linpy/geometry.py

   1 # Copyright 2014 MINES ParisTech
   2 #
   3 # This file is part of LinPy.
   4 #
   5 # LinPy is free software: you can redistribute it and/or modify
   6 # it under the terms of the GNU General Public License as published by
   7 # the Free Software Foundation, either version 3 of the License, or
   8 # (at your option) any later version.
   9 #
  10 # LinPy is distributed in the hope that it will be useful,
  11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13 # GNU General Public License for more details.
  14 #
  15 # You should have received a copy of the GNU General Public License
  16 # along with LinPy.  If not, see <http://www.gnu.org/licenses/>.
  17
  18 import math
  19 import numbers
  20 import operator
  21
  22 from abc import ABC, abstractproperty, abstractmethod
  23 from collections import OrderedDict, Mapping
  24
  25 from .linexprs import Symbol
  26
  27
  28 __all__ = [
  29     'GeometricObject',
  30     'Point',
  31     'Vector',
  32 ]
  33
  34
  35 class GeometricObject(ABC):
  36
  37     @abstractproperty
  38     def symbols(self):
  39         pass
  40
  41     @property
  42     def dimension(self):
  43         return len(self.symbols)
  44
  45     @abstractmethod
  46     def aspolyhedron(self):
  47         pass
  48
  49     def asdomain(self):
  50         return self.aspolyhedron()
  51
  52
  53 class Coordinates:
  54
  55     __slots__ = (
  56         '_coordinates',
  57     )
  58
  59     def __new__(cls, coordinates):
  60         if isinstance(coordinates, Mapping):
  61             coordinates = coordinates.items()
  62         self = object().__new__(cls)
  63         self._coordinates = OrderedDict()
  64         for symbol, coordinate in sorted(coordinates,
  65                 key=lambda item: item[0].sortkey()):
  66             if not isinstance(symbol, Symbol):
  67                 raise TypeError('symbols must be Symbol instances')
  68             if not isinstance(coordinate, numbers.Real):
  69                 raise TypeError('coordinates must be real numbers')
  70             self._coordinates[symbol] = coordinate
  71         return self
  72
  73     @property
  74     def symbols(self):
  75         return tuple(self._coordinates)
  76
  77     @property
  78     def dimension(self):
  79         return len(self.symbols)
  80
  81     def coordinates(self):
  82         yield from self._coordinates.items()
  83
  84     def coordinate(self, symbol):
  85         if not isinstance(symbol, Symbol):
  86             raise TypeError('symbol must be a Symbol instance')
  87         return self._coordinates[symbol]
  88
  89     __getitem__ = coordinate
  90
  91     def values(self):
  92         yield from self._coordinates.values()
  93
  94     def __bool__(self):
  95         return any(self._coordinates.values())
  96
  97     def __hash__(self):
  98         return hash(tuple(self.coordinates()))
  99
 100     def __repr__(self):
 101         string = ', '.join(['{!r}: {!r}'.format(symbol, coordinate)
 102             for symbol, coordinate in self.coordinates()])
 103         return '{}({{{}}})'.format(self.__class__.__name__, string)
 104
 105     def _map(self, func):
 106         for symbol, coordinate in self.coordinates():
 107             yield symbol, func(coordinate)
 108
 109     def _iter2(self, other):
 110         if self.symbols != other.symbols:
 111             raise ValueError('arguments must belong to the same space')
 112         coordinates1 = self._coordinates.values()
 113         coordinates2 = other._coordinates.values()
 114         yield from zip(self.symbols, coordinates1, coordinates2)
 115
 116     def _map2(self, other, func):
 117         for symbol, coordinate1, coordinate2 in self._iter2(other):
 118             yield symbol, func(coordinate1, coordinate2)
 119
 120
 121 class Point(Coordinates, GeometricObject):
 122     """
 123     This class represents points in space.
 124     """
 125
 126     def isorigin(self):
 127         """
 128         Return True if a Point is the origin.
 129         """
 130         return not bool(self)
 131
 132     def __hash__(self):
 133         return super().__hash__()
 134
 135     def __add__(self, other):
 136         """
 137         Adds a Point to a Vector and returns the result as a Point.
 138         """
 139         if not isinstance(other, Vector):
 140             return NotImplemented
 141         coordinates = self._map2(other, operator.add)
 142         return Point(coordinates)
 143
 144     def __sub__(self, other):
 145         """
 146         Returns the difference between two Points as a Vector.
 147         """
 148         coordinates = []
 149         if isinstance(other, Point):
 150             coordinates = self._map2(other, operator.sub)
 151             return Vector(coordinates)
 152         elif isinstance(other, Vector):
 153             coordinates = self._map2(other, operator.sub)
 154             return Point(coordinates)
 155         else:
 156             return NotImplemented
 157
 158     def __eq__(self, other):
 159         """
 160         Compares two Points for equality.
 161         """
 162         return isinstance(other, Point) and \
 163             self._coordinates == other._coordinates
 164
 165     def aspolyhedron(self):
 166         """
 167         Return a Point as a polyhedron.
 168         """
 169         from .polyhedra import Polyhedron
 170         equalities = []
 171         for symbol, coordinate in self.coordinates():
 172             equalities.append(symbol - coordinate)
 173         return Polyhedron(equalities)
 174
 175
 176 class Vector(Coordinates):
 177     """
 178     This class represents displacements in space.
 179     """
 180
 181     def __new__(cls, initial, terminal=None):
 182         if not isinstance(initial, Point):
 183             initial = Point(initial)
 184         if terminal is None:
 185             coordinates = initial._coordinates
 186         else:
 187             if not isinstance(terminal, Point):
 188                 terminal = Point(terminal)
 189             coordinates = terminal._map2(initial, operator.sub)
 190         return super().__new__(cls, coordinates)
 191
 192     def isnull(self):
 193         """
 194         Returns true if a Vector is null.
 195         """
 196         return not bool(self)
 197
 198     def __hash__(self):
 199         return super().__hash__()
 200
 201     def __add__(self, other):
 202         """
 203         Adds either a Point or Vector to a Vector.
 204         """
 205         if isinstance(other, (Point, Vector)):
 206             coordinates = self._map2(other, operator.add)
 207             return other.__class__(coordinates)
 208         return NotImplemented
 209
 210     def angle(self, other):
 211         """
 212         Retrieve the angle required to rotate the vector into the vector passed
 213         in argument. The result is an angle in radians, ranging between -pi and
 214         pi.
 215         """
 216         if not isinstance(other, Vector):
 217             raise TypeError('argument must be a Vector instance')
 218         cosinus = self.dot(other) / (self.norm()*other.norm())
 219         return math.acos(cosinus)
 220
 221     def cross(self, other):
 222         """
 223         Calculate the cross product of two Vector3D structures.
 224         """
 225         if not isinstance(other, Vector):
 226             raise TypeError('other must be a Vector instance')
 227         if self.dimension != 3 or other.dimension != 3:
 228             raise ValueError('arguments must be three-dimensional vectors')
 229         if self.symbols != other.symbols:
 230             raise ValueError('arguments must belong to the same space')
 231         x, y, z = self.symbols
 232         coordinates = []
 233         coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
 234         coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
 235         coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
 236         return Vector(coordinates)
 237
 238     def __truediv__(self, other):
 239         """
 240         Divide the vector by the specified scalar and returns the result as a
 241         vector.
 242         """
 243         if not isinstance(other, numbers.Real):
 244             return NotImplemented
 245         coordinates = self._map(lambda coordinate: coordinate / other)
 246         return Vector(coordinates)
 247
 248     def dot(self, other):
 249         """
 250         Calculate the dot product of two vectors.
 251         """
 252         if not isinstance(other, Vector):
 253             raise TypeError('argument must be a Vector instance')
 254         result = 0
 255         for symbol, coordinate1, coordinate2 in self._iter2(other):
 256             result += coordinate1 * coordinate2
 257         return result
 258
 259     def __eq__(self, other):
 260         """
 261         Compares two Vectors for equality.
 262         """
 263         return isinstance(other, Vector) and \
 264             self._coordinates == other._coordinates
 265
 266     def __hash__(self):
 267         return hash(tuple(self.coordinates()))
 268
 269     def __mul__(self, other):
 270         """
 271         Multiplies a Vector by a scalar value.
 272         """
 273         if not isinstance(other, numbers.Real):
 274             return NotImplemented
 275         coordinates = self._map(lambda coordinate: other * coordinate)
 276         return Vector(coordinates)
 277
 278     __rmul__ = __mul__
 279
 280     def __neg__(self):
 281         """
 282         Returns the negated form of a Vector.
 283         """
 284         coordinates = self._map(operator.neg)
 285         return Vector(coordinates)
 286
 287     def norm(self):
 288         """
 289         Normalizes a Vector.
 290         """
 291         return math.sqrt(self.norm2())
 292
 293     def norm2(self):
 294         result = 0
 295         for coordinate in self._coordinates.values():
 296             result += coordinate ** 2
 297         return result
 298
 299     def asunit(self):
 300         return self / self.norm()
 301
 302     def __sub__(self, other):
 303         """
 304         Subtract a Point or Vector from a Vector.
 305         """
 306         if isinstance(other, (Point, Vector)):
 307             coordinates = self._map2(other, operator.sub)
 308             return other.__class__(coordinates)
 309         return NotImplemented