Coverage for pygeodesy/booleans.py: 94%
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2# -*- coding: utf-8 -*-
4u'''I{Boolean} operations on I{composite} polygons and I{clip}s.
6Classes L{BooleanFHP} and L{BooleanGH} are I{composites} and
7provide I{boolean} operations C{intersection}, C{difference},
8C{reverse-difference}, C{sum} and C{union}.
10@note: A I{clip} is defined as a single, usually closed polygon,
11 a I{composite} is a collection of one or more I{clip}s.
13@see: U{Forster-Hormann-Popa<https://www.ScienceDirect.com/science/
14 article/pii/S259014861930007X>} and U{Greiner-Hormann
15 <http://www.Inf.USI.CH/hormann/papers/Greiner.1998.ECO.pdf>}.
16'''
17# make sure int/int division yields float quotient, see .basics
18from __future__ import division as _; del _ # PYCHOK semicolon
20from pygeodesy.basics import isodd, issubclassof, map2, _xscalar
21from pygeodesy.constants import EPS, EPS2, INT0, _0_0, _0_5, _1_0
22from pygeodesy.errors import ClipError, _IsnotError, _TypeError, \
23 _ValueError, _xattr, _xkwds_get
24from pygeodesy.fmath import favg, hypot, hypot2
25# from pygeodesy.fsums import fsum1 # _MODS
26from pygeodesy.interns import NN, _BANG_, _clip_, _clipid_, _COMMASPACE_, \
27 _composite_, _DOT_, _e_, _ELLIPSIS_, _few_, \
28 _height_, _lat_, _LatLon_, _lon_, _not_, \
29 _points_, _SPACE_, _too_, _X_, _x_, \
30 _B_, _d_, _R_ # PYCHOK used!
31from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
32from pygeodesy.latlonBase import LatLonBase, \
33 LatLon2Tuple, Property_RO, property_RO
34from pygeodesy.named import Fmt, _Named, _NotImplemented, pairs, unstr
35# from pygeodesy.namedTuples import LatLon2Tupe # from .latlonBase
36# from pygeodesy.points import boundsOf # _MODS
37# from pygeodesy.props import Property_RO, property_RO # from .latlonBase
38# from pygeodesy.streprs import Fmt, pairs, unstr # from .named
39from pygeodesy.units import Height, HeightX
40from pygeodesy.utily import fabs, _unrollon, _Wrap
42# from math import fabs # from .utily
44__all__ = _ALL_LAZY.booleans
45__version__ = '24.05.15'
47_0_EPS = EPS # near-zero, positive
48_EPS_0 = -EPS # near-zero, negative
49_1_EPS = _1_0 + EPS # near-one, over
50_EPS_1 = _1_0 - EPS # near-one, under
51_10EPS = EPS * 10 # see ._2Abs, ._10eps
53_alpha_ = 'alpha'
54_boolean_ = 'boolean'
55_case_ = 'case'
56_corners_ = 'corners'
57_duplicate_ = 'duplicate'
58_open_ = 'open'
61def _Enum(txt, enum): # PYCHOK unused
62 return txt # NN(txt, _TILDE_, enum)
65class _L(object): # Intersection labels
66 CROSSING = _Enum(_X_, 1) # C++ enum
67 CROSSING_D = _Enum(_X_ + _d_, 8)
68 CROSSINGs = (CROSSING, CROSSING_D)
69 BOUNCING = _Enum(_B_, 2)
70 BOUNCING_D = _Enum(_B_ + _d_, 9)
71 BOUNCINGs = (BOUNCING, BOUNCING_D) + CROSSINGs
72 LEFT_ON = _Enum('Lo', 3)
73 ON_ON = _Enum('oo', 5)
74 ON_LEFT = _Enum('oL', 6)
75 ON_RIGHT = _Enum('oR', 7)
76 RIGHT_ON = _Enum('Ro', 4)
77 RIGHT_LEFT_ON = (RIGHT_ON, LEFT_ON)
78 # Entry/Exit flags
79 ENTRY = _Enum(_e_, 1)
80 EXIT = _Enum(_x_, 0)
81 Toggle = {ENTRY: EXIT,
82 EXIT: ENTRY,
83 None: None}
85_L = _L() # PYCHOK singleton
88class _RP(object): # RelativePositions
89 IS_Pm = _Enum('Pm', 2) # C++ enum
90 IS_Pp = _Enum('Pp', 3)
91 LEFT = _Enum('L', 0)
92 RIGHT = _Enum(_R_, 1)
94_RP = _RP() # PYCHOK singleton
96_RP2L = {(_RP.LEFT, _RP.RIGHT): _L.CROSSING,
97 (_RP.RIGHT, _RP.LEFT): _L.CROSSING,
98 (_RP.LEFT, _RP.LEFT): _L.BOUNCING,
99 (_RP.RIGHT, _RP.RIGHT): _L.BOUNCING,
100 # overlapping cases
101 (_RP.RIGHT, _RP.IS_Pp): _L.LEFT_ON,
102 (_RP.IS_Pp, _RP.RIGHT): _L.LEFT_ON,
103 (_RP.LEFT, _RP.IS_Pp): _L.RIGHT_ON,
104 (_RP.IS_Pp, _RP.LEFT): _L.RIGHT_ON,
105 (_RP.IS_Pm, _RP.IS_Pp): _L.ON_ON,
106 (_RP.IS_Pp, _RP.IS_Pm): _L.ON_ON,
107 (_RP.IS_Pm, _RP.RIGHT): _L.ON_LEFT,
108 (_RP.RIGHT, _RP.IS_Pm): _L.ON_LEFT,
109 (_RP.LEFT, _RP.IS_Pm): _L.ON_RIGHT,
110 (_RP.IS_Pm, _RP.LEFT): _L.ON_RIGHT}
113class _LatLonBool(_Named):
114 '''(INTERNAL) Base class for L{LatLonFHP} and L{LatLonGH}.
115 '''
116 _alpha = None # point AND intersection else length
117 _checked = False # checked in phase 3 iff intersection
118 _clipid = INT0 # (polygonal) clip identifier, number
119 _dupof = None # original of a duplicate
120# _e_x_str = NN # shut up PyChecker
121 _height = Height(0) # interpolated height, usually meter
122 _linked = None # link to neighbor iff intersection
123 _next = None # link to the next vertex
124 _prev = None # link to the previous vertex
126 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0,
127 wrap=False, name=NN):
128 '''New C{LatLon[FHP|GH]} from separate C{lat}, C{lon}, C{height}
129 and C{clipid} scalars or from a previous C{LatLon[FHP|GH]},
130 a C{Clip[FHP|GH]4Tuple} or some other C{LatLon} instance.
132 @arg lat_ll: Latitude (C{scalar}) or a lat/longitude
133 (C{LatLon[FHP|GH]}, aC{Clip[FHP|GH]4Tuple}
134 or some other C{LatLon}).
135 @kwarg lon: Longitude (C{scalar}), iff B{C{lat_ll}} is
136 scalar, ignored otherwise.
137 @kwarg height: Height (C{scalar}), conventionally C{meter}.
138 @kwarg clipid: Clip identifier (C{int}).
139 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}}
140 and B{C{lon}} (C{bool}).
141 @kwarg name: Optional name (C{str}).
142 '''
143 if lon is None:
144 y, x = lat_ll.lat, lat_ll.lon
145 h = _xattr(lat_ll, height=height)
146 c = _xattr(lat_ll, clipid=clipid)
147 else:
148 y, x = lat_ll, lon
149 h, c = height, clipid
150 self.y, self.x = _Wrap.latlon(y, x) if wrap else (y, x)
151 # don't duplicate defaults
152 if self._height != h:
153 self._height = h
154 if self._clipid != c:
155 self._clipid = c
156 if name:
157 self.name = name
159 def __abs__(self):
160 return max(fabs(self.x), fabs(self.y))
162 def __eq__(self, other):
163 return other is self or bool(_other(self, other) and
164 other.x == self.x and
165 other.y == self.y)
167 def __ne__(self, other): # required for Python 2
168 return not self.__eq__(other)
170 def __repr__(self):
171 '''String C{repr} of this lat-/longitude.
172 '''
173 if self._prev or self._next:
174 t = _ELLIPSIS_(self._prev, self._next)
175 t = _SPACE_(self, Fmt.ANGLE(t))
176 else:
177 t = str(self)
178 return t
180 def __str__(self):
181 '''String C{str} of this lat-/longitude.
182 '''
183 t = (_lat_, self.lat), (_lon_, self.lon)
184 if self._height:
185 X = _X_ if self.isintersection else NN
186 t += (_height_ + X, self._height),
187 if self._clipid:
188 t += (_clipid_, self._clipid),
189 if self._alpha is not None:
190 t += (_alpha_, self._alpha),
191# if self._dupof: # recursion risk
192# t += (_dupof_, self._dupof.name),
193 t = pairs(t, prec=8, fmt=Fmt.g, ints=True)
194 t = Fmt.PAREN(_COMMASPACE_.join(t))
195 if self._linked:
196 k = _DOT_ if self._checked else _BANG_
197 t = NN(t, self._e_x_str(k)) # PYCHOK expected
198 return NN(self.name, t)
200 def __sub__(self, other):
201 _other(self, other)
202 return self.__class__(self.y - other.y, # classof
203 self.x - other.x)
205 def _2A(self, p2, p3):
206 # I{Signed} area of a triangle, I{doubled}.
207 x, y = self.x, self.y
208 return (p2.x - x) * (p3.y - y) - \
209 (p3.x - x) * (p2.y - y)
211 def _2Abs(self, p2, p3, eps=_10EPS):
212 # I{Unsigned} area of a triangle, I{doubled}
213 # or 0 if below the given threshold C{eps}.
214 a = fabs(self._2A(p2, p3))
215 return 0 if a < eps else a
217 @property_RO
218 def clipid(self):
219 '''Get the I{clipid} (C{int} or C{0}).
220 '''
221 return self._clipid
223 def _equi(self, llb, eps):
224 # Is this LLB I{equivalent} to B{C{llb}} within
225 # the given I{non-negative} tolerance B{C{eps}}?
226 return not (fabs(llb.lon - self.x) > eps or
227 fabs(llb.lat - self.y) > eps)
229 @property_RO
230 def height(self):
231 '''Get the I{height} (C{Height} or C{int}).
232 '''
233 h = self._height
234 return HeightX(h) if self.isintersection else (
235 Height(h) if h else _LatLonBool._height)
237 def isequalTo(self, other, eps=None):
238 '''Is this point equal to an B{C{other}} within a given,
239 I{non-negative} tolerance, ignoring C{height}?
241 @arg other: The other point (C{LatLon}).
242 @kwarg eps: Tolerance for equality (C{degrees} or C{None}).
244 @return: C{True} if equivalent, C{False} otherwise (C{bool}).
246 @raise TypeError: Invalid B{C{other}}.
247 '''
248 try:
249 return self._equi(other, _eps0(eps))
250 except (AttributeError, TypeError, ValueError):
251 raise _IsnotError(_LatLon_, other=other)
253 @property_RO
254 def isintersection(self):
255 '''Is this an intersection? May be C{ispoint} too!
256 '''
257 return bool(self._linked)
259 @property_RO
260 def ispoint(self):
261 '''Is this an I{original} point? May be C{isintersection} too!
262 '''
263 return self._alpha is None
265 @property_RO
266 def lat(self):
267 '''Get the latitude (C{scalar}).
268 '''
269 return self.y
271 @property_RO
272 def latlon(self):
273 '''Get the lat- and longitude (L{LatLon2Tuple}).
274 '''
275 return LatLon2Tuple(self.y, self.x)
277 def _link(self, other):
278 # Make this and an other point neighbors.
279 # assert _other(self, other)
280 self._linked = other
281 other._linked = self
283 @property_RO
284 def lon(self):
285 '''Get the longitude (C{scalar}).
286 '''
287 return self.x
289 def _toClas(self, Clas, clipid):
290 # Return this vertex as a C{Clas} instance
291 # (L{Clip[FHP|GH]4Tuple} or L{LatLon[FHP|GH]}).
292 return Clas(self.lat, self.lon, self.height, clipid)
295class LatLonFHP(_LatLonBool):
296 '''A point or intersection in a L{BooleanFHP} clip or composite.
297 '''
298 _en_ex = None
299 _label = None
300 _2split = None # or C{._Clip}
301 _2xing = False
303 def __init__(self, lat_ll, *lon_h_clipid, **wrap_name):
304 '''New C{LatLonFHP} from separate C{lat}, C{lon}, C{h}eight
305 and C{clipid} scalars, or from a previous L{LatLonFHP},
306 a L{ClipFHP4Tuple} or some other C{LatLon} instance.
308 @arg lat_ll: Latitude (C{scalar}) or a lat/longitude
309 (L{LatLonFHP}, C{LatLon} or L{ClipFHP4Tuple}).
310 @arg lon_h_clipid: Longitude (C{scalar}), C{h}eight and
311 C{clipid} iff B{C{lat_ll}} is scalar,
312 ignored otherwise.
313 @kwarg wrap_name: Keyword arguments C{B{wrap}=False} and
314 C{B{name}=NN}. If C{B{wrap} is True}, wrap
315 or I{normalize} the lat- and longitude
316 (C{bool}). Optional B{C{name}} (C{str}).
317 '''
318 _LatLonBool.__init__(self, lat_ll, *lon_h_clipid, **wrap_name)
320 def __add__(self, other):
321 _other(self, other)
322 return self.__class__(self.y + other.y, self.x + other.x)
324 def __mod__(self, other): # cross product
325 _other(self, other)
326 return self.x * other.y - self.y * other.x
328 def __mul__(self, other): # dot product
329 _other(self, other)
330 return self.x * other.x + self.y * other.y
332 def __rmul__(self, other): # scalar product
333 _xscalar(other=other)
334 return self.__class__(self.y * other, self.x * other)
336 def _e_x_str(self, t): # PYCHOK no cover
337 if self._label:
338 t = NN(self._label, t)
339 if self._en_ex:
340 t = NN(t, self._en_ex)
341 return t
343 @property_RO
344 def _isduplicate(self):
345 # Is this point a I{duplicate} intersection?
346 p = self._dupof
347 return bool(p and self._linked
348 and p is not self
349 and p == self
350# and p._alpha in (None, self._alpha)
351 and self._alpha in (_0_0, p._alpha))
353# @property_RO
354# def _isduplicated(self):
355# # Return the number of I{duplicates}?
356# d, v = 0, self
357# while v:
358# if v._dupof is self:
359# d += 1
360# v = v._next
361# if v is self:
362# break
363# return d
365 def isenclosedBy(self, *composites_points, **wrap):
366 '''Is this point inside one or more composites or polygons based
367 the U{winding number<https://www.ScienceDirect.com/science/
368 article/pii/S0925772101000128>}?
370 @arg composites_points: Composites and/or iterables of points
371 (L{ClipFHP4Tuple}, L{ClipGH4Tuple}, L{LatLonFHP},
372 L{LatLonGH} or any C{LatLon}).
373 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
374 C{points} (C{bool}).
376 @raise ValueError: Some C{points} invalid.
378 @see: U{Algorithm 6<https://www.ScienceDirect.com/science/
379 article/pii/S0925772101000128>}.
380 '''
381 class _Pseudo(object):
382 # Pseudo-_CompositeBase._clips tuple
384 @property_RO
385 def _clips(self):
386 for cp in _Cps(_CompositeFHP, composites_points,
387 LatLonFHP.isenclosedBy): # PYCHOK yield
388 for c in cp._clips:
389 yield c
391 return self._isinside(_Pseudo(), **wrap)
393 def _isinside(self, composite, *excludes, **wrap):
394 # Is this point inside a composite, excluding
395 # certain C{_Clip}s? I{winding number}?
396 x, y, i = self.x, self.y, False
397 for c in composite._clips:
398 if c not in excludes:
399 w = 0
400 for p1, p2 in c._edges2(**wrap):
401 # edge [p1,p2] must straddle y
402 if (p1.y < y) is not (p2.y < y): # or ^
403 r = p2.x > x
404 s = p2.y > p1.y
405 if p1.x < x:
406 b = r and (s is (p1._2A(p2, self) > 0))
407 else:
408 b = r or (s is (p1._2A(p2, self) > 0))
409 if b:
410 w += 1 if s else -1
411 if isodd(w):
412 i = not i
413 return i
415 @property_RO
416 def _prev_next2(self):
417 # Adjust 2-tuple (._prev, ._next) iff a I{duplicate} intersection
418 p, n = self, self._next
419 if self._isduplicate:
420 p = self._dupof
421 while p._isduplicate:
422 p = p._dupof
423 while n._isduplicate:
424 n = n._next
425 return p._prev, n
427# def _edge2(self):
428# # Return the start and end point of the
429# # edge containing I{intersection} C{v}.
430# n = p = self
431# while p.isintersection:
432# p = p._prev
433# if p is self:
434# break
435# while n.isintersection:
436# n = n._next
437# if n is self:
438# break
439# # assert p == self or not p._2Abs(self, n)
440# return p, n
442 def _RPoracle(self, p1, p2, p3):
443 # Relative Position oracle
444 if p1._linked is self: # or p1._linked2(self):
445 T = _RP.IS_Pm
446 elif p3._linked is self: # or p3._linked2(self):
447 T = _RP.IS_Pp
448 elif p1._2A(p2, p3) > 0: # left turn
449 T = _RP.LEFT if self._2A(p1, p2) > 0 and \
450 self._2A(p2, p3) > 0 else \
451 _RP.RIGHT # PYCHOK indent
452 else: # right turn (or straight)
453 T = _RP.RIGHT if self._2A(p1, p2) < 0 and \
454 self._2A(p2, p3) < 0 else \
455 _RP.LEFT # PYCHOK indent
456 return T
459class LatLonGH(_LatLonBool):
460 '''A point or intersection in a L{BooleanGH} clip or composite.
461 '''
462 _entry = None # entry or exit iff intersection
464 def __init__(self, lat_ll, *lon_h_clipid, **wrap_name):
465 '''New C{LatLonGH} from separate C{lat}, C{lon}, C{h}eight
466 and C{clipid} scalars, or from a previous L{LatLonGH},
467 L{ClipGH4Tuple} or some other C{LatLon} instance.
469 @arg lat_ll: Latitude (C{scalar}) or a lat/longitude
470 (L{LatLonGH}, C{LatLon} or L{ClipGH4Tuple}).
471 @arg lon_h_clipid: Longitude (C{scalar}), C{h}eight and
472 C{clipid} iff B{C{lat_ll}} is scalar,
473 ignored otherwise.
474 @kwarg wrap_name: Keyword arguments C{B{wrap}=False} and
475 C{B{name}=NN}. If C{B{wrap} is True}, wrap
476 or I{normalize} the lat- and longitude
477 (C{bool}). Optional B{C{name}} (C{str}).
478 '''
479 _LatLonBool.__init__(self, lat_ll, *lon_h_clipid, **wrap_name)
481 def _check(self):
482 # Check-mark this vertex and its link.
483 self._checked = True
484 k = self._linked
485 if k and not k._checked:
486 k._checked = True
488 def _e_x_str(self, t): # PYCHOK no cover
489 return t if self._entry is None else NN(t,
490 (_e_ if self._entry else _x_))
492 def isenclosedBy(self, *composites_points, **wrap):
493 '''Is this point inside one or more composites or polygons based
494 on the U{even-odd-rule<https://www.ScienceDirect.com/science/
495 article/pii/S0925772101000128>}?
497 @arg composites_points: Composites and/or iterables of points
498 (L{ClipFHP4Tuple}, L{ClipGH4Tuple}, L{LatLonFHP},
499 L{LatLonGH} or any C{LatLon}).
500 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
501 C{points} (C{bool}).
503 @raise ValueError: Some B{C{points}} invalid.
504 '''
505 class _Pseudo(object):
506 # Pseudo-_CompositeBase._edges3 method
508 def _edges3(self, **kwds):
509 for cp in _Cps(_CompositeGH, composites_points,
510 LatLonGH.isenclosedBy): # PYCHOK yield
511 for e in cp._edges3(**kwds):
512 yield e
514 return self._isinside(_Pseudo(), **wrap)
516 def _isinside(self, composite, *bottom_top, **wrap):
517 # Is this vertex inside the composite? I{even-odd rule}?
519 def _x(y, p1, p2):
520 # return C{x} at given C{y} on edge [p1,p2]
521 return (y - p1.y) / (p2.y - p1.y) * (p2.x - p1.x)
523 # The I{even-odd} rule counts the number of edges
524 # intersecting a ray emitted from this point to
525 # east-bound infinity. When I{odd} this point lies
526 # inside, if I{even} outside.
527 y, i = self.y, False
528 if not (bottom_top and _outside(y, y, *bottom_top)):
529 x = self.x
530 for p1, p2, _ in composite._edges3(**wrap):
531 if (p1.y < y) is not (p2.y < y): # or ^
532 r = p2.x > x
533 if p1.x < x:
534 b = r and (_x(y, p1, p2) > x)
535 else:
536 b = r or (_x(y, p1, p2) > x)
537 if b:
538 i = not i
539 return i
542class _Clip(_Named):
543 '''(INTERNAL) A I{doubly-linked} list representing a I{closed}
544 polygon of L{LatLonFHP} or L{LatLonGH} points, duplicates
545 and intersections with other clips.
546 '''
547 _composite = None
548 _dups = 0
549 _first = None
550 _id = 0
551 _identical = False
552 _noInters = False
553 _last = None
554 _LL = None
555 _len = 0
556 _pushback = False
558 def __init__(self, composite, clipid=INT0):
559 '''(INTERNAL) New C{_Clip}.
560 '''
561 # assert isinstance(composite, _CompositeBase)
562 if clipid in composite._clipids:
563 raise ClipError(clipid=clipid, txt=_duplicate_)
564 self._composite = composite
565 self._id = clipid
566 self._LL = composite._LL
567 composite._clips = composite._clips + (self,)
569 def __contains__(self, point): # PYCHOK no cover
570 '''Is the B{C{point}} in this clip?
571 '''
572 for v in self:
573 if v is point: # or ==?
574 return True
575 return False
577 def __eq__(self, other):
578 '''Is this clip I{equivalent} to an B{C{other}} clip,
579 do both have the same C{len}, the same points, in
580 the same order, possibly rotated?
581 '''
582 return self._equi(_other(self, other), 0)
584 def __ge__(self, other):
585 '''See method C{__lt__}.
586 '''
587 return not self.__lt__(other)
589 def __gt__(self, other):
590 '''Is this clip C{"above"} an B{C{other}} clip,
591 located or stretched farther North or East?
592 '''
593 return self._bltr4 > _other(self, other)._bltr4
595 def __hash__(self): # PYCHOK no over
596 return hash(self._bltr4)
598 def __iter__(self):
599 '''Yield the points, duplicates and intersections.
600 '''
601 v = f = self._first
602 while v:
603 yield v
604 v = v._next
605 if v is f:
606 break
608 def __le__(self, other):
609 '''See method C{__gt__}.
610 '''
611 return not self.__gt__(other)
613 def __len__(self):
614 '''Return the number of points, duplicates and
615 intersections in this clip.
616 '''
617 return self._len
619 def __lt__(self, other):
620 '''Is this clip C{"below"} an B{C{other}} clip,
621 located or stretched farther South or West?
622 '''
623 return self._bltr4 < _other(self, other)._bltr4
625 def __ne__(self, other): # required for Python 2
626 '''See method C{__eq__}.
627 '''
628 return not self.__eq__(other)
630 _all = __iter__
632 @property_RO
633 def _all_ON_ON(self):
634 # Check whether all vertices are ON_ON.
635 L_ON_ON = _L.ON_ON
636 return all(v._label is L_ON_ON for v in self)
638 def _append(self, y_v, *x_h_clipid):
639 # Append a point given as C{y}, C{x}, C{h}eight and
640 # C{clipid} args or as a C{LatLon[FHP|GH]}.
641 self._last = v = self._LL(y_v, *x_h_clipid) if x_h_clipid else y_v
642 self._len += 1
643 # assert v._clipid == self._id
645 v._next = n = self._first
646 if n is None: # set ._first
647 self._first = p = n = v
648 else: # insert before ._first
649 v._prev = p = n._prev
650 p._next = n._prev = v
651 return v
653# def _appendedup(self, v, clipid=0):
654# # Like C{._append}, but only append C{v} if not a
655# # duplicate of the one previously append[edup]'ed.
656# y, x, p = v.y, v.x, self._last
657# if p is None or y != p.y or x != p.x or clipid != p._clipid:
658# p = self._append(y, x, v._height, clipid)
659# if v._linked:
660# p._linked = True # to force errors
661# return p
663 @Property_RO
664 def _bltr4(self):
665 # Get the bounds as 4-tuple C{(bottom, left, top, right)}.
666 return map2(float, _MODS.points.boundsOf(self, wrap=False))
668 def _bltr4eps(self, eps):
669 # Get the ._bltr4 bounds tuple, oversized.
670 if eps > 0: # > EPS
671 yb, xl, yt, xr = self._bltr4
672 yb, yt = _low_high_eps2(yb, yt, eps)
673 xl, xr = _low_high_eps2(xl, xr, eps)
674 t = yb, xl, yt, xr
675 else:
676 t = self._bltr4
677 return t
679 def _closed(self, raiser): # PYCHOK unused
680 # End a clip, un-close it and check C{len}.
681 p, f = self._last, self._first
682 if f and f._prev is p and p is not f and \
683 p._next is f and p == f: # PYCHOK no cover
684 # un-close the clip
685 f._prev = p = p._prev
686 p._next = f
687 self._len -= 1
688# elif f and raiser:
689# raise self._OpenClipError(p, f)
690 if len(self) < 3:
691 raise self._Error(_too_(_few_))
693 def _dup(self, q):
694 # Duplicate a point (or intersection) as intersection.
695 v = self._insert(q.y, q.x, q)
696 v._alpha = q._alpha or _0_0 # _0_0 replaces None
697 v._dupof = q._dupof or q
698 # assert v._prev is q
699 # assert q._next is v
700 return v
702 def _edges2(self, wrap=False, **unused):
703 # Yield each I{original} edge as a 2-tuple
704 # (p1, p2), a pair of C{LatLon[FHP|GH])}s.
705 p1 = p = f = self._first
706 while p:
707 p2 = p = p._next
708 if p.ispoint:
709 if wrap and p is not f:
710 p2 = _unrollon(p1, p)
711 yield p1, p2
712 p1 = p2
713 if p is f:
714 break
716 def _equi(self, clip, eps):
717 # Is this clip I{equivalent} to B{C{clip}} within
718 # the given I{non-negative} tolerance B{C{eps}}?
719 r, f = len(self), self._first
720 if f and r == len(clip) and self._bltr4eps(eps) \
721 == clip._bltr4eps(eps):
722 _equi = _LatLonBool._equi
723 for v in clip:
724 if _equi(f, v, eps):
725 s, n = f, v
726 for _ in range(r):
727 s, n = s._next, n._next
728 if not _equi(s, n, eps):
729 break # next v
730 else: # equivalent
731 return True
732 return False
734 def _Error(self, txt): # PYCHOK no cover
735 # Build a C{ClipError} instance
736 kwds = dict(len=len(self), txt=txt)
737 if self._dups:
738 kwds.update(dups=self._dups)
739 cp = self._composite
740 if self._id:
741 try:
742 i = cp._clips.index(self)
743 if i != self._id:
744 kwds[_clip_] = i
745 except ValueError:
746 pass
747 kwds[_clipid_] = self._id
748 return ClipError(cp._kind, cp.name, **kwds)
750 def _index(self, clips, eps):
751 # see _CompositeBase._equi
752 for i, c in enumerate(clips):
753 if c._equi(self, eps):
754 return i
755 raise ValueError(NN) # like clips.index(self)
757 def _insert(self, y, x, start, *end_alpha):
758 # insertVertex between points C{start} and
759 # C{end}, ordered by C{alpha} iff given.
760 v = self._LL(y, x, start._height, start._clipid)
761 n = start._next
762 if end_alpha:
763 end, alpha = end_alpha
764 v._alpha = alpha
765 v._height = favg(v._height, end._height, f=alpha)
766 # assert start is not end
767 while n is not end and n._alpha < alpha:
768 n = n._next
769 v._next = n
770 v._prev = p = n._prev
771 p._next = n._prev = v
772 self._len += 1
773# _Clip._bltr4._update(self)
774# _Clip._ishole._update(self)
775 return v
777 def _intersection(self, unused, q, *p1_p2_alpha):
778 # insert an intersection or make a point both
779 if p1_p2_alpha: # intersection on edge
780 v = self._insert(q.y, q.x, *p1_p2_alpha)
781 else: # intersection at point
782 v = q
783 # assert not v._linked
784 # assert v._alpha is None
785 return v
787 def _intersections(self):
788 # Yield all intersections, some may be points too.
789 for v in self:
790 if v.isintersection:
791 yield v
793 @Property_RO
794 def _ishole(self): # PYCHOK no cover
795 # Is this clip a hole inside its composite?
796 v = self._first
797 return v._isinside(self._composite, self) if v else False
799 @property_RO
800 def _nodups(self):
801 # Yield all non-duplicates.
802 for v in self:
803 if not v._dupof:
804 yield v
806 def _noXings(self, Union):
807 # Are all intersections non-CROSSINGs, -BOUNCINGs?
808 Ls = _L.BOUNCINGs if Union else _L.CROSSINGs
809 return all(v._label not in Ls for v in self._intersections())
811 def _OpenClipError(self, s, e): # PYCHOK no cover
812 # Return a C{CloseError} instance
813 t = NN(s, _ELLIPSIS_(_COMMASPACE_, e))
814 return self._Error(_SPACE_(_open_, t))
816 def _point2(self, insert):
817 # getNonIntersectionPoint and -Vertex
818 if not (insert and self._noInters):
819 for p in self._points(may_be=False): # not p._isduplicated?
820 return p, None
821 for n in self._intersections():
822 p, _ = n._prev_next2
823 k = p._linked
824 if k:
825 if n._linked not in k._prev_next2:
826 # create a pseudo-point
827 k = _0_5 * (p + n)
828 if insert:
829 k = self._insert(k.y, k.x, n._prev)
830 r = k # to remove later
831 else: # no ._prev, ._next
832 k._clipid = n._clipid
833 r = None
834 return k, r
835 return None, None
837 def _points(self, may_be=True):
838 # Yield all points I{in original order}, which may be intersections too.
839 for v in self:
840 if v.ispoint and (may_be or not v.isintersection):
841 yield v
843 def _remove2(self, v):
844 # Remove vertex C{v}.
845 # assert not v._isduplicated
846 if len(self) > 1:
847 p = v._prev
848 p._next = n = v._next
849 n._prev = p
850 if self._first is v:
851 self._first = n
852 if self._last is v:
853 self._last = p
854 self._len -= 1
855 else:
856 n = self._last = \
857 p = self._first = None
858 self._len = 0
859 return p, n
861 def _update_all(self): # PYCHOK no cover
862 # Zap the I{cached} properties.
863 _Clip._bltr4._update( self)
864 _Clip._ishole._update(self)
865 return self # for _special_identicals
867 def _Xings(self):
868 # Yield all I{un-checked} CROSSING intersections.
869 CROSSING = _L.CROSSING
870 for v in self._intersections():
871 if v._label is CROSSING and not v._checked:
872 yield v
875class _CompositeBase(_Named):
876 '''(INTERNAL) Base class for L{BooleanFHP} and L{BooleanGH}
877 (C{_CompositeFHP} and C{_CompositeGH}).
878 '''
879 _clips = () # tuple of C{_Clips}
880 _eps = EPS # null edges
881 _kind = _corners_
882 _LL = _LatLonBool # shut up PyChecker
883 _raiser = False
884 _xtend = False
886 def __init__(self, lls, name=NN, kind=NN, eps=EPS):
887 '''(INTERNAL) See L{BooleanFHP} and L{BooleanGH}.
888 '''
889 n = name or _xattr(lls, name=NN)
890 if n:
891 self.name = n
892 if kind:
893 self._kind = kind
894 if self._eps < eps:
895 self._eps = eps
897 c = _Clip(self)
898 lp = None
899 for ll in lls:
900 ll = self._LL(ll)
901 if lp is None:
902 c._id = ll._clipid # keep clipid
903 lp = c._append(ll)
904 elif ll._clipid != lp._clipid: # new clip
905 c._closed(self.raiser)
906 c = _Clip(self, ll._clipid)
907 lp = c._append(ll)
908 elif abs(ll - lp) > eps: # PYCHOK lp
909 lp = c._append(ll)
910 else:
911 c._dups += 1
912 c._closed(self.raiser)
914 def __contains__(self, point): # PYCHOK no cover
915 '''Is the B{C{point}} in one of the clips?
916 '''
917 for c in self._clips:
918 if point in c:
919 return True
920 return False
922 def __eq__(self, other):
923 '''Is this I{composite} equivalent to an B{C{other}}, i.e.
924 do both contain I{equivalent} clips in the same or in a
925 different order? Two clips are considered I{equivalent}
926 if both have the same points etc. in the same order,
927 possibly rotated.
928 '''
929 return self._equi(_other(self, other), 0)
931 def __iter__(self):
932 '''Yield all points, duplicates and intersections.
933 '''
934 for c in self._clips:
935 for v in c:
936 yield v
938 def __ne__(self, other): # required for Python 2
939 '''See method C{__eq__}.
940 '''
941 return not self.__eq__(other)
943 def __len__(self):
944 '''Return the I{total} number of points.
945 '''
946 return sum(map(len, self._clips)) if self._clips else 0
948 def __repr__(self):
949 '''String C{repr} of this composite.
950 '''
951 c = len(self._clips)
952 c = Fmt.SQUARE(c) if c > 1 else NN
953 n = Fmt.SQUARE(len(self))
954 t = Fmt.PAREN(self) # XXX not unstr
955 return NN(self.__class__.__name__, c, n, t)
957 def __str__(self):
958 '''String C{str} of this composite.
959 '''
960 return _COMMASPACE_.join(map(str, self))
962 @property_RO
963 def _bottom_top_eps2(self):
964 # Get the bottom and top C{y} bounds, oversized.
965 return _min_max_eps2(min(v.y for v in self),
966 max(v.y for v in self))
968 def _class(self, corners, kwds, **dflts):
969 # Return a new instance
970 _g = kwds.get
971 kwds = dict((n, _g(n, v)) for n, v in dflts.items())
972 return self.__class__(corners or (), **kwds)
974 @property_RO
975 def _clipids(self): # PYCHOK no cover
976 for c in self._clips:
977 yield c._id
979 def clipids(self):
980 '''Return a tuple with all C{clipid}s, I{ordered}.
981 '''
982 return tuple(self._clipids)
984# def _clipidups(self, other):
985# # Number common C{clipid}s between this and an C{other} composite
986# return len(set(self._clipids).intersection(set(other._clipids)))
988 def _edges3(self, **raiser_wrap):
989 # Yield each I{original} edge as a 3-tuple
990 # C{(LatLon[FHP|GH], LatLon[FHP|GH], _Clip)}.
991 for c in self._clips:
992 for p1, p2 in c._edges2(**raiser_wrap):
993 yield p1, p2, c
995 def _encloses(self, lat, lon, **wrap):
996 # see function .points.isenclosedBy
997 return self._LL(lat, lon).isenclosedBy(self, **wrap)
999 @property
1000 def eps(self):
1001 '''Get the null edges tolerance (C{degrees}, usually).
1002 '''
1003 return self._eps
1005 @eps.setter # PYCHOK setter!
1006 def eps(self, eps):
1007 '''Set the null edges tolerance (C{degrees}, usually).
1008 '''
1009 self._eps = eps
1011 def _10eps(self, **eps):
1012 # Get eps for _LatLonBool._2Abs
1013 e = _xkwds_get(eps, eps=self._eps)
1014 if e != EPS:
1015 e *= _10EPS / EPS
1016 else:
1017 e = _10EPS
1018 return e
1020 def _equi(self, other, eps):
1021 # Is this composite I{equivalent} to an B{C{other}} within
1022 # the given, I{non-negative} tolerance B{C{eps}}?
1023 cs, co = self._clips, other._clips
1024 if cs and len(cs) == len(co):
1025 if eps > 0:
1026 _index = _Clip._index
1027 else:
1028 def _index(c, cs, unused):
1029 return cs.index(c)
1030 try:
1031 cs = list(sorted(cs))
1032 for c in sorted(co):
1033 cs.pop(_index(c, cs, eps))
1034 except ValueError: # from ._index
1035 pass
1036 return False if cs else True
1037 else: # both null?
1038 return False if cs or co else True
1040 def _intersections(self):
1041 # Yield all intersections.
1042 for c in self._clips:
1043 for v in c._intersections():
1044 yield v
1046 def isequalTo(self, other, eps=None):
1047 '''Is this boolean/composite equal to an B{C{other}} within
1048 a given, I{non-negative} tolerance?
1050 @arg other: The other boolean/composite (C{Boolean[FHP|GB]}).
1051 @kwarg eps: Tolerance for equality (C{degrees} or C{None}).
1053 @return: C{True} if equivalent, C{False} otherwise (C{bool}).
1055 @raise TypeError: Invalid B{C{other}}.
1057 @see: Method C{__eq__}.
1058 '''
1059 if isinstance(other, _CompositeBase):
1060 return self._equi(other, _eps0(eps))
1061 raise _IsnotError(_boolean_, _composite_, other=other)
1063 def _kwds(self, op, **more):
1064 # Get all keyword arguments as C{dict}.
1065 kwds = dict(raiser=self.raiser, eps=self.eps,
1066 name=self.name or op.__name__)
1067 kwds.update(more)
1068 return kwds
1070 @property_RO
1071 def _left_right_eps2(self):
1072 # Get the left and right C{x} bounds, oversized.
1073 return _min_max_eps2(min(v.x for v in self),
1074 max(v.x for v in self))
1076 def _points(self, may_be=True): # PYCHOK no cover
1077 # Yield all I{original} points, which may be intersections too.
1078 for c in self._clips:
1079 for v in c._points(may_be=may_be):
1080 yield v
1082 @property
1083 def raiser(self):
1084 '''Get the option to throw L{ClipError} exceptions (C{bool}).
1085 '''
1086 return self._raiser
1088 @raiser.setter # PYCHOK setter!
1089 def raiser(self, throw):
1090 '''Set the option to throw L{ClipError} exceptions (C{bool}).
1091 '''
1092 self._raiser = bool(throw)
1094 def _results(self, _presults, Clas, closed=False, inull=False, **eps):
1095 # Yield the dedup'd results, as L{ClipFHP4Tuple}s
1096 C = self._LL if Clas is None else Clas
1097 e = self._10eps(**eps)
1098 for clipid, ns in enumerate(_presults):
1099 f = p = v = None
1100 for n in ns:
1101 if f is None:
1102 yield n._toClas(C, clipid)
1103 f = p = n
1104 elif v is None:
1105 v = n # got f, p, v
1106 elif inull or p._2Abs(v, n, eps=e):
1107 yield v._toClas(C, clipid)
1108 p, v = v, n
1109 else: # null, colinear, ... skipped
1110 v = n
1111 if v and (inull or p._2Abs(v, f, eps=e)):
1112 yield v._toClas(C, clipid)
1113 p = v
1114 if f and p != f and closed: # close clip
1115 yield f._toClas(C, clipid)
1117 def _sum(self, other, op):
1118 # Combine this and an C{other} composite
1119 LL = self._LL
1120 sp = self.copy(name=self.name or op.__name__)
1121 sp._clips, sid = (), INT0 # new clips
1122 for cp in (self, other):
1123 for c in cp._clips:
1124 _ap = _Clip(sp, sid)._append
1125 for v in c._nodups:
1126 _ap(LL(v.y, v.x, v.height, sid))
1127 sid += 1
1128 return sp
1130 def _sum1(self, _a_p, *args, **kwds): # in .karney, .points
1131 # Sum the area or perimeter of all clips
1132 return _MODS.fsums.fsum1((_a_p(c, *args, **kwds) for c in self._clips), floats=True)
1134 def _sum2(self, LL, _a_p, *args, **kwds): # in .sphericalNvector, -Trigonometry
1135 # Sum the area or perimeter of all clips
1137 def _lls(clip): # convert clip to LLs
1138 _LL = LL
1139 for v in clip:
1140 yield _LL(v.lat, v.lon) # datum=Sphere
1142 return _MODS.fsums.fsum1((_a_p(_lls(c), *args, **kwds) for c in self._clips), floats=True)
1144 def toLatLon(self, LatLon=None, closed=False, **LatLon_kwds):
1145 '''Yield all (non-duplicate) points and intersections
1146 as an instance of B{C{LatLon}}.
1148 @kwarg LatLon: Class to use (C{LatLon}) or if C{None},
1149 L{LatLonFHP} or L{LatLonGH}.
1150 @kwarg closed: If C{True}, close each clip (C{bool}).
1151 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}
1152 keyword arguments, ignore if
1153 C{B{LatLon} is None}.
1155 @raise TypeError: Invalid B{C{LatLon}}.
1157 @note: For intersections, C{height} is an instance
1158 of L{HeightX}, otherwise of L{Height}.
1159 '''
1160 if LatLon is None:
1161 LL, kwds = self._LL, {}
1162 elif issubclassof(LatLon, _LatLonBool, LatLonBase):
1163 LL, kwds = LatLon, LatLon_kwds
1164 else:
1165 raise _TypeError(LatLon=LatLon)
1167 for c in self._clips:
1168 lf, cid = None, c._id
1169 for v in c._nodups:
1170 ll = LL(v.y, v.x, **kwds)
1171 ll._height = v.height
1172 if ll._clipid != cid:
1173 ll._clipid = cid
1174 yield ll
1175 if lf is None:
1176 lf = ll
1177 if closed and lf:
1178 yield lf
1181class _CompositeFHP(_CompositeBase):
1182 '''(INTERNAL) A list of clips representing a I{composite}
1183 of L{LatLonFHP} points, duplicates and intersections
1184 with an other I{composite}.
1185 '''
1186 _LL = LatLonFHP
1187 _Union = False
1189 def __init__(self, lls, raiser=False, **name_kind_eps):
1190 # New L{_CompositeFHP}.
1191 if raiser:
1192 self._raiser = True
1193 _CompositeBase.__init__(self, lls, **name_kind_eps)
1195 def _classify(self):
1196 # 2) Classify intersection chains.
1197 L = _L
1198 for v in self._intersections():
1199 n, b = v, v._label
1200 if b in L.RIGHT_LEFT_ON: # next chain
1201 while True:
1202 n._label = None # n.__dict__.pop('_label')
1203 n = n._next
1204 if n is v or n._label is not L.ON_ON: # n._label and ...
1205 break
1206 a = L.LEFT_ON if n._label is L.ON_LEFT else L.RIGHT_ON
1207 v._label = n._label = L.BOUNCING_D if a is b else L.CROSSING_D
1209 # 3) Copy labels
1210 for v in self._intersections():
1211 v._linked._label = v._label
1213 def _clip(self, corners, Union=False, Clas=None,
1214 **closed_inull_raiser_eps):
1215 # Clip this composite with another one, C{corners},
1216 # using Foster-Hormann-Popa's algorithm.
1217 P = self
1218 Q = self._class(corners, closed_inull_raiser_eps,
1219 eps=P._eps, raiser=False)
1220 if Union:
1221 P._Union = Q._Union = True
1223 bt = Q._bottom_top_eps2
1224 lr = Q._left_right_eps2
1225 # compute and insert intersections
1226 for p1, p2, Pc in P._edges3(**closed_inull_raiser_eps):
1227 if not (_outside(p1.x, p2.x, *lr) or
1228 _outside(p1.y, p2.y, *bt)):
1229 e = _EdgeFHP(p1, p2)
1230 if e._dp2 > EPS2: # non-null edge
1231 for q1, q2, Qc in Q._edges3(**closed_inull_raiser_eps):
1232 for T, p, q in e._intersect3(q1, q2):
1233 p = Pc._intersection(T, *p)
1234 q = Qc._intersection(T, *q)
1235 # assert not p._linked
1236 # assert not q._linked
1237 p._link(q)
1239 # label and classify intersections
1240 P._labelize()
1241 P._classify()
1243 # check for special cases
1244 P._special_cases(Q)
1245 Q._special_cases(P)
1246 # handle identicals
1247 P._special_identicals(Q)
1249 # set Entry/Exit flags
1250 P._set_entry_exits(Q)
1251 Q._set_entry_exits(P)
1253 # handle splits and crossings
1254 P._splits_xings(Q)
1256 # yield the results
1257 return P._results(P._presults(Q), Clas, **closed_inull_raiser_eps)
1259 @property_RO
1260 def _identicals(self):
1261 # Yield all clips marked C{._identical}.
1262 for c in self._clips:
1263 if c._identical:
1264 yield c
1266 def _labelize(self):
1267 # 1) Intersections classification
1268 for p in self._intersections():
1269 q = p._linked
1270 # determine local configuration at this intersection
1271 # and positions of Q- and Q+ relative to (P-, I, P+)
1272 p1, p3 = p._prev_next2
1273 q1, q3 = q._prev_next2
1274 t = (q1._RPoracle(p1, p, p3),
1275 q3._RPoracle(p1, p, p3))
1276 # check intersecting and overlapping cases
1277 p._label = _RP2L.get(t, None)
1279 def _presults(self, other):
1280 # Yield the result clips, each as a generator
1281 # of the L{_LatLonFHP}s in that clip
1282 for cp in (self, other):
1283 for c in cp._clips:
1284 if c._pushback:
1285 yield c._all()
1286 for c in self._clips:
1287 for X in c._Xings():
1288 yield self._resultX(X)
1290 def _resultX(self, X):
1291 # Yield the results from CROSSING C{X}.
1292 L, U, v = _L, self._Union, X
1293 while v:
1294 v._checked = True
1295 r = v # in P or Q
1296 s = L.Toggle[v._en_ex]
1297 e = (s is L.EXIT) ^ U
1298 while True:
1299 v = v._next if e else v._prev
1300 yield v
1301 v._checked = True
1302 if v._en_ex is s or v is X:
1303 break
1304 if v is r: # full circle
1305 raise ClipError(full_circle=v, clipid=v._clipid)
1306 if v is not X:
1307 v = v._linked
1308 if v is X:
1309 break
1311 def _set_entry_exits(self, other): # MCCABE 14
1312 # 4) Set entry/exit flags
1313 L, U = _L, self._Union
1314 for c in self._clips:
1315 n, k = c._point2(True)
1316 if n:
1317 f = n
1318 s = L.EXIT if n._isinside(other) else L.ENTRY
1319 t = L.EXIT # first_chain_vertex = True
1320 while True:
1321 if n.isintersection:
1322 b = n._label
1323 if b is L.CROSSING:
1324 n._en_ex = s
1325 s = L.Toggle[s]
1326 elif b is L.BOUNCING and ((s is L.EXIT) ^ U):
1327 n._2split = c # see ._splits_xings
1328 elif b is L.CROSSING_D:
1329 n._en_ex = s
1330 if (s is t) ^ U:
1331 n._label = L.CROSSING
1332 t = L.Toggle[t]
1333 if t is L.EXIT: # first_chain_vertex == True
1334 s = L.Toggle[s]
1335 elif b is L.BOUNCING_D:
1336 n._en_ex = s
1337 if (s is t) ^ U:
1338 n._2xing = True # see ._splits_xings
1339 s = L.Toggle[s]
1340 t = L.Toggle[t]
1341 n = n._next # _, n = n._prev_next2
1342 if n is f:
1343 break # PYCHOK attr?
1344 if k:
1345 c._remove2(k)
1347 def _special_cases(self, other):
1348 # 3.5) Check special cases
1349 U = self._Union
1350 for c in self._clips:
1351 if c._noXings(U):
1352 c._noInters = True
1353 if c._all_ON_ON:
1354 c._identical = True
1355 else:
1356 p, _ = c._point2(False)
1357 if p and (p._isinside(other) ^ U):
1358 c._pushback = True
1360 def _special_identicals(self, other):
1361 # 3.5) Handle identicals
1362 _u = _Clip._update_all
1363 cds = dict((c._id, _u(c)) for c in other._identicals)
1364 # assert len(cds) == len(other._identicals)
1365 if cds: # PYCHOK no cover
1366 for c in self._identicals:
1367 c._update_all()
1368 for v in c._intersections():
1369 d = cds.get(v._linked._clipid, None)
1370 if d and d._ishole is c._ishole:
1371 c._pushback = True
1372 break # next c
1374 @property_RO
1375 def _2splits(self):
1376 # Yield all intersections marked C{._2split}
1377 for p in self._intersections():
1378 if p._2split:
1379 # assert isinstance(p._2split, _Clip)
1380 yield p
1382 def _splits_xings(self, other): # MCCABE 15
1383 # 5) Handle split pairs and 6) crossing candidates
1385 def _2A_dup2(p, P): # PYCHOK unused
1386 p1, p2 = p._prev_next2
1387 ap = p1._2A(p, p2)
1388 Pc = p._2split
1389 # assert Pc in P._clips
1390 # assert p in Pc
1391 return ap, Pc._dup(p)
1393 def _links2(ps, qs): # PYCHOK P unused?
1394 # Yield each link as a 2-tuple(p, q)
1395 id_qs = set(map(id, qs))
1396 if id_qs:
1397 for p in ps:
1398 q = p._linked
1399 if q and id(q) in id_qs:
1400 yield p, q
1402 L = _L
1403 E = L.ENTRY if self._Union else L.EXIT
1404 X = L.Toggle[E]
1405 for p, q in _links2(self._2splits, other._2splits):
1406 ap, pp = _2A_dup2(p, self)
1407 aq, qq = _2A_dup2(q, other)
1408 if (ap * aq) > 0: # PYCHOK no cover
1409 p._link(qq) # overwrites ...
1410 q._link(pp) # ... p-q link
1411 else:
1412 pp._link(qq)
1413 p._en_ex = q._en_ex = E
1414 pp._en_ex = qq._en_ex = X
1415 p._label = pp._label = \
1416 q._label = qq._label = L.CROSSING
1418 for p, q in _links2(self._2xings, other._2xings):
1419 p._label = q._label = L.CROSSING
1421 @property_RO
1422 def _2xings(self):
1423 # Yield all intersections marked C{._2xing}
1424 for p in self._intersections():
1425 if p._2xing:
1426 yield p
1429class _CompositeGH(_CompositeBase):
1430 '''(INTERNAL) A list of clips representing a I{composite}
1431 of L{LatLonGH} points, duplicates and intersections
1432 with an other I{composite}.
1433 '''
1434 _LL = LatLonGH
1435 _xtend = False
1437 def __init__(self, lls, raiser=False, xtend=False, **name_kind_eps):
1438 # New L{_CompositeGH}.
1439 if xtend:
1440 self._xtend = True
1441 elif raiser:
1442 self._raiser = True
1443 _CompositeBase.__init__(self, lls, **name_kind_eps)
1445 def _clip(self, corners, s_entry, c_entry, Clas=None,
1446 **closed_inull_raiser_xtend_eps):
1447 # Clip this polygon with another one, C{corners}.
1449 # Core of Greiner/Hormann's algorithm, enhanced U{Correia's
1450 # <https://GitHub.com/helderco/univ-polyclip>} implementation***
1451 # and extended to optionally handle so-called "degenerate cases"
1452 S = self
1453 C = self._class(corners, closed_inull_raiser_xtend_eps,
1454 raiser=False, xtend=False)
1455 bt = C._bottom_top_eps2
1456 lr = C._left_right_eps2
1457 # 1. find intersections
1458 for s1, s2, Sc in S._edges3(**closed_inull_raiser_xtend_eps):
1459 if not (_outside(s1.x, s2.x, *lr) or
1460 _outside(s1.y, s2.y, *bt)):
1461 e = _EdgeGH(s1, s2, **closed_inull_raiser_xtend_eps)
1462 if e._hypot2 > EPS2: # non-null edge
1463 for c1, c2, Cc in C._edges3(**closed_inull_raiser_xtend_eps):
1464 for y, x, sa, ca in e._intersect4(c1, c2):
1465 s = Sc._insert(y, x, s1, s2, sa)
1466 c = Cc._insert(y, x, c1, c2, ca)
1467 s._link(c)
1469 # 2. identify entry/exit intersections
1470 if S._first:
1471 s_entry ^= S._first._isinside(C, *bt)
1472 for v in S._intersections():
1473 v._entry = s_entry = not s_entry
1475 if C._first:
1476 c_entry ^= C._first._isinside(S)
1477 for v in C._intersections():
1478 v._entry = c_entry = not c_entry
1480 # 3. yield the result(s)
1481 return S._results(S._presults(), Clas, **closed_inull_raiser_xtend_eps)
1483 @property_RO
1484 def _first(self):
1485 # Get the very first vertex of the first clip
1486 for v in self:
1487 return v
1488 return None # PYCHOK no cover
1490 def _kwds(self, op, **more):
1491 # Get the kwds C{dict}.
1492 return _CompositeBase._kwds(self, op, xtend=self.xtend, **more)
1494 def _presults(self):
1495 # Yield the unchecked intersection(s).
1496 for c in self._clips:
1497 for v in c._intersections():
1498 if not v._checked:
1499 yield self._resultU(v)
1501 def _resultU(self, v):
1502 # Yield the result from an un-checked intersection.
1503 while v and not v._checked:
1504 v._check()
1505 yield v
1506 r = v
1507 e = v._entry
1508 while True:
1509 v = v._next if e else v._prev
1510 yield v
1511 if v._linked:
1512 break
1513 if v is r:
1514 raise ClipError(full_circle=v, clipid=v._clipid)
1515 v = v._linked # switch
1517 @property
1518 def xtend(self):
1519 '''Get the option to handle I{degenerate cases} (C{bool}).
1520 '''
1521 return self._xtend
1523 @xtend.setter # PYCHOK setter!
1524 def xtend(self, xtend):
1525 '''Set the option to handle I{degenerate cases} (C{bool}).
1526 '''
1527 self._xtend = bool(xtend)
1530class _EdgeFHP(object):
1531 # An edge between two L{LatLonFHP} points.
1533 X_INTERSECT = _Enum('Xi', 1) # C++ enum
1534 X_OVERLAP = _Enum('Xo', 5)
1535 P_INTERSECT = _Enum('Pi', 3)
1536 P_OVERLAP = _Enum('Po', 7)
1537 Ps = (P_INTERSECT, P_OVERLAP, X_OVERLAP)
1538 Q_INTERSECT = _Enum('Qi', 2)
1539 Q_OVERLAP = _Enum('Qo', 6)
1540 Qs = (Q_INTERSECT, Q_OVERLAP, X_OVERLAP)
1541 V_INTERSECT = _Enum('Vi', 4)
1542 V_OVERLAP = _Enum('Vo', 8)
1543 Vs = (V_INTERSECT, V_OVERLAP)
1545 def __init__(self, p1, p2, **unused):
1546 # New edge between points C{p1} and C{p2}, each a L{LatLonFHP}.
1547 self._p1_p2 = p1, p2
1548 self._dp = dp = p2 - p1
1549 self._dp2 = dp * dp # dot product, hypot2
1551 self._lr, \
1552 self._bt = _left_right_bottom_top_eps2(p1, p2)
1554 def _intersect3(self, q1, q2):
1555 # Yield intersection(s) Type or C{None}
1556 if not (_outside(q1.x, q2.x, *self._lr) or
1557 _outside(q1.y, q2.y, *self._bt)):
1558 dq = q2 - q1
1559 dq2 = dq * dq # dot product, hypot2
1560 if dq2 > EPS2: # like ._clip
1561 T, E = None, _EdgeFHP # self.__class__
1562 p1, p2 = self._p1_p2
1563 ap1 = p1._2A(q1, q2)
1564 ap2_1 = p2._2A(q1, q2) - ap1
1565 if fabs(ap2_1) > _0_EPS: # non-parallel edges
1566 aq1 = q1._2A(p1, p2)
1567 aq2_1 = q2._2A(p1, p2) - aq1
1568 if fabs(aq2_1) > _0_EPS:
1569 # compute and classify alpha and beta
1570 a, a_0, a_0_1, _ = _alpha4(-ap1 / ap2_1)
1571 b, b_0, b_0_1, _ = _alpha4(-aq1 / aq2_1)
1572 # distinguish intersection types
1573 T = E.X_INTERSECT if a_0_1 and b_0_1 else (
1574 E.P_INTERSECT if a_0_1 and b_0 else (
1575 E.Q_INTERSECT if a_0 and b_0_1 else (
1576 E.V_INTERSECT if a_0 and b_0 else None)))
1578 elif fabs(ap1) < _0_EPS: # parallel or colinear edges
1579 dp = self._dp
1580 d1 = q1 - p1
1581 # compute and classify alpha and beta
1582 a, a_0, a_0_1, _a_0_1 = _alpha4((d1 * dp) / self._dp2)
1583 b, b_0, b_0_1, _b_0_1 = _alpha4((d1 * dq) / (-dq2))
1584 # distinguish overlap type
1585 T = E.X_OVERLAP if a_0_1 and b_0_1 else (
1586 E.P_OVERLAP if a_0_1 and _b_0_1 else (
1587 E.Q_OVERLAP if _a_0_1 and b_0_1 else (
1588 E.V_OVERLAP if a_0 and b_0 else None)))
1590 if T:
1591 if T is E.X_INTERSECT:
1592 v = p1 + a * self._dp
1593 yield T, (v, p1, p2, a), (v, q1, q2, b)
1594 elif T in E.Vs:
1595 yield T, (p1,), (q1,)
1596 else:
1597 if T in E.Qs:
1598 yield T, (p1,), (p1, q1, q2, b)
1599 if T in E.Ps:
1600 yield T, (q1, p1, p2, a), (q1,)
1603class _EdgeGH(object):
1604 # An edge between two L{LatLonGH} points.
1606 _raiser = False
1607 _xtend = False
1609 def __init__(self, s1, s2, raiser=False, xtend=False, **unused):
1610 # New edge between points C{s1} and C{s2}, each a L{LatLonGH}.
1611 self._s1, self._s2 = s1, s2
1612 self._x_sx_y_sy = (s1.x, s2.x - s1.x,
1613 s1.y, s2.y - s1.y)
1614 self._lr, \
1615 self._bt = _left_right_bottom_top_eps2(s1, s2)
1617 if xtend:
1618 self._xtend = True
1619 elif raiser:
1620 self._raiser = True
1622 def _alpha2(self, x, y, dx, dy):
1623 # Return C{(alpha)}, see .points.nearestOn5
1624 a = (y * dy + x * dx) / self._hypot2
1625 d = (y * dx - x * dy) / self._hypot0
1626 return a, fabs(d)
1628 def _Error(self, n, *args, **kwds): # PYCHOK no cover
1629 t = unstr(_EdgeGH.__name__, self._s1, self._s2)
1630 t = _DOT_(t, _EdgeGH._intersect4.__name__)
1631 t = unstr(t, *args, **kwds)
1632 return ClipError(_case_, n, txt=t)
1634 @Property_RO
1635 def _hypot0(self):
1636 _, sx, _, sy = self._x_sx_y_sy
1637 return hypot(sx, sy) * _0_EPS
1639 @Property_RO
1640 def _hypot2(self):
1641 _, sx, _, sy = self._x_sx_y_sy
1642 return hypot2(sx, sy)
1644 def _intersect4(self, c1, c2, parallel=True): # MCCABE 14
1645 # Yield the intersection(s) of this and another edge.
1647 # @return: None, 1 or 2 intersections, each a 4-Tuple
1648 # (y, x, s_alpha, c_alpha) with intersection
1649 # coordinates x and y and both alphas.
1651 # @raise ClipError: Intersection unhandled.
1653 # @see: U{Intersection point of two line segments
1654 # <http://PaulBourke.net/geometry/pointlineplane/>}.
1655 c1_x, c1_y = c1.x, c1.y
1656 if not (_outside(c1_x, c2.x, *self._lr) or
1657 _outside(c1_y, c2.y, *self._bt)):
1658 x, sx, \
1659 y, sy = self._x_sx_y_sy
1661 cx = c2.x - c1_x
1662 cy = c2.y - c1_y
1663 d = cy * sx - cx * sy
1665 if fabs(d) > _0_EPS: # non-parallel edges
1666 dx = x - c1_x
1667 dy = y - c1_y
1668 ca = (sx * dy - sy * dx) / d
1669 if _0_EPS < ca < _EPS_1 or (self._xtend and
1670 _EPS_0 < ca < _1_EPS):
1671 sa = (cx * dy - cy * dx) / d
1672 if _0_EPS < sa < _EPS_1 or (self._xtend and
1673 _EPS_0 < sa < _1_EPS):
1674 yield (y + sa * sy), (x + sa * sx), sa, ca
1676 # unhandled, "degenerate" cases 1, 2 or 3
1677 elif self._raiser and not (sa < _EPS_0 or sa > _1_EPS): # PYCHOK no cover
1678 raise self._Error(1, c1, c2, sa=sa) # intersection at s1 or s2
1680 elif self._raiser and not (ca < _EPS_0 or ca > _1_EPS): # PYCHOK no cover
1681 # intersection at c1 or c2 or at c1 or c2 and s1 or s2
1682 sa = (cx * dy - cy * dx) / d
1683 e = 2 if sa < _EPS_0 or sa > _1_EPS else 3
1684 raise self._Error(e, c1, c2, ca=ca)
1686 elif parallel and (sx or sy) and (cx or cy): # PYCHOK no cover
1687 # non-null, parallel or colinear edges
1688 sa1, d1 = self._alpha2(c1_x - x, c1_y - y, sx, sy)
1689 sa2, d2 = self._alpha2(c2.x - x, c2.y - y, sx, sy)
1690 if max(d1, d2) < _0_EPS:
1691 if self._xtend and not _outside(sa1, sa2, _EPS_0, _1_EPS):
1692 if sa1 > sa2: # anti-parallel
1693 sa1, sa2 = sa2, sa1
1694 ca1, ca2 = _1_0, _0_0
1695 else: # parallel
1696 ca1, ca2 = _0_0, _1_0
1697 ca = fabs((sx / cx) if cx else (sy / cy))
1698 # = hypot(sx, sy) / hypot(cx, cy)
1699 if sa1 < 0: # s1 is between c1 and c2
1700 ca *= ca1 + sa1
1701 yield y, x, ca1, _alpha1(ca)
1702 else: # c1 is between s1 and s2
1703 yield (y + sa1 * sy), (x + sa1 * sx), sa1, ca1
1704 if sa2 > 1: # s2 is between c1 and c2
1705 ca *= sa2 - _1_0
1706 yield (y + sy), (x + sx), ca2, _alpha1(ca2 - ca)
1707 else: # c2 is between s1 and s2
1708 yield (y + sa2 * sy), (x + sa2 * sx), sa2, ca2
1709 elif self._raiser and not _outside(sa1, sa2, _0_0, _1_EPS):
1710 raise self._Error(4, c1, c2, d1=d1, d2=d2)
1713class _BooleanBase(object):
1714 # Shared C{Boolean[FHP|GH]} methods.
1716 def __add__(self, other):
1717 '''Sum: C{this + other} clips.
1718 '''
1719 return self._sum(_other(self, other), self.__add__) # PYCHOK OK
1721 def __and__(self, other):
1722 '''Intersection: C{this & other}.
1723 '''
1724 return self._boolean(other, False, False, self.__and__) # PYCHOK OK
1726 def __iadd__(self, other):
1727 '''In-place sum: C{this += other} clips.
1728 '''
1729 return self._inplace(self.__add__(other))
1731 def __iand__(self, other):
1732 '''In-place intersection: C{this &= other}.
1733 '''
1734 return self._inplace(self.__and__(other))
1736 def __ior__(self, other):
1737 '''In-place union: C{this |= other}.
1738 '''
1739 return self._inplace(self.__or__(other))
1741 def __or__(self, other):
1742 '''Union: C{this | other}.
1743 '''
1744 return self._boolean(other, True, True, self.__or__) # PYCHOK OK
1746 def __radd__(self, other):
1747 '''Reverse sum: C{other + this} clips.
1748 '''
1749 return _other(self, other)._sum(self, self.__radd__)
1751 def __rand__(self, other):
1752 '''Reverse intersection: C{other & this}
1753 '''
1754 return _other(self, other).__and__(self)
1756 def __ror__(self, other):
1757 '''Reverse union: C{other | this}
1758 '''
1759 return _other(self, other).__or__(self)
1761 def _boolean4(self, other, op):
1762 # Set up a new C{Boolean[FHP|GH]}.
1763 C = self.__class__
1764 kwds = C._kwds(self, op)
1765 a = C(self, **kwds)
1766 b = _other(self, other)
1767 return a, b, C, kwds
1769 def _inplace(self, r):
1770 # Replace this with a L{Boolean*} result.
1771 self._clips, r._clips = r._clips, None
1772# if self._raiser != r._raiser:
1773# self._raiser = r._raiser
1774# if self._xtend != r._xtend:
1775# self._xtend = r._xtend
1776# if self._eps != r._eps:
1777# self._eps = r._eps
1778 return self
1781class BooleanFHP(_CompositeFHP, _BooleanBase):
1782 '''I{Composite} class providing I{boolean} operations between two
1783 I{composites} using U{Forster-Hormann-Popa<https://www.ScienceDirect.com/
1784 science/article/pii/S259014861930007X>}'s C++ implementation, transcoded
1785 to pure Python.
1787 The supported operations between (composite) polygon A and B are:
1789 - C = A & B or A &= B, intersection of A and B
1791 - C = A + B or A += B, sum of A and B clips
1793 - C = A | B or A |= B, union of A and B
1795 - A == B or A != B, equivalent A and B clips
1797 - A.isequalTo(B, eps), equivalent within tolerance
1799 @see: Methods C{__eq__} and C{isequalTo}, function L{clipFHP4}
1800 and class L{BooleanGH}.
1801 '''
1802 _kind = _boolean_
1804 def __init__(self, lls, raiser=False, eps=EPS, name=NN):
1805 '''New L{BooleanFHP} operand for I{boolean} operation.
1807 @arg lls: The polygon points and clips (iterable of L{LatLonFHP}s,
1808 L{ClipFHP4Tuple}s or other C{LatLon}s).
1809 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}).
1810 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same
1811 units as the B{C{lls}} coordinates).
1812 @kwarg name: Optional name (C{str}).
1813 '''
1814 _CompositeFHP.__init__(self, lls, raiser=raiser,
1815 eps=eps, name=name)
1817 def __isub__(self, other):
1818 '''Not implemented.'''
1819 return _NotImplemented(self, other)
1821 def __rsub__(self, other):
1822 '''Not implemented.'''
1823 return _NotImplemented(self, other)
1825 def __sub__(self, other):
1826 '''Not implemented.'''
1827 return _NotImplemented(self, other)
1829 def _boolean(self, other, Union, unused, op):
1830 # One C{BooleanFHP} operation.
1831 p, q, C, kwds = self._boolean4(other, op)
1832 r = p._clip(q, Union=Union, **kwds)
1833 return C(r, **kwds)
1836class BooleanGH(_CompositeGH, _BooleanBase):
1837 '''I{Composite} class providing I{boolean} operations between two
1838 I{composites} using the U{Greiner-Hormann<http://www.Inf.USI.CH/
1839 hormann/papers/Greiner.1998.ECO.pdf>} algorithm and U{Correia
1840 <https://GitHub.com/helderco/univ-polyclip>}'s implementation,
1841 modified and extended.
1843 The supported operations between (composite) polygon A and B are:
1845 - C = A - B or A -= B, difference A less B
1847 - C = B - A or B -= A, difference B less B
1849 - C = A & B or A &= B, intersection of A and B
1851 - C = A + B or A += B, sum of A and B clips
1853 - C = A | B or A |= B, union of A and B
1855 - A == B or A != B, equivalent A and B clips
1857 - A.isequalTo(B, eps), equivalent within tolerance
1859 @note: To handle I{degenerate cases} like C{point-edge} and
1860 C{point-point} intersections, use class L{BooleanFHP}.
1862 @see: Methods C{__eq__} and C{isequalTo}, function L{clipGH4}
1863 and class L{BooleanFHP}.
1864 '''
1865 _kind = _boolean_
1867 def __init__(self, lls, raiser=True, xtend=False, eps=EPS, name=NN):
1868 '''New L{BooleanFHP} operand for I{boolean} operation.
1870 @arg lls: The polygon points and clips (iterable of L{LatLonGH}s,
1871 L{ClipGH4Tuple}s or other C{LatLon}s).
1872 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}).
1873 @kwarg xtend: If C{True}, extend edges of I{degenerate cases}, an
1874 attempt to handle the latter (C{bool}).
1875 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same
1876 units as the B{C{lls}} coordinates).
1877 @kwarg name: Optional name (C{str}).
1878 '''
1879 _CompositeGH.__init__(self, lls, raiser=raiser, xtend=xtend,
1880 eps=eps, name=name)
1882 def _boolean(self, other, s_entry, c_entry, op):
1883 # One C{BooleanGH} operation.
1884 s, c, C, kwds = self._boolean4(other, op)
1885 r = s._clip(c, s_entry, c_entry, **kwds)
1886 return C(r, **kwds)
1888 def __isub__(self, other):
1889 '''In-place difference: C{this -= other}.
1890 '''
1891 return self._inplace(self.__sub__(other))
1893 def __rsub__(self, other):
1894 ''' Reverse difference: C{other - this}
1895 '''
1896 return _other(self, other).__sub__(self)
1898 def __sub__(self, other):
1899 '''Difference: C{this - other}.
1900 '''
1901 return self._boolean(other, True, False, self.__sub__)
1904def _alpha1(alpha):
1905 # Return C{alpha} in C{[0..1]} range
1906 if _EPS_0 < alpha < _1_EPS:
1907 return max(_0_0, min(alpha, _1_0))
1908 t = _not_(Fmt.SQUARE(_ELLIPSIS_(0, 1)))
1909 raise ClipError(_alpha_, alpha, txt=t)
1912def _alpha4(a):
1913 # Return 4-tuple (alpha, -EPS < alpha < EPS,
1914 # 0 < alpha < 1,
1915 # not 0 < alpha < 1)
1916 return (a, False, True, False) if _0_EPS < a < _EPS_1 else (
1917 (a, False, False, True) if _0_EPS < fabs(a) else
1918 (a, True, False, False))
1921def _Cps(Cp, composites_points, where):
1922 # Yield composites and points as a C{Cp} composite.
1923 try:
1924 kwds = dict(kind=_points_, name=where.__name__)
1925 for cp in composites_points:
1926 yield cp if isBoolean(cp) else Cp(cp, **kwds)
1927 except (AttributeError, ClipError, TypeError, ValueError) as x:
1928 raise _ValueError(points=cp, cause=x)
1931def _eps0(eps):
1932 # Adjust C{eps} or C{None}.
1933 return eps if eps and eps > EPS else 0
1936def isBoolean(obj):
1937 '''Check for C{Boolean} composites.
1939 @arg obj: The object (any C{type}).
1941 @return: C{True} if B{C{obj}} is L{BooleanFHP},
1942 L{BooleanGH} oe some other composite,
1943 C{False} otherwise.
1944 '''
1945 return isinstance(obj, _CompositeBase)
1948def _left_right_bottom_top_eps2(p1, p2):
1949 '''(INTERNAL) Return 2-tuple C{(left, right), (bottom, top)}, oversized.
1950 '''
1951 return (_min_max_eps2(p1.x, p2.x),
1952 _min_max_eps2(p1.y, p2.y))
1955def _low_high_eps2(lo, hi, eps):
1956 '''(INTERNAL) Return 2-tuple C{(lo, hi)}, oversized.
1957 '''
1958 lo *= (_1_0 + eps) if lo < 0 else (_1_0 - eps)
1959 hi *= (_1_0 - eps) if hi < 0 else (_1_0 + eps)
1960 return (lo or -eps), (hi or eps)
1963def _min_max_eps2(*xs):
1964 '''(INTERNAL) Return 2-tuple C{(min, max)}, oversized.
1965 '''
1966 lo, hi = min(xs), max(xs)
1967 lo *= _1_EPS if lo < 0 else _EPS_1
1968 hi *= _EPS_1 if hi < 0 else _1_EPS
1969 return (lo or _EPS_0), (hi or _0_EPS)
1972def _other(this, other):
1973 '''(INTERNAL) Check for compatible C{type}s.
1974 '''
1975 C = this.__class__
1976 if isinstance(other, C):
1977 return other
1978 raise _IsnotError(C.__name__, other=other)
1981def _outside(x1, x2, lo, hi):
1982 '''(INTERNAL) Is C{(x1, x2)} outside C{(lo, hi)}?
1983 '''
1984 return max(x1, x2) < lo or min(x1, x2) > hi
1987__all__ += _ALL_DOCS(_BooleanBase, _Clip,
1988 _CompositeBase, _CompositeFHP, _CompositeGH,
1989 _LatLonBool)
1991# **) MIT License
1992#
1993# Copyright (C) 2018-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1994#
1995# Permission is hereby granted, free of charge, to any person obtaining a
1996# copy of this software and associated documentation files (the "Software"),
1997# to deal in the Software without restriction, including without limitation
1998# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1999# and/or sell copies of the Software, and to permit persons to whom the
2000# Software is furnished to do so, subject to the following conditions:
2001#
2002# The above copyright notice and this permission notice shall be included
2003# in all copies or substantial portions of the Software.
2004#
2005# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
2006# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
2007# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
2008# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
2009# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
2010# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
2011# OTHER DEALINGS IN THE SOFTWARE.
2013# ***) GNU GPL 3
2014#
2015# Copyright (C) 2011-2012 Helder Correia <Helder.MC@Gmail.com>
2016#
2017# This program is free software: you can redistribute it and/or
2018# modify it under the terms of the GNU General Public License as
2019# published by the Free Software Foundation, either version 3 of
2020# the License, or any later version.
2021#
2022# This program is distributed in the hope that it will be useful,
2023# but WITHOUT ANY WARRANTY; without even the implied warranty of
2024# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
2025# GNU General Public License for more details.
2026#
2027# You should have received a copy of the GNU General Public License
2028# along with this program. If not, see <http://www.GNU.org/licenses/>.
2029#
2030# You should have received the README file along with this program.
2031# If not, see <https://GitHub.com/helderco/univ-polyclip>.