1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 | #!/usr/bin/python2.4 # # Copyright 2007 Google Inc. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. """A library for manipulating points and polylines. This is a library for creating and manipulating points on the unit sphere, as an approximate model of Earth. The primary use of this library is to make manipulation and matching of polylines easy in the transitfeed library. NOTE: in this library, Earth is modelled as a sphere, whereas GTFS specifies that latitudes and longitudes are in WGS84. For the purpose of comparing and matching latitudes and longitudes that are relatively close together on the surface of the earth, this is adequate; for other purposes, this library may not be accurate enough. """ __author__ = 'chris.harrelson.code@gmail.com (Chris Harrelson)' import copy import decimal import heapq import math class ShapeError(Exception): """Thrown whenever there is a shape parsing error.""" pass EARTH_RADIUS_METERS = 6371010.0 class Point(object): """ A class representing a point on the unit sphere in three dimensions. """ def __init__(self, x, y, z): self.x = x self.y = y self.z = z def __hash__(self): return hash((self.x, self.y, self.z)) def __cmp__(self, other): if not isinstance(other, Point): raise TypeError('Point.__cmp__(x,y) requires y to be a "Point", ' 'not a "%s"' % type(other).__name__) return cmp((self.x, self.y, self.z), (other.x, other.y, other.z)) def __str__(self): return "(%.15f, %.15f, %.15f) " % (self.x, self.y, self.z) def Norm2(self): """ Returns the L_2 (Euclidean) norm of self. """ sum = self.x * self.x + self.y * self.y + self.z * self.z return math.sqrt(float(sum)) def IsUnitLength(self): return abs(self.Norm2() - 1.0) < 1e-14 def Plus(self, other): """ Returns a new point which is the pointwise sum of self and other. """ return Point(self.x + other.x, self.y + other.y, self.z + other.z) def Minus(self, other): """ Returns a new point which is the pointwise subtraction of other from self. """ return Point(self.x - other.x, self.y - other.y, self.z - other.z) def DotProd(self, other): """ Returns the (scalar) dot product of self with other. """ return self.x * other.x + self.y * other.y + self.z * other.z def Times(self, val): """ Returns a new point which is pointwise multiplied by val. """ return Point(self.x * val, self.y * val, self.z * val) def Normalize(self): """ Returns a unit point in the same direction as self. """ return self.Times(1 / self.Norm2()) def RobustCrossProd(self, other): """ A robust version of cross product. If self and other are not nearly the same point, returns the same value as CrossProd() modulo normalization. Otherwise returns an arbitrary unit point orthogonal to self. """ assert(self.IsUnitLength() and other.IsUnitLength()) x = self.Plus(other).CrossProd(other.Minus(self)) if abs(x.x) > 1e-15 or abs(x.y) > 1e-15 or abs(x.z) > 1e-15: return x.Normalize() else: return self.Ortho() def LargestComponent(self): """ Returns (i, val) where i is the component index (0 - 2) which has largest absolute value and val is the value of the component. """ if abs(self.x) > abs(self.y): if abs(self.x) > abs(self.z): return (0, self.x) else: return (2, self.z) else: if abs(self.y) > abs(self.z): return (1, self.y) else: return (2, self.z) def Ortho(self): """Returns a unit-length point orthogonal to this point""" (index, val) = self.LargestComponent() index = index - 1 if index < 0: index = 2 temp = Point(0.012, 0.053, 0.00457) if index == 0: temp.x = 1 elif index == 1: temp.y = 1 elif index == 2: temp.z = 1 return self.CrossProd(temp).Normalize() def CrossProd(self, other): """ Returns the cross product of self and other. """ return Point( self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x) @staticmethod def _approxEq(a, b): return abs(a - b) < 1e-11 def Equals(self, other): """ Returns true of self and other are approximately equal. """ return (self._approxEq(self.x, other.x) and self._approxEq(self.y, other.y) and self._approxEq(self.z, other.z)) def Angle(self, other): """ Returns the angle in radians between self and other. """ return math.atan2(self.CrossProd(other).Norm2(), self.DotProd(other)) def ToLatLng(self): """ Returns that latitude and longitude that this point represents under a spherical Earth model. """ rad_lat = math.atan2(self.z, math.sqrt(self.x * self.x + self.y * self.y)) rad_lng = math.atan2(self.y, self.x) return (rad_lat * 180.0 / math.pi, rad_lng * 180.0 / math.pi) @staticmethod def FromLatLng(lat, lng): """ Returns a new point representing this latitude and longitude under a spherical Earth model. """ phi = lat * (math.pi / 180.0) theta = lng * (math.pi / 180.0) cosphi = math.cos(phi) return Point(math.cos(theta) * cosphi, math.sin(theta) * cosphi, math.sin(phi)) def GetDistanceMeters(self, other): assert(self.IsUnitLength() and other.IsUnitLength()) return self.Angle(other) * EARTH_RADIUS_METERS def SimpleCCW(a, b, c): """ Returns true if the triangle abc is oriented counterclockwise. """ return c.CrossProd(a).DotProd(b) > 0 def GetClosestPoint(x, a, b): """ Returns the point on the great circle segment ab closest to x. """ assert(x.IsUnitLength()) assert(a.IsUnitLength()) assert(b.IsUnitLength()) a_cross_b = a.RobustCrossProd(b) # project to the great circle going through a and b p = x.Minus( a_cross_b.Times( x.DotProd(a_cross_b) / a_cross_b.Norm2())) # if p lies between a and b, return it if SimpleCCW(a_cross_b, a, p) and SimpleCCW(p, b, a_cross_b): return p.Normalize() # otherwise return the closer of a or b if x.Minus(a).Norm2() <= x.Minus(b).Norm2(): return a else: return b class Poly(object): """ A class representing a polyline. """ def __init__(self, points = [], name=None): self._points = list(points) self._name = name def AddPoint(self, p): """ Adds a new point to the end of the polyline. """ assert(p.IsUnitLength()) self._points.append(p) def GetName(self): return self._name def GetPoint(self, i): return self._points[i] def GetPoints(self): return self._points def GetNumPoints(self): return len(self._points) def _GetPointSafe(self, i): try: return self.GetPoint(i) except IndexError: return None def GetClosestPoint(self, p): """ Returns (closest_p, closest_i), where closest_p is the closest point to p on the piecewise linear curve represented by the polyline, and closest_i is the index of the point on the polyline just before the polyline segment that contains closest_p. """ assert(len(self._points) > 0) closest_point = self._points[0] closest_i = 0 for i in range(0, len(self._points) - 1): (a, b) = (self._points[i], self._points[i+1]) cur_closest_point = GetClosestPoint(p, a, b) if p.Angle(cur_closest_point) < p.Angle(closest_point): closest_point = cur_closest_point.Normalize() closest_i = i return (closest_point, closest_i) def LengthMeters(self): """Return length of this polyline in meters.""" assert(len(self._points) > 0) length = 0 for i in range(0, len(self._points) - 1): length += self._points[i].GetDistanceMeters(self._points[i+1]) return length def Reversed(self): """Return a polyline that is the reverse of this polyline.""" return Poly(reversed(self.GetPoints()), self.GetName()) def CutAtClosestPoint(self, p): """ Let x be the point on the polyline closest to p. Then CutAtClosestPoint returns two new polylines, one representing the polyline from the beginning up to x, and one representing x onwards to the end of the polyline. x is the first point returned in the second polyline. """ (closest, i) = self.GetClosestPoint(p) tmp = [closest] tmp.extend(self._points[i+1:]) return (Poly(self._points[0:i+1]), Poly(tmp)) def GreedyPolyMatchDist(self, shape): """ Tries a greedy matching algorithm to match self to the given shape. Returns the maximum distance in meters of any point in self to its matched point in shape under the algorithm. Args: shape, a Poly object. """ tmp_shape = Poly(shape.GetPoints()) max_radius = 0 for (i, point) in enumerate(self._points): tmp_shape = tmp_shape.CutAtClosestPoint(point)[1] dist = tmp_shape.GetPoint(0).GetDistanceMeters(point) max_radius = max(max_radius, dist) return max_radius @staticmethod def MergePolys(polys, merge_point_threshold=10): """ Merge multiple polylines, in the order that they were passed in. Merged polyline will have the names of their component parts joined by ';'. Example: merging [a,b], [c,d] and [e,f] will result in [a,b,c,d,e,f]. However if the endpoints of two adjacent polylines are less than merge_point_threshold meters apart, we will only use the first endpoint in the merged polyline. """ name = ";".join((p.GetName(), '')[p.GetName() is None] for p in polys) merged = Poly([], name) if polys: first_poly = polys[0] for p in first_poly.GetPoints(): merged.AddPoint(p) last_point = merged._GetPointSafe(-1) for poly in polys[1:]: first_point = poly._GetPointSafe(0) if (last_point and first_point and last_point.GetDistanceMeters(first_point) <= merge_point_threshold): points = poly.GetPoints()[1:] else: points = poly.GetPoints() for p in points: merged.AddPoint(p) last_point = merged._GetPointSafe(-1) return merged def __str__(self): return self._ToString(str) def ToLatLngString(self): return self._ToString(lambda p: str(p.ToLatLng())) def _ToString(self, pointToStringFn): return "%s: %s" % (self.GetName() or "", ", ".join([pointToStringFn(p) for p in self._points])) class PolyCollection(object): """ A class representing a collection of polylines. """ def __init__(self): self._name_to_shape = {} pass def AddPoly(self, poly, smart_duplicate_handling=True): """ Adds a new polyline to the collection. """ inserted_name = poly.GetName() if poly.GetName() in self._name_to_shape: if not smart_duplicate_handling: raise ShapeError("Duplicate shape found: " + poly.GetName()) print ("Warning: duplicate shape id being added to collection: " + poly.GetName()) if poly.GreedyPolyMatchDist(self._name_to_shape[poly.GetName()]) < 10: print " (Skipping as it apears to be an exact duplicate)" else: print " (Adding new shape variant with uniquified name)" inserted_name = "%s-%d" % (inserted_name, len(self._name_to_shape)) self._name_to_shape[inserted_name] = poly def NumPolys(self): return len(self._name_to_shape) def FindMatchingPolys(self, start_point, end_point, max_radius=150): """ Returns a list of polylines in the collection that have endpoints within max_radius of the given start and end points. """ matches = [] for shape in self._name_to_shape.itervalues(): if start_point.GetDistanceMeters(shape.GetPoint(0)) < max_radius and \ end_point.GetDistanceMeters(shape.GetPoint(-1)) < max_radius: matches.append(shape) return matches class PolyGraph(PolyCollection): """ A class representing a graph where the edges are polylines. """ def __init__(self): PolyCollection.__in |