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