | Hacker. 500 | 501 | , 1 April 1990 502 | Ty Coon, President of Vice 503 | 504 | That's all there is to it! 505 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Delaunator-Python 2 | Fast Delaunay triangulation of 2D points implemented in Python. 3 | 4 | This code was ported from [Mapbox's Delaunator Project](https://github.com/mapbox/delaunator) (JavaScript). 5 | 6 | 7 | 8 | Test on FreeCAD. 9 | 10 | ![Test](https://user-images.githubusercontent.com/3831435/75558770-60245280-5a53-11ea-8d1f-855c9e3f9c13.png) 11 | 12 | 13 | 14 | Comparison result between python alternatives. 15 | 16 | ![delauny_comparison](https://user-images.githubusercontent.com/3831435/76827861-cc170100-6830-11ea-868e-9cb5893d8543.png) 17 | 18 | ## Usage 19 | ```python 20 | from Delaunator import Delaunator 21 | 22 | points = [[168, 180], [168, 178], [168, 179], [168, 181], [168, 183], ...] 23 | 24 | triangles = Delaunator(points).triangles 25 | print(triangles) 26 | 27 | >> [623, 636, 619, 636, 444, 619, ...] 28 | ``` 29 | 30 | ## API Reference 31 | 32 | ### Delaunator(points) 33 | 34 | Constructs a delaunay triangulation object given an array of points (`[x, y]` by default). 35 | Duplicate points are skipped. 36 | 37 | ### Delaunator(points).triangles 38 | 39 | An array of triangle vertex indices (each group of three numbers forms a triangle). 40 | All triangles are directed counterclockwise. 41 | 42 | To get the coordinates of all triangles, use: 43 | 44 | ```python 45 | coordinates = [] 46 | 47 | for i in range(0, len(triangles), 3): 48 | coordinates.append([ 49 | points[triangles[i]], 50 | points[triangles[i + 1]], 51 | points[triangles[i + 2]]]) 52 | ``` 53 | 54 | ### Delaunator(points).halfedges 55 | 56 | An array of triangle half-edge indices that allows you to traverse the triangulation. 57 | `i`-th half-edge in the array corresponds to vertex `triangles[i]` the half-edge is coming from. 58 | `halfedges[i]` is the index of a twin half-edge in an adjacent triangle 59 | (or `-1` for outer half-edges on the convex hull). 60 | 61 | The flat array-based data structures might be counterintuitive, 62 | but they're one of the key reasons this library is fast. 63 | 64 | ### Delaunator(points).hull 65 | 66 | An array of indices that reference points on the convex hull of the input data, counter-clockwise. 67 | 68 | ### Delaunator(points).coords 69 | 70 | An array of input coordinates in the form `[x0, y0, x1, y1, ....]`, 71 | of the type provided in the constructor. 72 | 73 | ### Delaunator(points).update() 74 | 75 | Updates the triangulation if you modified `Delaunator(points).coords` values in place, avoiding expensive memory allocations. 76 | Useful for iterative relaxation algorithms such as [Lloyd's](https://en.wikipedia.org/wiki/Lloyd%27s_algorithm). 77 | -------------------------------------------------------------------------------- /Test.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | from Delaunator import Delaunator 3 | import time 4 | 5 | start_time = time.process_time() 6 | 7 | #create random 2000 2d points between 4000000 and 4500000 8 | points = np.random.randint(1,1677.7215,size=(10000,2)) 9 | 10 | point_creation_time = time.process_time() - start_time 11 | 12 | triangles = Delaunator(points).triangles 13 | halfedges = Delaunator(points).halfedges 14 | hull = Delaunator(points).hull 15 | coords = Delaunator(points).coords 16 | 17 | print("\ncoords = "+str(coords)) 18 | print("\ntriangles = "+str(triangles)) 19 | print("\nhalfedges = "+str(halfedges)) 20 | print("\nhull = "+str(hull)) 21 | 22 | triangulation_time = time.process_time() - point_creation_time 23 | print("\n" + str(point_creation_time)) 24 | print("\n" + str(triangulation_time)) 25 | --------------------------------------------------------------------------------