Coverage for pygeodesy/clipy.py: 96%

315 statements  

« prev     ^ index     » next       coverage.py v7.6.1, created at 2025-01-06 12:20 -0500

1 

2# -*- coding: utf-8 -*- 

3 

4u'''Clip a path or polygon of C{LatLon} points against a rectangular box or 

5an arbitrary (convex) region. 

6 

7Box clip functions L{clipCS4} I{Cohen-Sutherland} and L{clipLB6} I{Liang-Barsky}, 

8region clip functions L{clipFHP4} I{Foster-Hormann-Popa}, L{clipGH4} 

9I{Greiner-Hormann} and L{clipSH} and L{clipSH3} I{Sutherland-Hodgeman}. 

10. 

11''' 

12# make sure int/int division yields float quotient, see .basics 

13from __future__ import division as _; del _ # PYCHOK semicolon 

14 

15# from pygeodesy.basics import len2 # from .fmath 

16from pygeodesy.constants import EPS, _0_0, _1_0 

17from pygeodesy.errors import _AssertionError, ClipError, PointsError 

18from pygeodesy.fmath import fabs, len2, Fsum 

19# from pygeodesy.fsums import Fsum # from .fmath 

20from pygeodesy.interns import NN, _clipid_, _convex_, _DOT_, _end_, _few_, \ 

21 _fi_, _height_, _i_, _invalid_, _j_, _lat_, \ 

22 _lon_, _near_, _not_, _points_, _start_, _too_ 

23from pygeodesy.iters import _imdex2, points2 

24from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS 

25from pygeodesy.named import _Named, _NamedTuple, _Pass, Property_RO 

26from pygeodesy.points import areaOf, boundsOf, isconvex_, LatLon_ 

27# from pygeodesy.props import Property_RO # from .named 

28from pygeodesy.units import Bool, FIx, HeightX, Lat, Lon, Number_ 

29 

30# from math import fabs # from .fmath 

31 

32__all__ = _ALL_LAZY.clipy 

33__version__ = '23.09.20' 

34 

35_fj_ = 'fj' 

36_original_ = 'original' 

37 

38 

39def _box4(lowerleft, upperight, name): 

40 '''(INTERNAL) Get the clip box edges. 

41 

42 @see: Class C{_Box} in .ellipsoidalBaseDI.py. 

43 ''' 

44 try: 

45 yb, yt = lowerleft.lat, upperight.lat 

46 xl, xr = lowerleft.lon, upperight.lon 

47 if xl > xr or yb > yt: 

48 raise ValueError(_invalid_) 

49 except (AttributeError, TypeError, ValueError) as x: 

50 raise ClipError(name, 2, (lowerleft, upperight), cause=x) 

51 return xl, yb, xr, yt 

52 

53 

54def _4corners(corners): 

55 '''(INTERNAL) Clip region or box. 

56 ''' 

57 n, cs = len2(corners) 

58 if n == 2: # make a box 

59 yb, xl, yt, xr = boundsOf(cs, wrap=False) 

60 cs = (LatLon_(yb, xl), LatLon_(yt, xl), 

61 LatLon_(yt, xr), LatLon_(yb, xr)) 

62 return cs 

63 

64 

65def _eq(p1, p2, eps=EPS): 

66 '''(INTERNAL) Check for near-equal points. 

67 ''' 

68 return not _neq(p1, p2, eps) 

69 

70 

71def _neq(p1, p2, eps=EPS): 

72 '''(INTERNAL) Check for not near-equal points. 

73 ''' 

74 return fabs(p1.lat - p2.lat) > eps or \ 

75 fabs(p1.lon - p2.lon) > eps 

76 

77 

78def _pts2(points, closed, inull): 

79 '''(INTERNAL) Get the points to clip as a list. 

80 ''' 

81 if closed and inull: 

82 n, pts = len2(points) 

83 # only remove the final, closing point 

84 if n > 1 and _eq(pts[n-1], pts[0]): 

85 n -= 1 

86 pts = pts[:n] 

87 if n < 2: 

88 raise PointsError(points=n, txt=_too_(_few_)) 

89 else: 

90 n, pts = points2(points, closed=closed) 

91 return n, list(pts) 

92 

93 

94class _CS(_Named): 

95 '''(INTERNAL) Cohen-Sutherland line clipping. 

96 ''' 

97 # single-bit clip codes 

98 _IN = 0 # inside clip box 

99 _XR = 1 # right of upperight.lon 

100 _XL = 2 # left of lowerleft.lon 

101 _YT = 4 # above upperight.lat 

102 _YB = 8 # below lowerleft.lat 

103 

104 _dx = _0_0 # pts edge delta lon 

105 _dy = _0_0 # pts edge delta lat 

106 _x1 = _0_0 # pts corner 

107 _y1 = _0_0 # pts corner 

108 

109 _xr = _0_0 # clip box upperight.lon 

110 _xl = _0_0 # clip box lowerleft.lon 

111 _yt = _0_0 # clip box upperight.lat 

112 _yb = _0_0 # clip box lowerleft.lat 

113 

114 def __init__(self, lowerleft, upperight, name=__name__): 

115 self._xl, self._yb, \ 

116 self._xr, self._yt = _box4(lowerleft, upperight, name) 

117 self.name = name 

118 

119# def clip4(self, p, c): # clip point p for code c 

120# if c & _CS._YB: 

121# return self.lon4(p, self._yb) 

122# elif c & _CS._YT: 

123# return self.lon4(p, self._yt) 

124# elif c & _CS._XL: 

125# return self.lat4(p, self._xl) 

126# elif c & _CS._XR: 

127# return self.lat4(p, self._xr) 

128# # should never get here 

129# raise _AssertionError(self._DOT_(self.clip4.__name__)) 

130 

131 def code4(self, p): # compute code for point p 

132 if p.lat < self._yb: 

133 c, m, b = _CS._YB, self.lon4, self._yb 

134 elif p.lat > self._yt: 

135 c, m, b = _CS._YT, self.lon4, self._yt 

136 else: 

137 c, m, b = _CS._IN, self.nop4, None 

138 if p.lon < self._xl: 

139 c |= _CS._XL 

140 m, b = self.lat4, self._xl 

141 elif p.lon > self._xr: 

142 c |= _CS._XR 

143 m, b = self.lat4, self._xr 

144 return c, m, b, p 

145 

146 def edge(self, p1, p2): # set edge p1 to p2 

147 self._y1, self._dy = p1.lat, float(p2.lat - p1.lat) 

148 self._x1, self._dx = p1.lon, float(p2.lon - p1.lon) 

149 return fabs(self._dx) > EPS or fabs(self._dy) > EPS 

150 

151 def lat4(self, x, p): # new lat and code at lon x 

152 y = self._y1 + self._dy * float(x - self._x1) / self._dx 

153 if y < self._yb: # still outside 

154 return _CS._YB, self.lon4, self._yb, p 

155 elif y > self._yt: # still outside 

156 return _CS._YT, self.lon4, self._yt, p 

157 else: # inside 

158 return _CS._IN, self.nop4, None, p.classof(y, x) 

159 

160 def lon4(self, y, p): # new lon and code at lat y 

161 x = self._x1 + self._dx * float(y - self._y1) / self._dy 

162 if x < self._xl: # still outside 

163 return _CS._XL, self.lat4, self._xl, p 

164 elif x > self._xr: # still outside 

165 return _CS._XR, self.lat4, self._xr, p 

166 else: # inside 

167 return _CS._IN, self.nop4, None, p.classof(y, x) 

168 

169 def nop4(self, b, p): # PYCHOK no cover 

170 if p: # should never get here 

171 raise _AssertionError(self._DOT_(self.nop4.__name__)) 

172 return _CS._IN, self.nop4, b, p 

173 

174 

175class ClipCS4Tuple(_NamedTuple): 

176 '''4-Tuple C{(start, end, i, j)} for each edge of a I{clipped} 

177 path with the C{start} and C{end} points (C{LatLon}) of the 

178 portion of the edge inside or on the clip box and the indices 

179 C{i} and C{j} (C{int}) of the edge start and end points in 

180 the original path. 

181 ''' 

182 _Names_ = (_start_, _end_, _i_, _j_) 

183 _Units_ = (_Pass, _Pass, Number_, Number_) 

184 

185 

186def clipCS4(points, lowerleft, upperight, closed=False, inull=False): 

187 '''Clip a path against a rectangular clip box using the U{Cohen-Sutherland 

188 <https://WikiPedia.org/wiki/Cohen-Sutherland_algorithm>} algorithm. 

189 

190 @arg points: The points (C{LatLon}[]). 

191 @arg lowerleft: Bottom-left corner of the clip box (C{LatLon}). 

192 @arg upperight: Top-right corner of the clip box (C{LatLon}). 

193 @kwarg closed: Optionally, close the path (C{bool}). 

194 @kwarg inull: Optionally, retain null edges if inside (C{bool}). 

195 

196 @return: Yield a L{ClipCS4Tuple}C{(start, end, i, j)} for each 

197 edge of the I{clipped} path. 

198 

199 @raise ClipError: The B{C{lowerleft}} and B{C{upperight}} corners 

200 specify an invalid clip box. 

201 

202 @raise PointsError: Insufficient number of B{C{points}}. 

203 ''' 

204 T4 = ClipCS4Tuple 

205 cs = _CS(lowerleft, upperight, name=clipCS4.__name__) 

206 n, pts = _pts2(points, closed, inull) 

207 

208 i, m = _imdex2(closed, n) 

209 cmbp = cs.code4(pts[i]) 

210 for j in range(m, n): 

211 c1, m1, b1, p1 = cmbp 

212 c2, m2, b2, p2 = cmbp = cs.code4(pts[j]) 

213 if c1 & c2: # edge outside 

214 pass 

215 elif cs.edge(p1, p2): 

216 for _ in range(5): 

217 if c1: # clip p1 

218 c1, m1, b1, p1 = m1(b1, p1) 

219 elif c2: # clip p2 

220 c2, m2, b2, p2 = m2(b2, p2) 

221 else: # inside 

222 if inull or _neq(p1, p2): 

223 yield T4(p1, p2, i, j) 

224 break 

225 if c1 & c2: # edge outside 

226 break 

227 else: # PYCHOK no cover 

228 raise _AssertionError(_DOT_(cs.name, 'for_else')) 

229 

230 elif inull and not c1: # null edge 

231 yield T4(p1, p1, i, j) 

232 elif inull and not c2: 

233 yield T4(p2, p2, i, j) 

234 

235 i = j 

236 

237 

238class ClipFHP4Tuple(_NamedTuple): 

239 '''4-Tuple C{(lat, lon, height, clipid)} for each point of the 

240 L{clipFHP4} result with the C{lat}-, C{lon}gitude, C{height} 

241 and C{clipid} of the polygon or clip. 

242 

243 @note: The C{height} is a L{HeightX} instance if this point is 

244 an intersection, otherwise a L{Height} or C{int(0)}. 

245 ''' 

246 _Names_ = (_lat_, _lon_, _height_, _clipid_) 

247 _Units_ = ( Lat, Lon, _Pass, Number_) 

248 

249 @Property_RO 

250 def isintersection(self): 

251 '''Is this an intersection? 

252 ''' 

253 return isinstance(self.height, HeightX) 

254 

255 @Property_RO 

256 def ispoint(self): 

257 '''Is this an original (polygon) point? 

258 ''' 

259 return not self.isintersection 

260 

261 

262def clipFHP4(points, corners, closed=False, inull=False, raiser=False, eps=EPS): 

263 '''Clip one or more polygons against a clip region or box using U{Forster-Hormann-Popa 

264 <https://www.ScienceDirect.com/science/article/pii/S259014861930007X>}'s C++ 

265 implementation transcoded to pure Python. 

266 

267 @arg points: The polygon points and clips (C{LatLon}[]). 

268 @arg corners: Three or more points defining the clip regions (C{LatLon}[]) 

269 or two points to specify a single, rectangular clip box. 

270 @kwarg closed: If C{True}, close each result clip (C{bool}). 

271 @kwarg inull: If C{True}, retain null edges in result clips (C{bool}). 

272 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}). 

273 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same units 

274 as the B{C{points}} and B{C{corners}} coordinates). 

275 

276 @return: Yield a L{ClipFHP4Tuple}C{(lat, lon, height, clipid)} for each 

277 clipped point. The result may consist of several clips, each 

278 a (closed) polygon with a unique C{clipid}. 

279 

280 @raise ClipError: Insufficient B{C{points}} or B{C{corners}} or an open clip. 

281 

282 @see: U{Forster, Hormann and Popa<https://www.ScienceDirect.com/science/ 

283 article/pii/S259014861930007X>}, class L{BooleanFHP} and function 

284 L{clipGH4}. 

285 ''' 

286 P = _MODS.booleans._CompositeFHP(points, kind=_points_, raiser=raiser, 

287 eps=eps, name__=clipFHP4) 

288 Q = _4corners(corners) 

289 return P._clip(Q, Union=False, Clas=ClipFHP4Tuple, closed=closed, 

290 inull=inull, raiser=P._raiser, eps=eps) 

291 

292 

293class ClipGH4Tuple(ClipFHP4Tuple): 

294 '''4-Tuple C{(lat, lon, height, clipid)} for each point of the 

295 L{clipGH4} result with the C{lat}-, C{lon}gitude, C{height} 

296 and C{clipid} of the polygon or clip. 

297 

298 @note: The C{height} is a L{HeightX} instance if this is 

299 an intersection, otherwise a L{Height} or C{int(0)}. 

300 ''' 

301 _Names_ = ClipFHP4Tuple._Names_ 

302 _Units_ = ClipFHP4Tuple._Units_ 

303 

304 

305def clipGH4(points, corners, closed=False, inull=False, raiser=True, xtend=False, eps=EPS): 

306 '''Clip one or more polygons against a clip region or box using the U{Greiner-Hormann 

307 <http://www.Inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>} algorithm, U{Correia 

308 <https://GitHub.com/helderco/univ-polyclip>}'s implementation modified and extended. 

309 

310 @arg points: The polygon points and clips (C{LatLon}[]). 

311 @arg corners: Three or more points defining the clip regions (C{LatLon}[]) 

312 or two points to specify a single, rectangular clip box. 

313 @kwarg closed: If C{True}, close each result clip (C{bool}). 

314 @kwarg inull: If C{True}, retain null edges in result clips (C{bool}). 

315 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}). 

316 @kwarg xtend: If C{True}, extend edges of I{degenerate cases}, an attempt 

317 to handle the latter (C{bool}). 

318 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same units 

319 as the B{C{points}} and B{C{corners}} coordinates). 

320 

321 @return: Yield a L{ClipGH4Tuple}C{(lat, lon, height, clipid)} for each 

322 clipped point. The result may consist of several clips, each 

323 a (closed) polygon with a unique C{clipid}. 

324 

325 @raise ClipError: Insufficient B{C{points}} or B{C{corners}}, an open clip, 

326 a I{degenerate case} or I{unhandled} intersection. 

327 

328 @note: To handle I{degenerate cases} like C{point-edge} and C{point-point} 

329 intersections, use function L{clipFHP4}. 

330 

331 @see: U{Greiner-Hormann<https://WikiPedia.org/wiki/Greiner–Hormann_clipping_algorithm>}, 

332 U{Ionel Daniel Stroe<https://Davis.WPI.edu/~matt/courses/clipping/>}, I{Correia}'s 

333 U{univ-polyclip<https://GitHub.com/helderco/univ-polyclip>}, class L{BooleanGH} 

334 and function L{clipFHP4}. 

335 ''' 

336 S = _MODS.booleans._CompositeGH(points, raiser=raiser, xtend=xtend, eps=eps, 

337 name__=clipGH4, kind=_points_) 

338 C = _4corners(corners) 

339 return S._clip(C, False, False, Clas=ClipGH4Tuple, closed=closed, inull=inull, 

340 raiser=S._raiser, xtend=S._xtend, eps=eps) 

341 

342 

343def _LBtrim(p, q, t): 

344 # Liang-Barsky trim t[0] or t[1] 

345 if p < 0: 

346 r = q / p 

347 if r > t[1]: 

348 return False # too far above 

349 elif r > t[0]: 

350 t[0] = r 

351 elif p > 0: 

352 r = q / p 

353 if r < t[0]: 

354 return False # too far below 

355 elif r < t[1]: 

356 t[1] = r 

357 elif q < 0: # vertical or horizontal 

358 return False # ... outside 

359 return True 

360 

361 

362class ClipLB6Tuple(_NamedTuple): 

363 '''6-Tuple C{(start, end, i, fi, fj, j)} for each edge of the 

364 I{clipped} path with the C{start} and C{end} points (C{LatLon}) 

365 of the portion of the edge inside or on the clip box, indices 

366 C{i} and C{j} (both C{int}) of the original path edge start 

367 and end points and I{fractional} indices C{fi} and C{fj} 

368 (both L{FIx}) of the C{start} and C{end} points along the 

369 edge of the original path. 

370 

371 @see: Class L{FIx} and function L{pygeodesy.fractional}. 

372 ''' 

373 _Names_ = (_start_, _end_, _i_, _fi_, _fj_, _j_) 

374 _Units_ = (_Pass, _Pass, Number_, _Pass, _Pass, Number_) 

375 

376 

377def clipLB6(points, lowerleft, upperight, closed=False, inull=False): 

378 '''Clip a path against a rectangular clip box using the U{Liang-Barsky 

379 <https://www.CSE.UNT.edu/~renka/4230/LineClipping.pdf>} algorithm. 

380 

381 @arg points: The points (C{LatLon}[]). 

382 @arg lowerleft: Bottom-left corner of the clip box (C{LatLon}). 

383 @arg upperight: Top-right corner of the clip box (C{LatLon}). 

384 @kwarg closed: Optionally, close the path (C{bool}). 

385 @kwarg inull: Optionally, retain null edges if inside (C{bool}). 

386 

387 @return: Yield a L{ClipLB6Tuple}C{(start, end, i, fi, fj, j)} for 

388 each edge of the I{clipped} path. 

389 

390 @raise ClipError: The B{C{lowerleft}} and B{C{upperight}} corners 

391 specify an invalid clip box. 

392 

393 @raise PointsError: Insufficient number of B{C{points}}. 

394 

395 @see: U{Liang-Barsky Line Clipping<https://www.CS.Helsinki.FI/group/goa/ 

396 viewing/leikkaus/intro.html>}, U{Liang-Barsky line clipping algorithm 

397 <https://www.Skytopia.com/project/articles/compsci/clipping.html>} and 

398 U{Liang-Barsky algorithm<https://WikiPedia.org/wiki/Liang-Barsky_algorithm>}. 

399 ''' 

400 xl, yb, \ 

401 xr, yt = _box4(lowerleft, upperight, clipLB6.__name__) 

402 n, pts = _pts2(points, closed, inull) 

403 

404 T6 = ClipLB6Tuple 

405 fin = n if closed else None # wrapping fi [n] to [0] 

406 _LB = _LBtrim 

407 

408 i, m = _imdex2(closed, n) 

409 for j in range(m, n): 

410 p1 = pts[i] 

411 y1 = p1.lat 

412 x1 = p1.lon 

413 

414 p2 = pts[j] 

415 dy = float(p2.lat - y1) 

416 dx = float(p2.lon - x1) 

417 if fabs(dx) > EPS or fabs(dy) > EPS: 

418 # non-null edge pts[i]...pts[j] 

419 t = [_0_0, _1_0] 

420 if _LB(-dx, -xl + x1, t) and \ 

421 _LB( dx, xr - x1, t) and \ 

422 _LB(-dy, -yb + y1, t) and \ 

423 _LB( dy, yt - y1, t): 

424 # clip edge pts[i]...pts[j] 

425 # at fractions t[0] to t[1] 

426 f, t = t 

427 if f > _0_0: # EPS 

428 p1 = p1.classof(y1 + f * dy, 

429 x1 + f * dx) 

430 fi = i + f 

431 else: 

432 fi = i 

433 

434 if (t - f) > EPS: # EPS0 

435 if t < _1_0: # EPS1 

436 p2 = p2.classof(y1 + t * dy, 

437 x1 + t * dx) 

438 fj = i + t 

439 else: 

440 fj = j 

441 fi = FIx(fi, fin=fin) 

442 fj = FIx(fj, fin=fin) 

443 yield T6(p1, p2, i, fi, fj, j) 

444 

445 elif inull: 

446 fi = FIx(fi, fin=fin) 

447 yield T6(p1, p1, i, fi, fi, j) 

448# else: # outside 

449# pass 

450 elif inull: # null edge 

451 yield T6(p1, p2, i, FIx(i, fin=fin), 

452 FIx(j, fin=fin), j) 

453 i = j 

454 

455 

456class _SH(_Named): 

457 '''(INTERNAL) Sutherland-Hodgman polyon clipping. 

458 ''' 

459 _cs = () # clip corners 

460 _cw = 0 # counter-/clockwise 

461 _ccw = 0 # clock-/counterwise 

462 _dx = _0_0 # clip edge[e] delta lon 

463 _dy = _0_0 # clip edge[e] delta lat 

464 _nc = 0 # len(._cs) 

465 _x1 = _0_0 # clip edge[e] lon origin 

466 _xy = _0_0 # see .clipedges 

467 _y1 = _0_0 # clip edge[e] lat origin 

468 

469 def __init__(self, corners, name=__name__): 

470 n, cs = 0, corners 

471 try: # check the clip box/region 

472 cs = _4corners(cs) 

473 n, cs = len2(cs) 

474 n, cs = points2(cs, closed=True) 

475 self._cs = cs = cs[:n] 

476 self._nc = n 

477 self._cw = isconvex_(cs, adjust=False, wrap=False) 

478 if not self._cw: 

479 raise ValueError(_not_(_convex_)) 

480 if areaOf(cs, adjust=True, radius=1, wrap=True) < EPS: 

481 raise ValueError(NN(_near_, 'zero area')) 

482 self._ccw = -self._cw 

483 except (PointsError, TypeError, ValueError) as x: 

484 raise ClipError(name, n, cs, cause=x) 

485 self.name = name 

486 

487 def clip2(self, points, closed, inull): # MCCABE 13, clip points 

488 np, pts = _pts2(points, closed, inull) 

489 pcs = _SHlist(inull) # clipped points 

490 _ap = pcs.append 

491 _d2 = self.dot2 

492 _in = self.intersect 

493 

494 ne = 0 # number of non-null clip edges 

495 for e in self.clipedges(): 

496 ne += 1 # non-null clip edge 

497 

498 # clip points, closed always 

499 d1, p1 = _d2(pts[np - 1]) 

500 for i in range(np): 

501 d2, p2 = _d2(pts[i]) 

502 if d1 < 0: # p1 inside, p2 ... 

503 # _ap(p1) 

504 _ap(p2 if d2 < 0 else # ... in- 

505 _in(p1, p2, e)) # ... outside 

506 elif d2 < 0: # p1 out-, p2 inside 

507 _ap(_in(p1, p2, e)) 

508 _ap(p2) 

509# elif d1 > 0: # both outside 

510# pass 

511 d1, p1 = d2, p2 

512 

513 # replace points, in-place 

514 pts[:] = pcs 

515 pcs[:] = [] 

516 np = len(pts) 

517 if not np: # all outside 

518 break 

519 else: 

520 if ne < 3: 

521 raise ClipError(self.name, ne, self._cs, txt=_too_(_few_)) 

522 

523 if np > 1: 

524 p = pts[0] 

525 if closed: # close clipped pts 

526 if _neq(pts[np - 1], p): 

527 pts.append(p) 

528 np += 1 

529 elif not inull: # open clipped pts 

530 while np > 0 and _eq(pts[np - 1], p): 

531 pts.pop() 

532 np -= 1 

533 # assert len(pts) == np 

534 return np, pts 

535 

536 def clipedges(self): # yield clip edge index 

537 # and set self._x1, ._y1, ._dx, ._dy and 

538 # ._xy for each non-null clip edge 

539 nc = self._nc 

540 cs = self._cs 

541 c = cs[nc - 1] 

542 for e in range(nc): 

543 y, x, c = c.lat, c.lon, cs[e] 

544 dy = float(c.lat - y) 

545 dx = float(c.lon - x) 

546 if fabs(dx) > EPS or fabs(dy) > EPS: 

547 self._y1, self._dy = y, dy 

548 self._x1, self._dx = x, dx 

549 self._xy = y * dx - x * dy 

550 yield e + 1 

551 

552 def clipped2(self, p): # return (clipped point [i], edge) 

553 if isinstance(p, _SHlli): # intersection point 

554 return p.classof(p.lat, p.lon), p.edge 

555 else: # original point 

556 return p, 0 

557 

558 def dot2(self, p): # dot product of point p to clip 

559 # corner c1 and clip edge c1 to c2, indicating where 

560 # point p is located: to the right, to the left or 

561 # on top of the (extended) clip edge from c1 to c2 

562 d = float(p.lat - self._y1) * self._dx - \ 

563 float(p.lon - self._x1) * self._dy 

564 # clockwise corners, +1 means point p is to the right 

565 # of, -1 means on the left of, 0 means on edge c1 to c2 

566 d = self._ccw if d < 0 else (self._cw if d > 0 else 0) 

567 return d, p 

568 

569 def intersect(self, p1, p2, edge): # compute intersection 

570 # of polygon edge p1 to p2 and the current clip edge, 

571 # where p1 and p2 are known to NOT be located on the 

572 # same side of or on the current, non-null clip edge 

573 # <https://StackOverflow.com/questions/563198/ 

574 # how-do-you-detect-where-two-line-segments-intersect> 

575 y, dy = p1.lat, self._dy 

576 x, dx = p1.lon, self._dx 

577 fy = float(p2.lat - y) 

578 fx = float(p2.lon - x) 

579 d = fy * dx - fx * dy # fdot((fx, fy), dx, -dy) 

580 if fabs(d) < EPS: # PYCHOK no cover 

581 raise _AssertionError(self._DOT_(self.intersect.__name__)) 

582 d = Fsum(self._xy, -y * dx, x * dy).fover(d) 

583 y += d * fy 

584 x += d * fx 

585 return _SHlli(y, x, p1.classof, edge) 

586 

587 

588class _SHlist(list): 

589 '''(INTERNAL) List of _SH clipped points. 

590 ''' 

591 _inull = False 

592 

593 def __init__(self, inull): 

594 self._inull = inull 

595 list.__init__(self) 

596 

597 def append(self, p): 

598 if (not self) or self._inull or _neq(p, self[-1]): 

599 list.append(self, p) 

600 

601 

602class _SHlli(LatLon_): 

603 '''(INTERNAL) LatLon_ for _SH intersections. 

604 ''' 

605 # __slots__ are no longer space savers, see 

606 # the comments at the class .points.LatLon_ 

607 # __slots__ = _lat_, _lon_, 'classof', 'edge', _name_ 

608 

609 def __init__(self, lat, lon, classof, edge): 

610 self.lat = lat 

611 self.lon = lon 

612 self.classof = classof 

613 self.edge = edge # clip edge 

614 self.name = NN 

615 

616 

617class ClipSH3Tuple(_NamedTuple): 

618 '''3-Tuple C{(start, end, original)} for each edge of a I{clipped} 

619 polygon, the C{start} and C{end} points (C{LatLon}) of the 

620 portion of the edge inside or on the clip region and C{original} 

621 indicates whether the edge is part of the original polygon or 

622 part of the clip region (C{bool}). 

623 ''' 

624 _Names_ = (_start_, _end_, _original_) 

625 _Units_ = (_Pass, _Pass, Bool) 

626 

627 

628def clipSH(points, corners, closed=False, inull=False): 

629 '''Clip a polygon against a clip region or box using the U{Sutherland-Hodgman 

630 <https://WikiPedia.org/wiki/Sutherland-Hodgman_algorithm>} algorithm. 

631 

632 @arg points: The polygon points (C{LatLon}[]). 

633 @arg corners: Three or more points defining a convex clip 

634 region (C{LatLon}[]) or two points to specify 

635 a rectangular clip box. 

636 @kwarg closed: Close the clipped points (C{bool}). 

637 @kwarg inull: Optionally, include null edges (C{bool}). 

638 

639 @return: Yield the clipped points (C{LatLon}[]). 

640 

641 @raise ClipError: The B{C{corners}} specify a polar, zero-area, 

642 non-convex or otherwise invalid clip box or 

643 region. 

644 

645 @raise PointsError: Insufficient number of B{C{points}}. 

646 ''' 

647 sh = _SH(corners, name=clipSH.__name__) 

648 n, pts = sh.clip2(points, closed, inull) 

649 for i in range(n): 

650 p, _ = sh.clipped2(pts[i]) 

651 yield p 

652 

653 

654def clipSH3(points, corners, closed=False, inull=False): 

655 '''Clip a polygon against a clip region or box using the U{Sutherland-Hodgman 

656 <https://WikiPedia.org/wiki/Sutherland-Hodgman_algorithm>} algorithm. 

657 

658 @arg points: The polygon points (C{LatLon}[]). 

659 @arg corners: Three or more points defining a convex clip 

660 region (C{LatLon}[]) or two points to specify 

661 a rectangular clip box. 

662 @kwarg closed: Close the clipped points (C{bool}). 

663 @kwarg inull: Optionally, include null edges (C{bool}). 

664 

665 @return: Yield a L{ClipSH3Tuple}C{(start, end, original)} for 

666 each edge of the I{clipped} polygon. 

667 

668 @raise ClipError: The B{C{corners}} specify a polar, zero-area, 

669 non-convex or otherwise invalid clip box or 

670 region. 

671 

672 @raise PointsError: Insufficient number of B{C{points}} or B{C{corners}}. 

673 ''' 

674 sh = _SH(corners, name=clipSH3.__name__) 

675 n, pts = sh.clip2(points, closed, inull) 

676 if n > 1: 

677 T3 = ClipSH3Tuple 

678 p1, e1 = sh.clipped2(pts[0]) 

679 for i in range(1, n): 

680 p2, e2 = sh.clipped2(pts[i]) 

681 yield T3(p1, p2, not bool(e1 and e2 and e1 == e2)) 

682 p1, e1 = p2, e2 

683 

684# **) MIT License 

685# 

686# Copyright (C) 2018-2025 -- mrJean1 at Gmail -- All Rights Reserved. 

687# 

688# Permission is hereby granted, free of charge, to any person obtaining a 

689# copy of this software and associated documentation files (the "Software"), 

690# to deal in the Software without restriction, including without limitation 

691# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

692# and/or sell copies of the Software, and to permit persons to whom the 

693# Software is furnished to do so, subject to the following conditions: 

694# 

695# The above copyright notice and this permission notice shall be included 

696# in all copies or substantial portions of the Software. 

697# 

698# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

699# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

700# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

701# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

702# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

703# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

704# OTHER DEALINGS IN THE SOFTWARE.