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 __bool__(self):
  75         return any(self._coordinates.values())
  76
  77     def __hash__(self):
  78         return hash(tuple(self.coordinates()))
  79
  80     def __repr__(self):
  81         string = ', '.join(['{!r}: {!r}'.format(symbol, coordinate)
  82             for symbol, coordinate in self.coordinates()])
  83         return '{}({{{}}})'.format(self.__class__.__name__, string)
  84
  85     def _map(self, func):
  86         for symbol, coordinate in self.coordinates():
  87             yield symbol, func(coordinate)
  88
  89     def _iter2(self, other):
  90         if self.symbols != other.symbols:
  91             raise ValueError('arguments must belong to the same space')
  92         coordinates1 = self._coordinates.values()
  93         coordinates2 = other._coordinates.values()
  94         yield from zip(self.symbols, coordinates1, coordinates2)
  95
  96     def _map2(self, other, func):
  97         for symbol, coordinate1, coordinate2 in self._iter2(other):
  98             yield symbol, func(coordinate1, coordinate2)
  99
 100
 101 class Point(Coordinates, GeometricObject):
 102     """
 103     This class represents points in space.
 104     """
 105
 106     def isorigin(self):
 107         return not bool(self)
 108
 109     def __hash__(self):
 110         return super().__hash__()
 111
 112     def __add__(self, other):
 113         if not isinstance(other, Vector):
 114             return NotImplemented
 115         coordinates = self._map2(other, operator.add)
 116         return Point(coordinates)
 117
 118     def __sub__(self, other):
 119         coordinates = []
 120         if isinstance(other, Point):
 121             coordinates = self._map2(other, operator.sub)
 122             return Vector(coordinates)
 123         elif isinstance(other, Vector):
 124             coordinates = self._map2(other, operator.sub)
 125             return Point(coordinates)
 126         else:
 127             return NotImplemented
 128
 129     def __eq__(self, other):
 130         return isinstance(other, Point) and \
 131             self._coordinates == other._coordinates
 132
 133     def aspolyhedron(self):
 134         from .polyhedra import Polyhedron
 135         equalities = []
 136         for symbol, coordinate in self.coordinates():
 137             equalities.append(symbol - coordinate)
 138         return Polyhedron(equalities)
 139
 140
 141 class Vector(Coordinates):
 142     """
 143     This class represents displacements in space.
 144     """
 145
 146     def __new__(cls, initial, terminal=None):
 147         if not isinstance(initial, Point):
 148             initial = Point(initial)
 149         if terminal is None:
 150             coordinates = initial._coordinates
 151         else:
 152             if not isinstance(terminal, Point):
 153                 terminal = Point(terminal)
 154             coordinates = terminal._map2(initial, operator.sub)
 155         return super().__new__(cls, coordinates)
 156
 157     def isnull(self):
 158         return not bool(self)
 159
 160     def __hash__(self):
 161         return super().__hash__()
 162
 163     def __add__(self, other):
 164         if isinstance(other, (Point, Vector)):
 165             coordinates = self._map2(other, operator.add)
 166             return other.__class__(coordinates)
 167         return NotImplemented
 168
 169     def angle(self, other):
 170         """
 171         Retrieve the angle required to rotate the vector into the vector passed
 172         in argument. The result is an angle in radians, ranging between -pi and
 173         pi.
 174         """
 175         if not isinstance(other, Vector):
 176             raise TypeError('argument must be a Vector instance')
 177         cosinus = self.dot(other) / (self.norm()*other.norm())
 178         return math.acos(cosinus)
 179
 180     def cross(self, other):
 181         """
 182         Calculate the cross product of two Vector3D structures.
 183         """
 184         if not isinstance(other, Vector):
 185             raise TypeError('other must be a Vector instance')
 186         if self.dimension != 3 or other.dimension != 3:
 187             raise ValueError('arguments must be three-dimensional vectors')
 188         if self.symbols != other.symbols:
 189             raise ValueError('arguments must belong to the same space')
 190         x, y, z = self.symbols
 191         coordinates = []
 192         coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
 193         coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
 194         coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
 195         return Vector(coordinates)
 196
 197     def __truediv__(self, other):
 198         """
 199         Divide the vector by the specified scalar and returns the result as a
 200         vector.
 201         """
 202         if not isinstance(other, numbers.Real):
 203             return NotImplemented
 204         coordinates = self._map(lambda coordinate: coordinate / other)
 205         return Vector(coordinates)
 206
 207     def dot(self, other):
 208         """
 209         Calculate the dot product of two vectors.
 210         """
 211         if not isinstance(other, Vector):
 212             raise TypeError('argument must be a Vector instance')
 213         result = 0
 214         for symbol, coordinate1, coordinate2 in self._iter2(other):
 215             result += coordinate1 * coordinate2
 216         return result
 217
 218     def __eq__(self, other):
 219         return isinstance(other, Vector) and \
 220             self._coordinates == other._coordinates
 221
 222     def __hash__(self):
 223         return hash(tuple(self.coordinates()))
 224
 225     def __mul__(self, other):
 226         if not isinstance(other, numbers.Real):
 227             return NotImplemented
 228         coordinates = self._map(lambda coordinate: other * coordinate)
 229         return Vector(coordinates)
 230
 231     __rmul__ = __mul__
 232
 233     def __neg__(self):
 234         coordinates = self._map(operator.neg)
 235         return Vector(coordinates)
 236
 237     def norm(self):
 238         return math.sqrt(self.norm2())
 239
 240     def norm2(self):
 241         result = 0
 242         for coordinate in self._coordinates.values():
 243             result += coordinate ** 2
 244         return result
 245
 246     def asunit(self):
 247         return self / self.norm()
 248
 249     def __sub__(self, other):
 250         if isinstance(other, (Point, Vector)):
 251             coordinates = self._map2(other, operator.sub)
 252             return other.__class__(coordinates)
 253         return NotImplemented