pypol/geometry.py~

   1 import math
   2 import numbers
   3 import operator
   4
   5 from abc import ABC, abstractproperty, abstractmethod
   6 from collections import OrderedDict, Mapping
   7
   8 from .linexprs import Symbol
   9
  10
  11 __all__ = [
  12     'GeometricObject',
  13     'Point',
  14     'Vector',
  15 ]
  16
  17
  18 class GeometricObject(ABC):
  19
  20     @abstractproperty
  21     def symbols(self):
  22         pass
  23
  24     @property
  25     def dimension(self):
  26         return len(self.symbols)
  27
  28     @abstractmethod
  29     def aspolyhedron(self):
  30         pass
  31
  32     def asdomain(self):
  33         return self.aspolyhedron()
  34
  35
  36 class Coordinates:
  37
  38     __slots__ = (
  39         '_coordinates',
  40     )
  41
  42     def __new__(cls, coordinates):
  43         if isinstance(coordinates, Mapping):
  44             coordinates = coordinates.items()
  45         self = object().__new__(cls)
  46         self._coordinates = OrderedDict()
  47         for symbol, coordinate in sorted(coordinates,
  48                 key=lambda item: item[0].sortkey()):
  49             if not isinstance(symbol, Symbol):
  50                 raise TypeError('symbols must be Symbol instances')
  51             if not isinstance(coordinate, numbers.Real):
  52                 raise TypeError('coordinates must be real numbers')
  53             self._coordinates[symbol] = coordinate
  54         return self
  55
  56     @property
  57     def symbols(self):
  58         return tuple(self._coordinates)
  59
  60     @property
  61     def dimension(self):
  62         return len(self.symbols)
  63
  64     def coordinates(self):
  65         yield from self._coordinates.items()
  66
  67     def coordinate(self, symbol):
  68         if not isinstance(symbol, Symbol):
  69             raise TypeError('symbol must be a Symbol instance')
  70         return self._coordinates[symbol]
  71
  72     __getitem__ = coordinate
  73
  74     def values(self):
  75         yield from self._coordinates.values()
  76
  77     def __bool__(self):
  78         return any(self._coordinates.values())
  79
  80     def __hash__(self):
  81         return hash(tuple(self.coordinates()))
  82
  83     def __repr__(self):
  84         string = ', '.join(['{!r}: {!r}'.format(symbol, coordinate)
  85             for symbol, coordinate in self.coordinates()])
  86         return '{}({{{}}})'.format(self.__class__.__name__, string)
  87
  88     def _map(self, func):
  89         for symbol, coordinate in self.coordinates():
  90             yield symbol, func(coordinate)
  91
  92     def _iter2(self, other):
  93         if self.symbols != other.symbols:
  94             raise ValueError('arguments must belong to the same space')
  95         coordinates1 = self._coordinates.values()
  96         coordinates2 = other._coordinates.values()
  97         yield from zip(self.symbols, coordinates1, coordinates2)
  98
  99     def _map2(self, other, func):
 100         for symbol, coordinate1, coordinate2 in self._iter2(other):
 101             yield symbol, func(coordinate1, coordinate2)
 102
 103
 104 class Point(Coordinates, GeometricObject):
 105     """
 106     This class represents points in space.
 107     """
 108
 109     def isorigin(self):
 110     """
 111     Return True if a Point is the origin.
 112     """
 113         return not bool(self)
 114
 115     def __hash__(self):
 116         return super().__hash__()
 117
 118     def __add__(self, other):
 119         if not isinstance(other, Vector):
 120             return NotImplemented
 121         coordinates = self._map2(other, operator.add)
 122         return Point(coordinates)
 123
 124     def __sub__(self, other):
 125         coordinates = []
 126         if isinstance(other, Point):
 127             coordinates = self._map2(other, operator.sub)
 128             return Vector(coordinates)
 129         elif isinstance(other, Vector):
 130             coordinates = self._map2(other, operator.sub)
 131             return Point(coordinates)
 132         else:
 133             return NotImplemented
 134
 135     def __eq__(self, other):
 136     """
 137     Compares two Points for equality.
 138     """
 139         return isinstance(other, Point) and \
 140             self._coordinates == other._coordinates
 141
 142     def aspolyhedron(self):
 143     """
 144     Return a Point as a polyhedron.
 145     """
 146         from .polyhedra import Polyhedron
 147         equalities = []
 148         for symbol, coordinate in self.coordinates():
 149             equalities.append(symbol - coordinate)
 150         return Polyhedron(equalities)
 151
 152
 153 class Vector(Coordinates):
 154     """
 155     This class represents displacements in space.
 156     """
 157
 158     def __new__(cls, initial, terminal=None):
 159         if not isinstance(initial, Point):
 160             initial = Point(initial)
 161         if terminal is None:
 162             coordinates = initial._coordinates
 163         else:
 164             if not isinstance(terminal, Point):
 165                 terminal = Point(terminal)
 166             coordinates = terminal._map2(initial, operator.sub)
 167         return super().__new__(cls, coordinates)
 168
 169     def isnull(self):
 170     """
 171     Returns true if a Vector is null.
 172     """
 173         return not bool(self)
 174
 175     def __hash__(self):
 176         return super().__hash__()
 177
 178     def __add__(self, other):
 179     """
 180     Adds either a Point or Vector to a Vector.
 181     """
 182         if isinstance(other, (Point, Vector)):
 183             coordinates = self._map2(other, operator.add)
 184             return other.__class__(coordinates)
 185         return NotImplemented
 186
 187     def angle(self, other):
 188         """
 189         Retrieve the angle required to rotate the vector into the vector passed in argument. The result is an angle in radians, ranging between -pi and pi.
 190         """
 191         if not isinstance(other, Vector):
 192             raise TypeError('argument must be a Vector instance')
 193         cosinus = self.dot(other) / (self.norm()*other.norm())
 194         return math.acos(cosinus)
 195
 196     def cross(self, other):
 197         """
 198         Calculate the cross product of two Vector3D structures.
 199         """
 200         if not isinstance(other, Vector):
 201             raise TypeError('other must be a Vector instance')
 202         if self.dimension != 3 or other.dimension != 3:
 203             raise ValueError('arguments must be three-dimensional vectors')
 204         if self.symbols != other.symbols:
 205             raise ValueError('arguments must belong to the same space')
 206         x, y, z = self.symbols
 207         coordinates = []
 208         coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
 209         coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
 210         coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
 211         return Vector(coordinates)
 212
 213     def __truediv__(self, other):
 214         """
 215         Divide the vector by the specified scalar and returns the result as a
 216         vector.
 217         """
 218         if not isinstance(other, numbers.Real):
 219             return NotImplemented
 220         coordinates = self._map(lambda coordinate: coordinate / other)
 221         return Vector(coordinates)
 222
 223     def dot(self, other):
 224         """
 225         Calculate the dot product of two vectors.
 226         """
 227         if not isinstance(other, Vector):
 228             raise TypeError('argument must be a Vector instance')
 229         result = 0
 230         for symbol, coordinate1, coordinate2 in self._iter2(other):
 231             result += coordinate1 * coordinate2
 232         return result
 233
 234     def __eq__(self, other):
 235     """
 236     Compares two Vectors for equality.
 237     """
 238         return isinstance(other, Vector) and \
 239             self._coordinates == other._coordinates
 240
 241     def __hash__(self):
 242         return hash(tuple(self.coordinates()))
 243
 244     def __mul__(self, other):
 245     """
 246     Multiplies a Vector by a scalar value.
 247     """
 248         if not isinstance(other, numbers.Real):
 249             return NotImplemented
 250         coordinates = self._map(lambda coordinate: other * coordinate)
 251         return Vector(coordinates)
 252
 253     __rmul__ = __mul__
 254
 255     def __neg__(self):
 256     """
 257     Returns the negated form of a Vector.
 258     """
 259         coordinates = self._map(operator.neg)
 260         return Vector(coordinates)
 261
 262     def norm(self):
 263     """
 264     Normalizes a Vector.
 265     """
 266         return math.sqrt(self.norm2())
 267
 268     def norm2(self):
 269         result = 0
 270         for coordinate in self._coordinates.values():
 271             result += coordinate ** 2
 272         return result
 273
 274     def asunit(self):
 275         return self / self.norm()
 276
 277     def __sub__(self, other):
 278     """
 279     Subtract a Point or Vector from a Vector.
 280     """
 281         if isinstance(other, (Point, Vector)):
 282             coordinates = self._map2(other, operator.sub)
 283             return other.__class__(coordinates)
 284         return NotImplemented