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, _xkwds_pop2
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_, _duplicate_, _e_, \
28 _ELLIPSIS_, _few_, _height_, _lat_, _LatLon_, \
29 _lon_, _not_, _points_, _SPACE_, _too_, _X_, \
30 _x_, _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 _name__, _Named, _NotImplemented, \
35 Fmt, pairs, unstr
36# from pygeodesy.namedTuples import LatLon2Tupe # from .latlonBase
37# from pygeodesy.points import boundsOf # _MODS
38# from pygeodesy.props import Property_RO, property_RO # from .latlonBase
39# from pygeodesy.streprs import Fmt, pairs, unstr # from .named
40from pygeodesy.units import Height, HeightX
41from pygeodesy.utily import fabs, _unrollon, _Wrap
43# from math import fabs # from .utily
45__all__ = _ALL_LAZY.booleans
46__version__ = '24.09.28'
48_0_EPS = EPS # near-zero, positive
49_EPS_0 = -EPS # near-zero, negative
50_1_EPS = _1_0 + EPS # near-one, over
51_EPS_1 = _1_0 - EPS # near-one, under
52_10EPS = EPS * 10 # see ._2Abs, ._10eps
54_alpha_ = 'alpha'
55_boolean_ = 'boolean'
56_case_ = 'case'
57_corners_ = 'corners'
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, wrap=False, **name):
127 '''New C{LatLon[FHP|GH]} from separate C{lat}, C{lon}, C{height} and C{clipid}
128 scalars or from a previous C{LatLon[FHP|GH]}, C{Clip[FHP|GH]4Tuple} or some
129 other C{LatLon} instance.
131 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (C{LatLon[FHP|GH]},
132 C{Clip[FHP|GH]4Tuple} or some other C{LatLon}).
133 @kwarg lon: Longitude (C{scalar}), required B{C{lat_ll}} is scalar,
134 ignored otherwise.
135 @kwarg height: Height (C{scalar}), conventionally C{meter}.
136 @kwarg clipid: Clip identifier (C{int}).
137 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}} (C{bool}).
138 @kwarg name: Optional C{B{name}=NN} (C{str}).
139 '''
140 h, name = _xkwds_pop2(name, h=height) if name else (height, name)
142 if lon is None:
143 y, x = lat_ll.lat, lat_ll.lon
144 h = _xattr(lat_ll, height=h)
145 c = _xattr(lat_ll, clipid=clipid)
146 else:
147 y, x, c = lat_ll, lon, clipid
148 self.y, self.x = _Wrap.latlon(y, x) if wrap else (y, x)
149 # don't duplicate defaults
150 if self._height != h:
151 self._height = h
152 if self._clipid != c:
153 self._clipid = c
154 if name:
155 self.name = name
157 def __abs__(self):
158 return max(fabs(self.x), fabs(self.y))
160 def __eq__(self, other):
161 return other is self or bool(_other(self, other) and
162 other.x == self.x and
163 other.y == self.y)
165 def __ne__(self, other): # required for Python 2
166 return not self.__eq__(other)
168 def __repr__(self):
169 '''String C{repr} of this lat-/longitude.
170 '''
171 if self._prev or self._next:
172 t = _ELLIPSIS_(self._prev, self._next)
173 t = _SPACE_(self, Fmt.ANGLE(t))
174 else:
175 t = str(self)
176 return t
178 def __str__(self):
179 '''String C{str} of this lat-/longitude.
180 '''
181 t = (_lat_, self.lat), (_lon_, self.lon)
182 if self._height:
183 X = _X_ if self.isintersection else NN
184 t += (_height_ + X, self._height),
185 if self._clipid:
186 t += (_clipid_, self._clipid),
187 if self._alpha is not None:
188 t += (_alpha_, self._alpha),
189# if self._dupof: # recursion risk
190# t += (_dupof_, self._dupof.name),
191 t = pairs(t, prec=8, fmt=Fmt.g, ints=True)
192 t = Fmt.PAREN(_COMMASPACE_.join(t))
193 if self._linked:
194 k = _DOT_ if self._checked else _BANG_
195 t = NN(t, self._e_x_str(k)) # PYCHOK expected
196 return NN(self.name, t)
198 def __sub__(self, other):
199 _other(self, other)
200 return self.__class__(self.y - other.y, # classof
201 self.x - other.x)
203 def _2A(self, p2, p3):
204 # I{Signed} area of a triangle, I{doubled}.
205 x, y = self.x, self.y
206 return (p2.x - x) * (p3.y - y) - \
207 (p3.x - x) * (p2.y - y)
209 def _2Abs(self, p2, p3, eps=_10EPS):
210 # I{Unsigned} area of a triangle, I{doubled}
211 # or 0 if below the given threshold C{eps}.
212 a = fabs(self._2A(p2, p3))
213 return 0 if a < eps else a
215 @property_RO
216 def clipid(self):
217 '''Get the I{clipid} (C{int} or C{0}).
218 '''
219 return self._clipid
221 def _equi(self, llb, eps):
222 # Is this LLB I{equivalent} to B{C{llb}} within
223 # the given I{non-negative} tolerance B{C{eps}}?
224 return not (fabs(llb.lon - self.x) > eps or
225 fabs(llb.lat - self.y) > eps)
227 @property_RO
228 def height(self):
229 '''Get the I{height} (C{Height} or C{int}).
230 '''
231 h = self._height
232 return HeightX(h) if self.isintersection else (
233 Height(h) if h else _LatLonBool._height)
235 def isequalTo(self, other, eps=None):
236 '''Is this point equal to an B{C{other}} within a given,
237 I{non-negative} tolerance, ignoring C{height}?
239 @arg other: The other point (C{LatLon}).
240 @kwarg eps: Tolerance for equality (C{degrees} or C{None}).
242 @return: C{True} if equivalent, C{False} otherwise (C{bool}).
244 @raise TypeError: Invalid B{C{other}}.
245 '''
246 try:
247 return self._equi(other, _eps0(eps))
248 except (AttributeError, TypeError, ValueError):
249 raise _IsnotError(_LatLon_, other=other)
251 @property_RO
252 def isintersection(self):
253 '''Is this an intersection? May be C{ispoint} too!
254 '''
255 return bool(self._linked)
257 @property_RO
258 def ispoint(self):
259 '''Is this an I{original} point? May be C{isintersection} too!
260 '''
261 return self._alpha is None
263 @property_RO
264 def lat(self):
265 '''Get the latitude (C{scalar}).
266 '''
267 return self.y
269 @property_RO
270 def latlon(self):
271 '''Get the lat- and longitude (L{LatLon2Tuple}).
272 '''
273 return LatLon2Tuple(self.y, self.x)
275 def _link(self, other):
276 # Make this and an other point neighbors.
277 # assert _other(self, other)
278 self._linked = other
279 other._linked = self
281 @property_RO
282 def lon(self):
283 '''Get the longitude (C{scalar}).
284 '''
285 return self.x
287 def _toClas(self, Clas, clipid):
288 # Return this vertex as a C{Clas} instance
289 # (L{Clip[FHP|GH]4Tuple} or L{LatLon[FHP|GH]}).
290 return Clas(self.lat, self.lon, self.height, clipid)
293class LatLonFHP(_LatLonBool):
294 '''A point or intersection in a L{BooleanFHP} clip or composite.
295 '''
296 _en_ex = None
297 _label = None
298 _2split = None # or C{._Clip}
299 _2xing = False
301 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, **wrap_name):
302 '''New C{LatLonFHP} from separate C{lat}, C{lon}, C{h}eight and C{clipid}
303 scalars, or from a previous L{LatLonFHP}, L{ClipFHP4Tuple} or some other
304 C{LatLon} instance.
306 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (L{LatLonFHP},
307 L{ClipFHP4Tuple} or some other C{LatLon}).
309 @see: L{Here<_LatLonBool.__init__>} for further details.
310 '''
311 _LatLonBool.__init__(self, lat_ll, lon, height, clipid, **wrap_name)
313 def __add__(self, other):
314 _other(self, other)
315 return self.__class__(self.y + other.y, self.x + other.x)
317 def __mod__(self, other): # cross product
318 _other(self, other)
319 return self.x * other.y - self.y * other.x
321 def __mul__(self, other): # dot product
322 _other(self, other)
323 return self.x * other.x + self.y * other.y
325 def __rmul__(self, other): # scalar product
326 _xscalar(other=other)
327 return self.__class__(self.y * other, self.x * other)
329 def _e_x_str(self, t): # PYCHOK no cover
330 if self._label:
331 t = NN(self._label, t)
332 if self._en_ex:
333 t = NN(t, self._en_ex)
334 return t
336 @property_RO
337 def _isduplicate(self):
338 # Is this point a I{duplicate} intersection?
339 p = self._dupof
340 return bool(p and self._linked
341 and p is not self
342 and p == self
343# and p._alpha in (None, self._alpha)
344 and self._alpha in (_0_0, p._alpha))
346# @property_RO
347# def _isduplicated(self):
348# # Return the number of I{duplicates}?
349# d, v = 0, self
350# while v:
351# if v._dupof is self:
352# d += 1
353# v = v._next
354# if v is self:
355# break
356# return d
358 def isenclosedBy(self, *composites_points, **wrap):
359 '''Is this point inside one or more composites or polygons based on
360 the U{winding number<https://www.ScienceDirect.com/science/article/
361 pii/S0925772101000128>}?
363 @arg composites_points: Composites and/or iterables of points
364 (L{ClipFHP4Tuple}, L{ClipGH4Tuple}, L{LatLonFHP},
365 L{LatLonGH} or any C{LatLon}).
366 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True},
367 wrap or I{normalize} and unroll all C{points} (C{bool}).
369 @raise ValueError: Some C{points} invalid.
371 @see: U{Algorithm 6<https://www.ScienceDirect.com/science/
372 article/pii/S0925772101000128>}.
373 '''
374 class _Pseudo(object):
375 # Pseudo-_CompositeBase._clips tuple
377 @property_RO
378 def _clips(self):
379 for cp in _Cps(_CompositeFHP, composites_points,
380 LatLonFHP.isenclosedBy): # PYCHOK yield
381 for c in cp._clips:
382 yield c
384 return self._isinside(_Pseudo(), **wrap)
386 def _isinside(self, composite, *excludes, **wrap):
387 # Is this point inside a composite, excluding
388 # certain C{_Clip}s? I{winding number}?
389 x, y, i = self.x, self.y, False
390 for c in composite._clips:
391 if c not in excludes:
392 w = 0
393 for p1, p2 in c._edges2(**wrap):
394 # edge [p1,p2] must straddle y
395 if (p1.y < y) is not (p2.y < y): # or ^
396 r = p2.x > x
397 s = p2.y > p1.y
398 if p1.x < x:
399 b = r and (s is (p1._2A(p2, self) > 0))
400 else:
401 b = r or (s is (p1._2A(p2, self) > 0))
402 if b:
403 w += 1 if s else -1
404 if isodd(w):
405 i = not i
406 return i
408 @property_RO
409 def _prev_next2(self):
410 # Adjust 2-tuple (._prev, ._next) iff a I{duplicate} intersection
411 p, n = self, self._next
412 if self._isduplicate:
413 p = self._dupof
414 while p._isduplicate:
415 p = p._dupof
416 while n._isduplicate:
417 n = n._next
418 return p._prev, n
420# def _edge2(self):
421# # Return the start and end point of the
422# # edge containing I{intersection} C{v}.
423# n = p = self
424# while p.isintersection:
425# p = p._prev
426# if p is self:
427# break
428# while n.isintersection:
429# n = n._next
430# if n is self:
431# break
432# # assert p == self or not p._2Abs(self, n)
433# return p, n
435 def _RPoracle(self, p1, p2, p3):
436 # Relative Position oracle
437 if p1._linked is self: # or p1._linked2(self):
438 T = _RP.IS_Pm
439 elif p3._linked is self: # or p3._linked2(self):
440 T = _RP.IS_Pp
441 elif p1._2A(p2, p3) > 0: # left turn
442 T = _RP.LEFT if self._2A(p1, p2) > 0 and \
443 self._2A(p2, p3) > 0 else \
444 _RP.RIGHT # PYCHOK indent
445 else: # right turn (or straight)
446 T = _RP.RIGHT if self._2A(p1, p2) < 0 and \
447 self._2A(p2, p3) < 0 else \
448 _RP.LEFT # PYCHOK indent
449 return T
452class LatLonGH(_LatLonBool):
453 '''A point or intersection in a L{BooleanGH} clip or composite.
454 '''
455 _entry = None # entry or exit iff intersection
457 def __init__(self, lat_ll, lon=None, height=0, clipid=INT0, **wrap_name):
458 '''New C{LatLonGH} from separate C{lat}, C{lon}, C{h}eight and C{clipid}
459 scalars, or from a previous L{LatLonGH}, L{ClipGH4Tuple} or some other
460 C{LatLon} instance.
462 @arg lat_ll: Latitude (C{scalar}) or a lat-/longitude (L{LatLonGH},
463 L{ClipGH4Tuple} or some other C{LatLon}).
465 @see: L{Here<_LatLonBool.__init__>} for further details.
466 '''
467 _LatLonBool.__init__(self, lat_ll, lon, height, clipid, **wrap_name)
469 def _check(self):
470 # Check-mark this vertex and its link.
471 self._checked = True
472 k = self._linked
473 if k and not k._checked:
474 k._checked = True
476 def _e_x_str(self, t): # PYCHOK no cover
477 return t if self._entry is None else NN(t,
478 (_e_ if self._entry else _x_))
480 def isenclosedBy(self, *composites_points, **wrap):
481 '''Is this point inside one or more composites or polygons based
482 on the U{even-odd-rule<https://www.ScienceDirect.com/science/
483 article/pii/S0925772101000128>}?
485 @arg composites_points: Composites and/or iterables of points
486 (L{ClipFHP4Tuple}, L{ClipGH4Tuple}, L{LatLonFHP},
487 L{LatLonGH} or any C{LatLon}).
488 @kwarg wrap: Optional keyword argument C{B{wrap}=False}, if C{True},
489 wrap or I{normalize} and unroll all C{points} (C{bool}).
491 @raise ValueError: Some B{C{points}} invalid.
492 '''
493 class _Pseudo(object):
494 # Pseudo-_CompositeBase._edges3 method
496 def _edges3(self, **kwds):
497 for cp in _Cps(_CompositeGH, composites_points,
498 LatLonGH.isenclosedBy): # PYCHOK yield
499 for e in cp._edges3(**kwds):
500 yield e
502 return self._isinside(_Pseudo(), **wrap)
504 def _isinside(self, composite, *bottom_top, **wrap):
505 # Is this vertex inside the composite? I{even-odd rule}?
507 def _x(y, p1, p2):
508 # return C{x} at given C{y} on edge [p1,p2]
509 return (y - p1.y) / (p2.y - p1.y) * (p2.x - p1.x)
511 # The I{even-odd} rule counts the number of edges
512 # intersecting a ray emitted from this point to
513 # east-bound infinity. When I{odd} this point lies
514 # inside, if I{even} outside.
515 y, i = self.y, False
516 if not (bottom_top and _outside(y, y, *bottom_top)):
517 x = self.x
518 for p1, p2, _ in composite._edges3(**wrap):
519 if (p1.y < y) is not (p2.y < y): # or ^
520 r = p2.x > x
521 if p1.x < x:
522 b = r and (_x(y, p1, p2) > x)
523 else:
524 b = r or (_x(y, p1, p2) > x)
525 if b:
526 i = not i
527 return i
530class _Clip(_Named):
531 '''(INTERNAL) A I{doubly-linked} list representing a I{closed}
532 polygon of L{LatLonFHP} or L{LatLonGH} points, duplicates
533 and intersections with other clips.
534 '''
535 _composite = None
536 _dups = 0
537 _first = None
538 _id = 0
539 _identical = False
540 _noInters = False
541 _last = None
542 _LL = None
543 _len = 0
544 _pushback = False
546 def __init__(self, composite, clipid=INT0):
547 '''(INTERNAL) New C{_Clip}.
548 '''
549 # assert isinstance(composite, _CompositeBase)
550 if clipid in composite._clipids:
551 raise ClipError(clipid=clipid, txt=_duplicate_)
552 self._composite = composite
553 self._id = clipid
554 self._LL = composite._LL
555 composite._clips = composite._clips + (self,)
557 def __contains__(self, point): # PYCHOK no cover
558 '''Is the B{C{point}} in this clip?
559 '''
560 for v in self:
561 if v is point: # or ==?
562 return True
563 return False
565 def __eq__(self, other):
566 '''Is this clip I{equivalent} to an B{C{other}} clip,
567 do both have the same C{len}, the same points, in
568 the same order, possibly rotated?
569 '''
570 return self._equi(_other(self, other), 0)
572 def __ge__(self, other):
573 '''See method C{__lt__}.
574 '''
575 return not self.__lt__(other)
577 def __gt__(self, other):
578 '''Is this clip C{"above"} an B{C{other}} clip,
579 located or stretched farther North or East?
580 '''
581 return self._bltr4 > _other(self, other)._bltr4
583 def __hash__(self): # PYCHOK no over
584 return hash(self._bltr4)
586 def __iter__(self):
587 '''Yield the points, duplicates and intersections.
588 '''
589 v = f = self._first
590 while v:
591 yield v
592 v = v._next
593 if v is f:
594 break
596 def __le__(self, other):
597 '''See method C{__gt__}.
598 '''
599 return not self.__gt__(other)
601 def __len__(self):
602 '''Return the number of points, duplicates and
603 intersections in this clip.
604 '''
605 return self._len
607 def __lt__(self, other):
608 '''Is this clip C{"below"} an B{C{other}} clip,
609 located or stretched farther South or West?
610 '''
611 return self._bltr4 < _other(self, other)._bltr4
613 def __ne__(self, other): # required for Python 2
614 '''See method C{__eq__}.
615 '''
616 return not self.__eq__(other)
618 _all = __iter__
620 @property_RO
621 def _all_ON_ON(self):
622 # Check whether all vertices are ON_ON.
623 L_ON_ON = _L.ON_ON
624 return all(v._label is L_ON_ON for v in self)
626 def _append(self, y_v, *x_h_clipid):
627 # Append a point given as C{y}, C{x}, C{h}eight and
628 # C{clipid} args or as a C{LatLon[FHP|GH]}.
629 self._last = v = self._LL(y_v, *x_h_clipid) if x_h_clipid else y_v
630 self._len += 1
631 # assert v._clipid == self._id
633 v._next = n = self._first
634 if n is None: # set ._first
635 self._first = p = n = v
636 else: # insert before ._first
637 v._prev = p = n._prev
638 p._next = n._prev = v
639 return v
641# def _appendedup(self, v, clipid=0):
642# # Like C{._append}, but only append C{v} if not a
643# # duplicate of the one previously append[edup]'ed.
644# y, x, p = v.y, v.x, self._last
645# if p is None or y != p.y or x != p.x or clipid != p._clipid:
646# p = self._append(y, x, v._height, clipid)
647# if v._linked:
648# p._linked = True # to force errors
649# return p
651 @Property_RO
652 def _bltr4(self):
653 # Get the bounds as 4-tuple C{(bottom, left, top, right)}.
654 return map2(float, _MODS.points.boundsOf(self, wrap=False))
656 def _bltr4eps(self, eps):
657 # Get the ._bltr4 bounds tuple, slightly oversized.
658 if eps > 0: # > EPS
659 yb, xl, yt, xr = self._bltr4
660 yb, yt = _low_high_eps2(yb, yt, eps)
661 xl, xr = _low_high_eps2(xl, xr, eps)
662 t = yb, xl, yt, xr
663 else:
664 t = self._bltr4
665 return t
667 def _closed(self, raiser): # PYCHOK unused
668 # End a clip, un-close it and check C{len}.
669 p, f = self._last, self._first
670 if f and f._prev is p and p is not f and \
671 p._next is f and p == f: # PYCHOK no cover
672 # un-close the clip
673 f._prev = p = p._prev
674 p._next = f
675 self._len -= 1
676# elif f and raiser:
677# raise self._OpenClipError(p, f)
678 if len(self) < 3:
679 raise self._Error(_too_(_few_))
681 def _dup(self, q):
682 # Duplicate a point (or intersection) as intersection.
683 v = self._insert(q.y, q.x, q)
684 v._alpha = q._alpha or _0_0 # _0_0 replaces None
685 v._dupof = q._dupof or q
686 # assert v._prev is q
687 # assert q._next is v
688 return v
690 def _edges2(self, wrap=False, **unused):
691 # Yield each I{original} edge as a 2-tuple
692 # (p1, p2), a pair of C{LatLon[FHP|GH])}s.
693 p1 = p = f = self._first
694 while p:
695 p2 = p = p._next
696 if p.ispoint:
697 if wrap and p is not f:
698 p2 = _unrollon(p1, p)
699 yield p1, p2
700 p1 = p2
701 if p is f:
702 break
704 def _equi(self, clip, eps):
705 # Is this clip I{equivalent} to B{C{clip}} within
706 # the given I{non-negative} tolerance B{C{eps}}?
707 r, f = len(self), self._first
708 if f and r == len(clip) and self._bltr4eps(eps) \
709 == clip._bltr4eps(eps):
710 _equi = _LatLonBool._equi
711 for v in clip:
712 if _equi(f, v, eps):
713 s, n = f, v
714 for _ in range(r):
715 s, n = s._next, n._next
716 if not _equi(s, n, eps):
717 break # next v
718 else: # equivalent
719 return True
720 return False
722 def _Error(self, txt): # PYCHOK no cover
723 # Build a C{ClipError} instance
724 kwds = dict(len=len(self), txt=txt)
725 if self._dups:
726 kwds.update(dups=self._dups)
727 cp = self._composite
728 if self._id:
729 try:
730 i = cp._clips.index(self)
731 if i != self._id:
732 kwds[_clip_] = i
733 except ValueError:
734 pass
735 kwds[_clipid_] = self._id
736 return ClipError(cp._kind, cp.name, **kwds)
738 def _index(self, clips, eps):
739 # see _CompositeBase._equi
740 for i, c in enumerate(clips):
741 if c._equi(self, eps):
742 return i
743 raise ValueError(NN) # like clips.index(self)
745 def _insert(self, y, x, start, *end_alpha):
746 # insertVertex between points C{start} and
747 # C{end}, ordered by C{alpha} iff given.
748 v = self._LL(y, x, start._height, start._clipid)
749 n = start._next
750 if end_alpha:
751 end, alpha = end_alpha
752 v._alpha = alpha
753 v._height = favg(v._height, end._height, f=alpha)
754 # assert start is not end
755 while n is not end and n._alpha < alpha:
756 n = n._next
757 v._next = n
758 v._prev = p = n._prev
759 p._next = n._prev = v
760 self._len += 1
761# _Clip._bltr4._update(self)
762# _Clip._ishole._update(self)
763 return v
765 def _intersection(self, unused, q, *p1_p2_alpha):
766 # insert an intersection or make a point both
767 if p1_p2_alpha: # intersection on edge
768 v = self._insert(q.y, q.x, *p1_p2_alpha)
769 else: # intersection at point
770 v = q
771 # assert not v._linked
772 # assert v._alpha is None
773 return v
775 def _intersections(self):
776 # Yield all intersections, some may be points too.
777 for v in self:
778 if v.isintersection:
779 yield v
781 @Property_RO
782 def _ishole(self): # PYCHOK no cover
783 # Is this clip a hole inside its composite?
784 v = self._first
785 return v._isinside(self._composite, self) if v else False
787 @property_RO
788 def _nodups(self):
789 # Yield all non-duplicates.
790 for v in self:
791 if not v._dupof:
792 yield v
794 def _noXings(self, Union):
795 # Are all intersections non-CROSSINGs, -BOUNCINGs?
796 Xings = _L.BOUNCINGs if Union else _L.CROSSINGs
797 return all(v._label not in Xings for v in self._intersections())
799 def _OpenClipError(self, s, e): # PYCHOK no cover
800 # Return a C{CloseError} instance
801 t = NN(s, _ELLIPSIS_(_COMMASPACE_, e))
802 return self._Error(_SPACE_(_open_, t))
804 def _point2(self, insert):
805 # getNonIntersectionPoint and -Vertex
806 if not (insert and self._noInters):
807 for p in self._points(may_be=False): # not p._isduplicated?
808 return p, None
809 for n in self._intersections():
810 p, _ = n._prev_next2
811 k = p._linked
812 if k:
813 if n._linked not in k._prev_next2:
814 # create a pseudo-point
815 k = _0_5 * (p + n)
816 if insert:
817 k = self._insert(k.y, k.x, n._prev)
818 r = k # to remove later
819 else: # no ._prev, ._next
820 k._clipid = n._clipid
821 r = None
822 return k, r
823 return None, None
825 def _points(self, may_be=True):
826 # Yield all points I{in original order}, which may be intersections too.
827 for v in self:
828 if v.ispoint and (may_be or not v.isintersection):
829 yield v
831 def _remove2(self, v):
832 # Remove vertex C{v}.
833 # assert not v._isduplicated
834 if len(self) > 1:
835 p = v._prev
836 p._next = n = v._next
837 n._prev = p
838 if self._first is v:
839 self._first = n
840 if self._last is v:
841 self._last = p
842 self._len -= 1
843 else:
844 n = self._last = \
845 p = self._first = None
846 self._len = 0
847 return p, n
849 def _update_all(self): # PYCHOK no cover
850 # Zap the I{cached} properties.
851 _Clip._bltr4._update( self)
852 _Clip._ishole._update(self)
853 return self # for _special_identicals
855 def _Xings(self):
856 # Yield all I{un-checked} CROSSING intersections.
857 CROSSING = _L.CROSSING
858 for v in self._intersections():
859 if v._label is CROSSING and not v._checked:
860 yield v
863class _CompositeBase(_Named):
864 '''(INTERNAL) Base class for L{BooleanFHP} and L{BooleanGH}
865 (C{_CompositeFHP} and C{_CompositeGH}).
866 '''
867 _clips = () # tuple of C{_Clips}
868 _eps = EPS # null edges
869 _kind = _corners_
870 _LL = _LatLonBool # shut up PyChecker
871 _raiser = False
872 _xtend = False
874 def __init__(self, lls, kind=NN, eps=EPS, **name):
875 '''(INTERNAL) See L{BooleanFHP} and L{BooleanGH}.
876 '''
877 n = _name__(name, _or_nameof=lls)
878 if n:
879 self.name = n
880 if kind:
881 self._kind = kind
882 if self._eps < eps:
883 self._eps = eps
885 c = _Clip(self)
886 lp = None
887 for ll in lls:
888 ll = self._LL(ll)
889 if lp is None:
890 c._id = ll._clipid # keep clipid
891 lp = c._append(ll)
892 elif ll._clipid != lp._clipid: # new clip
893 c._closed(self.raiser)
894 c = _Clip(self, ll._clipid)
895 lp = c._append(ll)
896 elif abs(ll - lp) > eps: # PYCHOK lp
897 lp = c._append(ll)
898 else:
899 c._dups += 1
900 c._closed(self.raiser)
902 def __contains__(self, point): # PYCHOK no cover
903 '''Is the B{C{point}} in one of the clips?
904 '''
905 for c in self._clips:
906 if point in c:
907 return True
908 return False
910 def __eq__(self, other):
911 '''Is this I{composite} equivalent to an B{C{other}}, i.e.
912 do both contain I{equivalent} clips in the same or in a
913 different order? Two clips are considered I{equivalent}
914 if both have the same points etc. in the same order,
915 possibly rotated.
916 '''
917 return self._equi(_other(self, other), 0)
919 def __iter__(self):
920 '''Yield all points, duplicates and intersections.
921 '''
922 for c in self._clips:
923 for v in c:
924 yield v
926 def __ne__(self, other): # required for Python 2
927 '''See method C{__eq__}.
928 '''
929 return not self.__eq__(other)
931 def __len__(self):
932 '''Return the I{total} number of points.
933 '''
934 return sum(map(len, self._clips)) if self._clips else 0
936 def __repr__(self):
937 '''String C{repr} of this composite.
938 '''
939 c = len(self._clips)
940 c = Fmt.SQUARE(c) if c > 1 else NN
941 n = Fmt.SQUARE(len(self))
942 t = Fmt.PAREN(self) # XXX not unstr
943 return NN(self.__class__.__name__, c, n, t)
945 def __str__(self):
946 '''String C{str} of this composite.
947 '''
948 return _COMMASPACE_.join(map(str, self))
950 @property_RO
951 def _bottom_top_eps2(self):
952 # Get the bottom and top C{y} bounds, oversized.
953 return _min_max_eps2(min(v.y for v in self),
954 max(v.y for v in self))
956 def _class(self, corners, kwds, **dflts):
957 # Return a new instance
958 _g = kwds.get
959 kwds = dict((n, _g(n, v)) for n, v in dflts.items())
960 return self.__class__(corners or (), **kwds)
962 @property_RO
963 def _clipids(self): # PYCHOK no cover
964 for c in self._clips:
965 yield c._id
967 def clipids(self):
968 '''Return a tuple with all C{clipid}s, I{ordered}.
969 '''
970 return tuple(self._clipids)
972# def _clipidups(self, other):
973# # Number common C{clipid}s between this and an C{other} composite
974# return len(set(self._clipids).intersection(set(other._clipids)))
976 def _edges3(self, **raiser_wrap):
977 # Yield each I{original} edge as a 3-tuple
978 # C{(LatLon[FHP|GH], LatLon[FHP|GH], _Clip)}.
979 for c in self._clips:
980 for p1, p2 in c._edges2(**raiser_wrap):
981 yield p1, p2, c
983 def _encloses(self, lat, lon, **wrap):
984 # see function .points.isenclosedBy
985 return self._LL(lat, lon).isenclosedBy(self, **wrap)
987 @property
988 def eps(self):
989 '''Get the null edges tolerance (C{degrees}, usually).
990 '''
991 return self._eps
993 @eps.setter # PYCHOK setter!
994 def eps(self, eps):
995 '''Set the null edges tolerance (C{degrees}, usually).
996 '''
997 self._eps = eps
999 def _10eps(self, **eps_):
1000 # Get eps for _LatLonBool._2Abs
1001 e = _xkwds_get(eps_, eps=self._eps)
1002 if e != EPS:
1003 e *= _10EPS / EPS
1004 else:
1005 e = _10EPS
1006 return e
1008 def _equi(self, other, eps):
1009 # Is this composite I{equivalent} to an B{C{other}} within
1010 # the given, I{non-negative} tolerance B{C{eps}}?
1011 cs, co = self._clips, other._clips
1012 if cs and len(cs) == len(co):
1013 if eps > 0:
1014 _index = _Clip._index
1015 else:
1016 def _index(c, cs, unused):
1017 return cs.index(c)
1018 try:
1019 cs = list(sorted(cs))
1020 for c in sorted(co):
1021 cs.pop(_index(c, cs, eps))
1022 except ValueError: # from ._index
1023 pass
1024 return False if cs else True
1025 else: # both null?
1026 return False if cs or co else True
1028 def _intersections(self):
1029 # Yield all intersections.
1030 for c in self._clips:
1031 for v in c._intersections():
1032 yield v
1034 def isequalTo(self, other, eps=None):
1035 '''Is this boolean/composite equal to an B{C{other}} within
1036 a given, I{non-negative} tolerance?
1038 @arg other: The other boolean/composite (C{Boolean[FHP|GB]}).
1039 @kwarg eps: Tolerance for equality (C{degrees} or C{None}).
1041 @return: C{True} if equivalent, C{False} otherwise (C{bool}).
1043 @raise TypeError: Invalid B{C{other}}.
1045 @see: Method C{__eq__}.
1046 '''
1047 if isinstance(other, _CompositeBase):
1048 return self._equi(other, _eps0(eps))
1049 raise _IsnotError(_boolean_, _composite_, other=other)
1051 def _kwds(self, op, **more):
1052 # Get all keyword arguments as C{dict}.
1053 kwds = dict(raiser=self.raiser, eps=self.eps,
1054 name=self.name or op.__name__)
1055 kwds.update(more)
1056 return kwds
1058 @property_RO
1059 def _left_right_eps2(self):
1060 # Get the left and right C{x} bounds, oversized.
1061 return _min_max_eps2(min(v.x for v in self),
1062 max(v.x for v in self))
1064 def _points(self, may_be=True): # PYCHOK no cover
1065 # Yield all I{original} points, which may be intersections too.
1066 for c in self._clips:
1067 for v in c._points(may_be=may_be):
1068 yield v
1070 @property
1071 def raiser(self):
1072 '''Get the option to throw L{ClipError} exceptions (C{bool}).
1073 '''
1074 return self._raiser
1076 @raiser.setter # PYCHOK setter!
1077 def raiser(self, throw):
1078 '''Set the option to throw L{ClipError} exceptions (C{bool}).
1079 '''
1080 self._raiser = bool(throw)
1082 def _results(self, _presults, Clas, closed=False, inull=False, **eps):
1083 # Yield the dedup'd results, as L{ClipFHP4Tuple}s
1084 C = self._LL if Clas is None else Clas
1085 e = self._10eps(**eps)
1086 for clipid, ns in enumerate(_presults):
1087 f = p = v = None
1088 for n in ns:
1089 if f is None:
1090 yield n._toClas(C, clipid)
1091 f = p = n
1092 elif v is None:
1093 v = n # got f, p, v
1094 elif inull or p._2Abs(v, n, eps=e):
1095 yield v._toClas(C, clipid)
1096 p, v = v, n
1097 else: # null, colinear, ... skipped
1098 v = n
1099 if v and (inull or p._2Abs(v, f, eps=e)):
1100 yield v._toClas(C, clipid)
1101 p = v
1102 if f and p != f and closed: # close clip
1103 yield f._toClas(C, clipid)
1105 def _sum(self, other, op):
1106 # Combine this and an C{other} composite
1107 LL = self._LL
1108 sp = self.copy(name=self.name or op.__name__)
1109 sp._clips, sid = (), INT0 # new clips
1110 for cp in (self, other):
1111 for c in cp._clips:
1112 _ap = _Clip(sp, sid)._append
1113 for v in c._nodups:
1114 _ap(LL(v.y, v.x, v.height, sid))
1115 sid += 1
1116 return sp
1118 def _sum1(self, _a_p, *args, **kwds): # in .karney, .points
1119 # Sum the area or perimeter of all clips
1120 return _MODS.fsums.fsum1((_a_p(c, *args, **kwds) for c in self._clips))
1122 def _sum2(self, LL, _a_p, *args, **kwds): # in .sphericalNvector, -Trigonometry
1123 # Sum the area or perimeter of all clips
1125 def _lls(clip): # convert clip to LLs
1126 _LL = LL
1127 for v in clip:
1128 yield _LL(v.lat, v.lon) # datum=Sphere
1130 return _MODS.fsums.fsum1((_a_p(_lls(c), *args, **kwds) for c in self._clips))
1132 def toLatLon(self, LatLon=None, closed=False, **LatLon_kwds):
1133 '''Yield all (non-duplicate) points and intersections
1134 as an instance of B{C{LatLon}}.
1136 @kwarg LatLon: Class to use (C{LatLon}) or if C{None},
1137 L{LatLonFHP} or L{LatLonGH}.
1138 @kwarg closed: If C{True}, close each clip (C{bool}).
1139 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}}
1140 keyword arguments, ignore if
1141 C{B{LatLon} is None}.
1143 @raise TypeError: Invalid B{C{LatLon}}.
1145 @note: For intersections, C{height} is an instance
1146 of L{HeightX}, otherwise of L{Height}.
1147 '''
1148 if LatLon is None:
1149 LL, kwds = self._LL, {}
1150 elif issubclassof(LatLon, _LatLonBool, LatLonBase):
1151 LL, kwds = LatLon, LatLon_kwds
1152 else:
1153 raise _TypeError(LatLon=LatLon)
1155 for c in self._clips:
1156 lf, cid = None, c._id
1157 for v in c._nodups:
1158 ll = LL(v.y, v.x, **kwds)
1159 ll._height = v.height
1160 if ll._clipid != cid:
1161 ll._clipid = cid
1162 yield ll
1163 if lf is None:
1164 lf = ll
1165 if closed and lf:
1166 yield lf
1169class _CompositeFHP(_CompositeBase):
1170 '''(INTERNAL) A list of clips representing a I{composite}
1171 of L{LatLonFHP} points, duplicates and intersections
1172 with an other I{composite}.
1173 '''
1174 _LL = LatLonFHP
1175 _Union = False
1177 def __init__(self, lls, raiser=False, **name_kind_eps):
1178 # New L{_CompositeFHP}.
1179 if raiser:
1180 self._raiser = True
1181 _CompositeBase.__init__(self, lls, **name_kind_eps)
1183 def _classify(self):
1184 # 2) Classify intersection chains.
1185 L = _L
1186 for v in self._intersections():
1187 n, b = v, v._label
1188 if b in L.RIGHT_LEFT_ON: # next chain
1189 while True:
1190 n._label = None # _xkwds_pop(n.__dict__, _label=None)
1191 n = n._next
1192 if n is v or n._label is not L.ON_ON: # n._label and ...
1193 break
1194 a = L.LEFT_ON if n._label is L.ON_LEFT else L.RIGHT_ON
1195 v._label = n._label = L.BOUNCING_D if a is b else L.CROSSING_D
1197 # 3) Copy labels
1198 for v in self._intersections():
1199 v._linked._label = v._label
1201 def _clip(self, corners, Union=False, Clas=None,
1202 **closed_inull_raiser_eps):
1203 # Clip this composite with another one, C{corners},
1204 # using Foster-Hormann-Popa's algorithm.
1205 P = self
1206 Q = self._class(corners, closed_inull_raiser_eps,
1207 eps=P._eps, raiser=False)
1208 if Union:
1209 P._Union = Q._Union = True
1211 bt = Q._bottom_top_eps2
1212 lr = Q._left_right_eps2
1213 # compute and insert intersections
1214 for p1, p2, Pc in P._edges3(**closed_inull_raiser_eps):
1215 if not (_outside(p1.x, p2.x, *lr) or
1216 _outside(p1.y, p2.y, *bt)):
1217 e = _EdgeFHP(p1, p2)
1218 if e._dp2 > EPS2: # non-null edge
1219 for q1, q2, Qc in Q._edges3(**closed_inull_raiser_eps):
1220 for T, p, q in e._intersect3(q1, q2):
1221 p = Pc._intersection(T, *p)
1222 q = Qc._intersection(T, *q)
1223 # assert not p._linked
1224 # assert not q._linked
1225 p._link(q)
1227 # label and classify intersections
1228 P._labelize()
1229 P._classify()
1231 # check for special cases
1232 P._special_cases(Q)
1233 Q._special_cases(P)
1234 # handle identicals
1235 P._special_identicals(Q)
1237 # set Entry/Exit flags
1238 P._set_entry_exits(Q)
1239 Q._set_entry_exits(P)
1241 # handle splits and crossings
1242 P._splits_xings(Q)
1244 # yield the results
1245 return P._results(P._presults(Q), Clas, **closed_inull_raiser_eps)
1247 @property_RO
1248 def _identicals(self):
1249 # Yield all clips marked C{._identical}.
1250 for c in self._clips:
1251 if c._identical:
1252 yield c
1254 def _labelize(self):
1255 # 1) Intersections classification
1256 for p in self._intersections():
1257 q = p._linked
1258 # determine local configuration at this intersection
1259 # and positions of Q- and Q+ relative to (P-, I, P+)
1260 p1, p3 = p._prev_next2
1261 q1, q3 = q._prev_next2
1262 t = (q1._RPoracle(p1, p, p3),
1263 q3._RPoracle(p1, p, p3))
1264 # check intersecting and overlapping cases
1265 p._label = _RP2L.get(t, None)
1267 def _presults(self, other):
1268 # Yield the result clips, each as a generator
1269 # of the L{_LatLonFHP}s in that clip
1270 for cp in (self, other):
1271 for c in cp._clips:
1272 if c._pushback:
1273 yield c._all()
1274 for c in self._clips:
1275 for X in c._Xings():
1276 yield self._resultX(X)
1278 def _resultX(self, X):
1279 # Yield the results from CROSSING C{X}.
1280 L, U, v = _L, self._Union, X
1281 while v:
1282 v._checked = True
1283 r = v # in P or Q
1284 s = L.Toggle[v._en_ex]
1285 e = (s is L.EXIT) ^ U
1286 while True:
1287 v = v._next if e else v._prev
1288 yield v
1289 v._checked = True
1290 if v._en_ex is s or v is X:
1291 break
1292 if v is r: # full circle
1293 raise ClipError(full_circle=v, clipid=v._clipid)
1294 if v is not X:
1295 v = v._linked
1296 if v is X:
1297 break
1299 def _set_entry_exits(self, other): # MCCABE 14
1300 # 4) Set entry/exit flags
1301 L, U = _L, self._Union
1302 for c in self._clips:
1303 n, k = c._point2(True)
1304 if n:
1305 f = n
1306 s = L.EXIT if n._isinside(other) else L.ENTRY
1307 t = L.EXIT # first_chain_vertex = True
1308 while True:
1309 if n.isintersection:
1310 b = n._label
1311 if b is L.CROSSING:
1312 n._en_ex = s
1313 s = L.Toggle[s]
1314 elif b is L.BOUNCING and ((s is L.EXIT) ^ U):
1315 n._2split = c # see ._splits_xings
1316 elif b is L.CROSSING_D:
1317 n._en_ex = s
1318 if (s is t) ^ U:
1319 n._label = L.CROSSING
1320 t = L.Toggle[t]
1321 if t is L.EXIT: # first_chain_vertex == True
1322 s = L.Toggle[s]
1323 elif b is L.BOUNCING_D:
1324 n._en_ex = s
1325 if (s is t) ^ U:
1326 n._2xing = True # see ._splits_xings
1327 s = L.Toggle[s]
1328 t = L.Toggle[t]
1329 n = n._next # _, n = n._prev_next2
1330 if n is f:
1331 break # PYCHOK attr?
1332 if k:
1333 c._remove2(k)
1335 def _special_cases(self, other):
1336 # 3.5) Check special cases
1337 U = self._Union
1338 for c in self._clips:
1339 if c._noXings(U):
1340 c._noInters = True
1341 if c._all_ON_ON:
1342 c._identical = True
1343 else:
1344 p, _ = c._point2(False)
1345 if p and (p._isinside(other) ^ U):
1346 c._pushback = True
1348 def _special_identicals(self, other):
1349 # 3.5) Handle identicals
1350 _u = _Clip._update_all
1351 cds = dict((c._id, _u(c)) for c in other._identicals)
1352 # assert len(cds) == len(other._identicals)
1353 if cds: # PYCHOK no cover
1354 for c in self._identicals:
1355 c._update_all()
1356 for v in c._intersections():
1357 d = cds.get(v._linked._clipid, None)
1358 if d and d._ishole is c._ishole:
1359 c._pushback = True
1360 break # next c
1362 @property_RO
1363 def _2splits(self):
1364 # Yield all intersections marked C{._2split}
1365 for p in self._intersections():
1366 if p._2split:
1367 # assert isinstance(p._2split, _Clip)
1368 yield p
1370 def _splits_xings(self, other): # MCCABE 15
1371 # 5) Handle split pairs and 6) crossing candidates
1373 def _2A_dup2(p, P): # PYCHOK unused
1374 p1, p2 = p._prev_next2
1375 ap = p1._2A(p, p2)
1376 Pc = p._2split
1377 # assert Pc in P._clips
1378 # assert p in Pc
1379 return ap, Pc._dup(p)
1381 def _links2(ps, qs): # PYCHOK P unused?
1382 # Yield each link as a 2-tuple(p, q)
1383 id_qs = set(map(id, qs))
1384 if id_qs:
1385 for p in ps:
1386 q = p._linked
1387 if q and id(q) in id_qs:
1388 yield p, q
1390 L = _L
1391 E = L.ENTRY if self._Union else L.EXIT
1392 X = L.Toggle[E]
1393 for p, q in _links2(self._2splits, other._2splits):
1394 ap, pp = _2A_dup2(p, self)
1395 aq, qq = _2A_dup2(q, other)
1396 if (ap * aq) > 0: # PYCHOK no cover
1397 p._link(qq) # overwrites ...
1398 q._link(pp) # ... p-q link
1399 else:
1400 pp._link(qq)
1401 p._en_ex = q._en_ex = E
1402 pp._en_ex = qq._en_ex = X
1403 p._label = pp._label = \
1404 q._label = qq._label = L.CROSSING
1406 for p, q in _links2(self._2xings, other._2xings):
1407 p._label = q._label = L.CROSSING
1409 @property_RO
1410 def _2xings(self):
1411 # Yield all intersections marked C{._2xing}
1412 for p in self._intersections():
1413 if p._2xing:
1414 yield p
1417class _CompositeGH(_CompositeBase):
1418 '''(INTERNAL) A list of clips representing a I{composite}
1419 of L{LatLonGH} points, duplicates and intersections
1420 with an other I{composite}.
1421 '''
1422 _LL = LatLonGH
1423 _xtend = False
1425 def __init__(self, lls, raiser=False, xtend=False, **name_kind_eps):
1426 # New L{_CompositeGH}.
1427 if xtend:
1428 self._xtend = True
1429 elif raiser:
1430 self._raiser = True
1431 _CompositeBase.__init__(self, lls, **name_kind_eps)
1433 def _clip(self, corners, s_entry, c_entry, Clas=None,
1434 **closed_inull_raiser_xtend_eps):
1435 # Clip this polygon with another one, C{corners}.
1437 # Core of Greiner/Hormann's algorithm, enhanced U{Correia's
1438 # <https://GitHub.com/helderco/univ-polyclip>} implementation***
1439 # and extended to optionally handle so-called "degenerate cases"
1440 S = self
1441 C = self._class(corners, closed_inull_raiser_xtend_eps,
1442 raiser=False, xtend=False)
1443 bt = C._bottom_top_eps2
1444 lr = C._left_right_eps2
1445 # 1. find intersections
1446 for s1, s2, Sc in S._edges3(**closed_inull_raiser_xtend_eps):
1447 if not (_outside(s1.x, s2.x, *lr) or
1448 _outside(s1.y, s2.y, *bt)):
1449 e = _EdgeGH(s1, s2, **closed_inull_raiser_xtend_eps)
1450 if e._hypot2 > EPS2: # non-null edge
1451 for c1, c2, Cc in C._edges3(**closed_inull_raiser_xtend_eps):
1452 for y, x, sa, ca in e._intersect4(c1, c2):
1453 s = Sc._insert(y, x, s1, s2, sa)
1454 c = Cc._insert(y, x, c1, c2, ca)
1455 s._link(c)
1457 # 2. identify entry/exit intersections
1458 if S._first:
1459 s_entry ^= S._first._isinside(C, *bt)
1460 for v in S._intersections():
1461 v._entry = s_entry = not s_entry
1463 if C._first:
1464 c_entry ^= C._first._isinside(S)
1465 for v in C._intersections():
1466 v._entry = c_entry = not c_entry
1468 # 3. yield the result(s)
1469 return S._results(S._presults(), Clas, **closed_inull_raiser_xtend_eps)
1471 @property_RO
1472 def _first(self):
1473 # Get the very first vertex of the first clip
1474 for v in self:
1475 return v
1476 return None # PYCHOK no cover
1478 def _kwds(self, op, **more):
1479 # Get the kwds C{dict}.
1480 return _CompositeBase._kwds(self, op, xtend=self.xtend, **more)
1482 def _presults(self):
1483 # Yield the unchecked intersection(s).
1484 for c in self._clips:
1485 for v in c._intersections():
1486 if not v._checked:
1487 yield self._resultU(v)
1489 def _resultU(self, v):
1490 # Yield the result from an un-checked intersection.
1491 while v and not v._checked:
1492 v._check()
1493 yield v
1494 r = v
1495 e = v._entry
1496 while True:
1497 v = v._next if e else v._prev
1498 yield v
1499 if v._linked:
1500 break
1501 if v is r:
1502 raise ClipError(full_circle=v, clipid=v._clipid)
1503 v = v._linked # switch
1505 @property
1506 def xtend(self):
1507 '''Get the option to handle I{degenerate cases} (C{bool}).
1508 '''
1509 return self._xtend
1511 @xtend.setter # PYCHOK setter!
1512 def xtend(self, xtend):
1513 '''Set the option to handle I{degenerate cases} (C{bool}).
1514 '''
1515 self._xtend = bool(xtend)
1518class _EdgeFHP(object):
1519 # An edge between two L{LatLonFHP} points.
1521 X_INTERSECT = _Enum('Xi', 1) # C++ enum
1522 X_OVERLAP = _Enum('Xo', 5)
1523 P_INTERSECT = _Enum('Pi', 3)
1524 P_OVERLAP = _Enum('Po', 7)
1525 Ps = (P_INTERSECT, P_OVERLAP, X_OVERLAP)
1526 Q_INTERSECT = _Enum('Qi', 2)
1527 Q_OVERLAP = _Enum('Qo', 6)
1528 Qs = (Q_INTERSECT, Q_OVERLAP, X_OVERLAP)
1529 V_INTERSECT = _Enum('Vi', 4)
1530 V_OVERLAP = _Enum('Vo', 8)
1531 Vs = (V_INTERSECT, V_OVERLAP)
1533 def __init__(self, p1, p2, **unused):
1534 # New edge between points C{p1} and C{p2}, each a L{LatLonFHP}.
1535 self._p1_p2 = p1, p2
1536 self._dp = dp = p2 - p1
1537 self._dp2 = dp * dp # dot product, hypot2
1539 self._lr, \
1540 self._bt = _left_right_bottom_top_eps2(p1, p2)
1542 def _intersect3(self, q1, q2):
1543 # Yield intersection(s) Type or C{None}
1544 if not (_outside(q1.x, q2.x, *self._lr) or
1545 _outside(q1.y, q2.y, *self._bt)):
1546 dq = q2 - q1
1547 dq2 = dq * dq # dot product, hypot2
1548 if dq2 > EPS2: # like ._clip
1549 T, E = None, _EdgeFHP # self.__class__
1550 p1, p2 = self._p1_p2
1551 ap1 = p1._2A(q1, q2)
1552 ap2_1 = p2._2A(q1, q2) - ap1
1553 if fabs(ap2_1) > _0_EPS: # non-parallel edges
1554 aq1 = q1._2A(p1, p2)
1555 aq2_1 = q2._2A(p1, p2) - aq1
1556 if fabs(aq2_1) > _0_EPS:
1557 # compute and classify alpha and beta
1558 a, a_0, a_0_1, _ = _alpha4(-ap1 / ap2_1)
1559 b, b_0, b_0_1, _ = _alpha4(-aq1 / aq2_1)
1560 # distinguish intersection types
1561 T = E.X_INTERSECT if a_0_1 and b_0_1 else (
1562 E.P_INTERSECT if a_0_1 and b_0 else (
1563 E.Q_INTERSECT if a_0 and b_0_1 else (
1564 E.V_INTERSECT if a_0 and b_0 else None)))
1566 elif fabs(ap1) < _0_EPS: # parallel or colinear edges
1567 dp = self._dp
1568 d1 = q1 - p1
1569 # compute and classify alpha and beta
1570 a, a_0, a_0_1, _a_0_1 = _alpha4((d1 * dp) / self._dp2)
1571 b, b_0, b_0_1, _b_0_1 = _alpha4((d1 * dq) / (-dq2))
1572 # distinguish overlap type
1573 T = E.X_OVERLAP if a_0_1 and b_0_1 else (
1574 E.P_OVERLAP if a_0_1 and _b_0_1 else (
1575 E.Q_OVERLAP if _a_0_1 and b_0_1 else (
1576 E.V_OVERLAP if a_0 and b_0 else None)))
1578 if T:
1579 if T is E.X_INTERSECT:
1580 v = p1 + a * self._dp
1581 yield T, (v, p1, p2, a), (v, q1, q2, b)
1582 elif T in E.Vs:
1583 yield T, (p1,), (q1,)
1584 else:
1585 if T in E.Qs:
1586 yield T, (p1,), (p1, q1, q2, b)
1587 if T in E.Ps:
1588 yield T, (q1, p1, p2, a), (q1,)
1591class _EdgeGH(object):
1592 # An edge between two L{LatLonGH} points.
1594 _raiser = False
1595 _xtend = False
1597 def __init__(self, s1, s2, raiser=False, xtend=False, **unused):
1598 # New edge between points C{s1} and C{s2}, each a L{LatLonGH}.
1599 self._s1, self._s2 = s1, s2
1600 self._x_sx_y_sy = (s1.x, s2.x - s1.x,
1601 s1.y, s2.y - s1.y)
1602 self._lr, \
1603 self._bt = _left_right_bottom_top_eps2(s1, s2)
1605 if xtend:
1606 self._xtend = True
1607 elif raiser:
1608 self._raiser = True
1610 def _alpha2(self, x, y, dx, dy):
1611 # Return C{(alpha)}, see .points.nearestOn5
1612 a = (y * dy + x * dx) / self._hypot2
1613 d = (y * dx - x * dy) / self._hypot0
1614 return a, fabs(d)
1616 def _Error(self, n, *args, **kwds): # PYCHOK no cover
1617 t = _DOT_(unstr(_EdgeGH, self._s1, self._s2),
1618 unstr(_EdgeGH._intersect4, *args, **kwds))
1619 return ClipError(_case_, n, txt=t)
1621 @Property_RO
1622 def _hypot0(self):
1623 _, sx, _, sy = self._x_sx_y_sy
1624 return hypot(sx, sy) * _0_EPS
1626 @Property_RO
1627 def _hypot2(self):
1628 _, sx, _, sy = self._x_sx_y_sy
1629 return hypot2(sx, sy)
1631 def _intersect4(self, c1, c2, parallel=True): # MCCABE 14
1632 # Yield the intersection(s) of this and another edge.
1634 # @return: None, 1 or 2 intersections, each a 4-Tuple
1635 # (y, x, s_alpha, c_alpha) with intersection
1636 # coordinates x and y and both alphas.
1638 # @raise ClipError: Intersection unhandled.
1640 # @see: U{Intersection point of two line segments
1641 # <http://PaulBourke.net/geometry/pointlineplane/>}.
1642 c1_x, c1_y = c1.x, c1.y
1643 if not (_outside(c1_x, c2.x, *self._lr) or
1644 _outside(c1_y, c2.y, *self._bt)):
1645 x, sx, \
1646 y, sy = self._x_sx_y_sy
1648 cx = c2.x - c1_x
1649 cy = c2.y - c1_y
1650 d = cy * sx - cx * sy
1652 if fabs(d) > _0_EPS: # non-parallel edges
1653 dx = x - c1_x
1654 dy = y - c1_y
1655 ca = (sx * dy - sy * dx) / d
1656 if _0_EPS < ca < _EPS_1 or (self._xtend and
1657 _EPS_0 < ca < _1_EPS):
1658 sa = (cx * dy - cy * dx) / d
1659 if _0_EPS < sa < _EPS_1 or (self._xtend and
1660 _EPS_0 < sa < _1_EPS):
1661 yield (y + sa * sy), (x + sa * sx), sa, ca
1663 # unhandled, "degenerate" cases 1, 2 or 3
1664 elif self._raiser and not (sa < _EPS_0 or sa > _1_EPS): # PYCHOK no cover
1665 raise self._Error(1, c1, c2, sa=sa) # intersection at s1 or s2
1667 elif self._raiser and not (ca < _EPS_0 or ca > _1_EPS): # PYCHOK no cover
1668 # intersection at c1 or c2 or at c1 or c2 and s1 or s2
1669 sa = (cx * dy - cy * dx) / d
1670 e = 2 if sa < _EPS_0 or sa > _1_EPS else 3
1671 raise self._Error(e, c1, c2, ca=ca)
1673 elif parallel and (sx or sy) and (cx or cy): # PYCHOK no cover
1674 # non-null, parallel or colinear edges
1675 sa1, d1 = self._alpha2(c1_x - x, c1_y - y, sx, sy)
1676 sa2, d2 = self._alpha2(c2.x - x, c2.y - y, sx, sy)
1677 if max(d1, d2) < _0_EPS:
1678 if self._xtend and not _outside(sa1, sa2, _EPS_0, _1_EPS):
1679 if sa1 > sa2: # anti-parallel
1680 sa1, sa2 = sa2, sa1
1681 ca1, ca2 = _1_0, _0_0
1682 else: # parallel
1683 ca1, ca2 = _0_0, _1_0
1684 ca = fabs((sx / cx) if cx else (sy / cy))
1685 # = hypot(sx, sy) / hypot(cx, cy)
1686 if sa1 < 0: # s1 is between c1 and c2
1687 ca *= ca1 + sa1
1688 yield y, x, ca1, _alpha1(ca)
1689 else: # c1 is between s1 and s2
1690 yield (y + sa1 * sy), (x + sa1 * sx), sa1, ca1
1691 if sa2 > 1: # s2 is between c1 and c2
1692 ca *= sa2 - _1_0
1693 yield (y + sy), (x + sx), ca2, _alpha1(ca2 - ca)
1694 else: # c2 is between s1 and s2
1695 yield (y + sa2 * sy), (x + sa2 * sx), sa2, ca2
1696 elif self._raiser and not _outside(sa1, sa2, _0_0, _1_EPS):
1697 raise self._Error(4, c1, c2, d1=d1, d2=d2)
1700class _BooleanBase(object):
1701 # Shared C{Boolean[FHP|GH]} methods.
1703 def __add__(self, other):
1704 '''Sum: C{this + other} clips.
1705 '''
1706 return self._sum(_other(self, other), self.__add__) # PYCHOK OK
1708 def __and__(self, other):
1709 '''Intersection: C{this & other}.
1710 '''
1711 return self._boolean(other, False, False, self.__and__) # PYCHOK OK
1713 def __iadd__(self, other):
1714 '''In-place sum: C{this += other} clips.
1715 '''
1716 return self._inplace(self.__add__(other))
1718 def __iand__(self, other):
1719 '''In-place intersection: C{this &= other}.
1720 '''
1721 return self._inplace(self.__and__(other))
1723 def __ior__(self, other):
1724 '''In-place union: C{this |= other}.
1725 '''
1726 return self._inplace(self.__or__(other))
1728 def __or__(self, other):
1729 '''Union: C{this | other}.
1730 '''
1731 return self._boolean(other, True, True, self.__or__) # PYCHOK OK
1733 def __radd__(self, other):
1734 '''Reverse sum: C{other + this} clips.
1735 '''
1736 return _other(self, other)._sum(self, self.__radd__)
1738 def __rand__(self, other):
1739 '''Reverse intersection: C{other & this}
1740 '''
1741 return _other(self, other).__and__(self)
1743 def __ror__(self, other):
1744 '''Reverse union: C{other | this}
1745 '''
1746 return _other(self, other).__or__(self)
1748 def _boolean4(self, other, op):
1749 # Set up a new C{Boolean[FHP|GH]}.
1750 C = self.__class__
1751 kwds = C._kwds(self, op)
1752 a = C(self, **kwds)
1753 b = _other(self, other)
1754 return a, b, C, kwds
1756 def _inplace(self, r):
1757 # Replace this with a L{Boolean*} result.
1758 self._clips, r._clips = r._clips, None
1759# if self._raiser != r._raiser:
1760# self._raiser = r._raiser
1761# if self._xtend != r._xtend:
1762# self._xtend = r._xtend
1763# if self._eps != r._eps:
1764# self._eps = r._eps
1765 return self
1768class BooleanFHP(_CompositeFHP, _BooleanBase):
1769 '''I{Composite} class providing I{boolean} operations between two
1770 I{composites} using U{Forster-Hormann-Popa<https://www.ScienceDirect.com/
1771 science/article/pii/S259014861930007X>}'s C++ implementation, transcoded
1772 to pure Python.
1774 The supported operations between (composite) polygon A and B are:
1776 - C = A & B or A &= B, intersection of A and B
1778 - C = A + B or A += B, sum of A and B clips
1780 - C = A | B or A |= B, union of A and B
1782 - A == B or A != B, equivalent A and B clips
1784 - A.isequalTo(B, eps), equivalent within tolerance
1786 @see: Methods C{__eq__} and C{isequalTo}, function L{clipFHP4}
1787 and class L{BooleanGH}.
1788 '''
1789 _kind = _boolean_
1791 def __init__(self, lls, raiser=False, eps=EPS, **name):
1792 '''New L{BooleanFHP} operand for I{boolean} operation.
1794 @arg lls: The polygon points and clips (iterable of L{LatLonFHP}s,
1795 L{ClipFHP4Tuple}s or other C{LatLon}s).
1796 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}).
1797 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same
1798 units as the B{C{lls}} coordinates).
1799 @kwarg name: Optional C{B{name}=NN} (C{str}).
1800 '''
1801 _CompositeFHP.__init__(self, lls, raiser=raiser, eps=eps, **name)
1803 def __isub__(self, other):
1804 '''Not implemented.'''
1805 return _NotImplemented(self, other)
1807 def __rsub__(self, other):
1808 '''Not implemented.'''
1809 return _NotImplemented(self, other)
1811 def __sub__(self, other):
1812 '''Not implemented.'''
1813 return _NotImplemented(self, other)
1815 def _boolean(self, other, Union, unused, op):
1816 # One C{BooleanFHP} operation.
1817 p, q, C, kwds = self._boolean4(other, op)
1818 r = p._clip(q, Union=Union, **kwds)
1819 return C(r, **kwds)
1822class BooleanGH(_CompositeGH, _BooleanBase):
1823 '''I{Composite} class providing I{boolean} operations between two
1824 I{composites} using the U{Greiner-Hormann<http://www.Inf.USI.CH/
1825 hormann/papers/Greiner.1998.ECO.pdf>} algorithm and U{Correia
1826 <https://GitHub.com/helderco/univ-polyclip>}'s implementation,
1827 modified and extended.
1829 The supported operations between (composite) polygon A and B are:
1831 - C = A - B or A -= B, difference A less B
1833 - C = B - A or B -= A, difference B less B
1835 - C = A & B or A &= B, intersection of A and B
1837 - C = A + B or A += B, sum of A and B clips
1839 - C = A | B or A |= B, union of A and B
1841 - A == B or A != B, equivalent A and B clips
1843 - A.isequalTo(B, eps), equivalent within tolerance
1845 @note: To handle I{degenerate cases} like C{point-edge} and
1846 C{point-point} intersections, use class L{BooleanFHP}.
1848 @see: Methods C{__eq__} and C{isequalTo}, function L{clipGH4}
1849 and class L{BooleanFHP}.
1850 '''
1851 _kind = _boolean_
1853 def __init__(self, lls, raiser=True, xtend=False, eps=EPS, **name):
1854 '''New L{BooleanFHP} operand for I{boolean} operation.
1856 @arg lls: The polygon points and clips (iterable of L{LatLonGH}s,
1857 L{ClipGH4Tuple}s or other C{LatLon}s).
1858 @kwarg raiser: If C{True}, throw L{ClipError} exceptions (C{bool}).
1859 @kwarg xtend: If C{True}, extend edges of I{degenerate cases}, an
1860 attempt to handle the latter (C{bool}).
1861 @kwarg esp: Tolerance for eliminating null edges (C{degrees}, same
1862 units as the B{C{lls}} coordinates).
1863 @kwarg name: Optional C{B{name}=NN} (C{str}).
1864 '''
1865 _CompositeGH.__init__(self, lls, raiser=raiser, xtend=xtend, eps=eps, **name)
1867 def _boolean(self, other, s_entry, c_entry, op):
1868 # One C{BooleanGH} operation.
1869 s, c, C, kwds = self._boolean4(other, op)
1870 r = s._clip(c, s_entry, c_entry, **kwds)
1871 return C(r, **kwds)
1873 def __isub__(self, other):
1874 '''In-place difference: C{this -= other}.
1875 '''
1876 return self._inplace(self.__sub__(other))
1878 def __rsub__(self, other):
1879 ''' Reverse difference: C{other - this}
1880 '''
1881 return _other(self, other).__sub__(self)
1883 def __sub__(self, other):
1884 '''Difference: C{this - other}.
1885 '''
1886 return self._boolean(other, True, False, self.__sub__)
1889def _alpha1(alpha):
1890 # Return C{alpha} in C{[0..1]} range
1891 if _EPS_0 < alpha < _1_EPS:
1892 return max(_0_0, min(alpha, _1_0))
1893 t = _not_(Fmt.SQUARE(_ELLIPSIS_(0, 1)))
1894 raise ClipError(_alpha_, alpha, txt=t)
1897def _alpha4(a):
1898 # Return 4-tuple (alpha, -EPS < alpha < EPS,
1899 # 0 < alpha < 1,
1900 # not 0 < alpha < 1)
1901 return (a, False, True, False) if _0_EPS < a < _EPS_1 else (
1902 (a, False, False, True) if _0_EPS < fabs(a) else
1903 (a, True, False, False))
1906def _Cps(Cp, composites_points, where):
1907 # Yield composites and points as a C{Cp} composite.
1908 try:
1909 kwds = dict(kind=_points_, name__=where)
1910 for cp in composites_points:
1911 yield cp if isBoolean(cp) else Cp(cp, **kwds)
1912 except (AttributeError, ClipError, TypeError, ValueError) as x:
1913 raise _ValueError(points=cp, cause=x)
1916def _eps0(eps):
1917 # Adjust C{eps} or C{None}.
1918 return eps if eps and eps > EPS else 0
1921def isBoolean(obj):
1922 '''Check for C{Boolean} composites.
1924 @arg obj: The object (any C{type}).
1926 @return: C{True} if B{C{obj}} is L{BooleanFHP}, L{BooleanGH}
1927 or some other composite, C{False} otherwise.
1928 '''
1929 return isinstance(obj, _CompositeBase)
1932def _left_right_bottom_top_eps2(p1, p2):
1933 '''(INTERNAL) Return 2-tuple C{(left, right), (bottom, top)}, oversized.
1934 '''
1935 return (_min_max_eps2(p1.x, p2.x),
1936 _min_max_eps2(p1.y, p2.y))
1939def _low_high_eps2(lo, hi, eps):
1940 '''(INTERNAL) Return 2-tuple C{(lo, hi)}, oversized.
1941 '''
1942 lo *= (_1_0 + eps) if lo < 0 else (_1_0 - eps)
1943 hi *= (_1_0 - eps) if hi < 0 else (_1_0 + eps)
1944 return (lo or -eps), (hi or eps)
1947def _min_max_eps2(*xs):
1948 '''(INTERNAL) Return 2-tuple C{(min, max)}, oversized.
1949 '''
1950 lo, hi = min(xs), max(xs)
1951 lo *= _1_EPS if lo < 0 else _EPS_1
1952 hi *= _EPS_1 if hi < 0 else _1_EPS
1953 return (lo or _EPS_0), (hi or _0_EPS)
1956def _other(this, other):
1957 '''(INTERNAL) Check for compatible C{type}s.
1958 '''
1959 C = this.__class__
1960 if isinstance(other, C):
1961 return other
1962 raise _IsnotError(C, other=other)
1965def _outside(x1, x2, lo, hi):
1966 '''(INTERNAL) Is C{(x1, x2)} outside C{(lo, hi)}?
1967 '''
1968 return max(x1, x2) < lo or min(x1, x2) > hi
1971__all__ += _ALL_DOCS(_BooleanBase, _Clip,
1972 _CompositeBase, _CompositeFHP, _CompositeGH,
1973 _LatLonBool)
1975# **) MIT License
1976#
1977# Copyright (C) 2018-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1978#
1979# Permission is hereby granted, free of charge, to any person obtaining a
1980# copy of this software and associated documentation files (the "Software"),
1981# to deal in the Software without restriction, including without limitation
1982# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1983# and/or sell copies of the Software, and to permit persons to whom the
1984# Software is furnished to do so, subject to the following conditions:
1985#
1986# The above copyright notice and this permission notice shall be included
1987# in all copies or substantial portions of the Software.
1988#
1989# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1990# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1991# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1992# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1993# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1994# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1995# OTHER DEALINGS IN THE SOFTWARE.
1997# ***) GNU GPL 3
1998#
1999# Copyright (C) 2011-2012 Helder Correia <Helder.MC@Gmail.com>
2000#
2001# This program is free software: you can redistribute it and/or
2002# modify it under the terms of the GNU General Public License as
2003# published by the Free Software Foundation, either version 3 of
2004# the License, or any later version.
2005#
2006# This program is distributed in the hope that it will be useful,
2007# but WITHOUT ANY WARRANTY; without even the implied warranty of
2008# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
2009# GNU General Public License for more details.
2010#
2011# You should have received a copy of the GNU General Public License
2012# along with this program. If not, see <http://www.GNU.org/licenses/>.
2013#
2014# You should have received the README file along with this program.
2015# If not, see <https://GitHub.com/helderco/univ-polyclip>.