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