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         """
 120         Adds a Point to a Vector and returns the result as a Point.
 121         """
 122         if not isinstance(other, Vector):
 123             return NotImplemented
 124         coordinates = self._map2(other, operator.add)
 125         return Point(coordinates)
 126
 127     def __sub__(self, other):
 128         """
 129         Returns the difference between two Points as a Vector.
 130         """
 131         coordinates = []
 132         if isinstance(other, Point):
 133             coordinates = self._map2(other, operator.sub)
 134             return Vector(coordinates)
 135         elif isinstance(other, Vector):
 136             coordinates = self._map2(other, operator.sub)
 137             return Point(coordinates)
 138         else:
 139             return NotImplemented
 140
 141     def __eq__(self, other):
 142         """
 143         Compares two Points for equality.
 144         """
 145         return isinstance(other, Point) and \
 146             self._coordinates == other._coordinates
 147
 148     def aspolyhedron(self):
 149         """
 150         Return a Point as a polyhedron.
 151         """
 152         from .polyhedra import Polyhedron
 153         equalities = []
 154         for symbol, coordinate in self.coordinates():
 155             equalities.append(symbol - coordinate)
 156         return Polyhedron(equalities)
 157
 158
 159 class Vector(Coordinates):
 160     """
 161     This class represents displacements in space.
 162     """
 163
 164     def __new__(cls, initial, terminal=None):
 165         if not isinstance(initial, Point):
 166             initial = Point(initial)
 167         if terminal is None:
 168             coordinates = initial._coordinates
 169         else:
 170             if not isinstance(terminal, Point):
 171                 terminal = Point(terminal)
 172             coordinates = terminal._map2(initial, operator.sub)
 173         return super().__new__(cls, coordinates)
 174
 175     def isnull(self):
 176         """
 177         Returns true if a Vector is null.
 178         """
 179         return not bool(self)
 180
 181     def __hash__(self):
 182         return super().__hash__()
 183
 184     def __add__(self, other):
 185         """
 186         Adds either a Point or Vector to a Vector.
 187         """
 188         if isinstance(other, (Point, Vector)):
 189             coordinates = self._map2(other, operator.add)
 190             return other.__class__(coordinates)
 191         return NotImplemented
 192
 193     def angle(self, other):
 194         """
 195         Retrieve the angle required to rotate the vector into the vector passed
 196         in argument. The result is an angle in radians, ranging between -pi and
 197         pi.
 198         """
 199         if not isinstance(other, Vector):
 200             raise TypeError('argument must be a Vector instance')
 201         cosinus = self.dot(other) / (self.norm()*other.norm())
 202         return math.acos(cosinus)
 203
 204     def cross(self, other):
 205         """
 206         Calculate the cross product of two Vector3D structures.
 207         """
 208         if not isinstance(other, Vector):
 209             raise TypeError('other must be a Vector instance')
 210         if self.dimension != 3 or other.dimension != 3:
 211             raise ValueError('arguments must be three-dimensional vectors')
 212         if self.symbols != other.symbols:
 213             raise ValueError('arguments must belong to the same space')
 214         x, y, z = self.symbols
 215         coordinates = []
 216         coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
 217         coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
 218         coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
 219         return Vector(coordinates)
 220
 221     def __truediv__(self, other):
 222         """
 223         Divide the vector by the specified scalar and returns the result as a
 224         vector.
 225         """
 226         if not isinstance(other, numbers.Real):
 227             return NotImplemented
 228         coordinates = self._map(lambda coordinate: coordinate / other)
 229         return Vector(coordinates)
 230
 231     def dot(self, other):
 232         """
 233         Calculate the dot product of two vectors.
 234         """
 235         if not isinstance(other, Vector):
 236             raise TypeError('argument must be a Vector instance')
 237         result = 0
 238         for symbol, coordinate1, coordinate2 in self._iter2(other):
 239             result += coordinate1 * coordinate2
 240         return result
 241
 242     def __eq__(self, other):
 243         """
 244         Compares two Vectors for equality.
 245         """
 246         return isinstance(other, Vector) and \
 247             self._coordinates == other._coordinates
 248
 249     def __hash__(self):
 250         return hash(tuple(self.coordinates()))
 251
 252     def __mul__(self, other):
 253         """
 254         Multiplies a Vector by a scalar value.
 255         """
 256         if not isinstance(other, numbers.Real):
 257             return NotImplemented
 258         coordinates = self._map(lambda coordinate: other * coordinate)
 259         return Vector(coordinates)
 260
 261     __rmul__ = __mul__
 262
 263     def __neg__(self):
 264         """
 265         Returns the negated form of a Vector.
 266         """
 267         coordinates = self._map(operator.neg)
 268         return Vector(coordinates)
 269
 270     def norm(self):
 271         """
 272         Normalizes a Vector.
 273         """
 274         return math.sqrt(self.norm2())
 275
 276     def norm2(self):
 277         result = 0
 278         for coordinate in self._coordinates.values():
 279             result += coordinate ** 2
 280         return result
 281
 282     def asunit(self):
 283         return self / self.norm()
 284
 285     def __sub__(self, other):
 286         """
 287         Subtract a Point or Vector from a Vector.
 288         """
 289         if isinstance(other, (Point, Vector)):
 290             coordinates = self._map2(other, operator.sub)
 291             return other.__class__(coordinates)
 292         return NotImplemented