pypol/coordinates.py

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