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 in argument. The result is an angle in radians, ranging between -pi and pi.
 196         """
 197         if not isinstance(other, Vector):
 198             raise TypeError('argument must be a Vector instance')
 199         cosinus = self.dot(other) / (self.norm()*other.norm())
 200         return math.acos(cosinus)
 201
 202     def cross(self, other):
 203         """
 204         Calculate the cross product of two Vector3D structures.
 205         """
 206         if not isinstance(other, Vector):
 207             raise TypeError('other must be a Vector instance')
 208         if self.dimension != 3 or other.dimension != 3:
 209             raise ValueError('arguments must be three-dimensional vectors')
 210         if self.symbols != other.symbols:
 211             raise ValueError('arguments must belong to the same space')
 212         x, y, z = self.symbols
 213         coordinates = []
 214         coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
 215         coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
 216         coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
 217         return Vector(coordinates)
 218
 219     def __truediv__(self, other):
 220         """
 221         Divide the vector by the specified scalar and returns the result as a
 222         vector.
 223         """
 224         if not isinstance(other, numbers.Real):
 225             return NotImplemented
 226         coordinates = self._map(lambda coordinate: coordinate / other)
 227         return Vector(coordinates)
 228
 229     def dot(self, other):
 230         """
 231         Calculate the dot product of two vectors.
 232         """
 233         if not isinstance(other, Vector):
 234             raise TypeError('argument must be a Vector instance')
 235         result = 0
 236         for symbol, coordinate1, coordinate2 in self._iter2(other):
 237             result += coordinate1 * coordinate2
 238         return result
 239
 240     def __eq__(self, other):
 241     """
 242     Compares two Vectors for equality.
 243     """
 244         return isinstance(other, Vector) and \
 245             self._coordinates == other._coordinates
 246
 247     def __hash__(self):
 248         return hash(tuple(self.coordinates()))
 249
 250     def __mul__(self, other):
 251     """
 252     Multiplies a Vector by a scalar value.
 253     """
 254         if not isinstance(other, numbers.Real):
 255             return NotImplemented
 256         coordinates = self._map(lambda coordinate: other * coordinate)
 257         return Vector(coordinates)
 258
 259     __rmul__ = __mul__
 260
 261     def __neg__(self):
 262     """
 263     Returns the negated form of a Vector.
 264     """
 265         coordinates = self._map(operator.neg)
 266         return Vector(coordinates)
 267
 268     def norm(self):
 269     """
 270     Normalizes a Vector.
 271     """
 272         return math.sqrt(self.norm2())
 273
 274     def norm2(self):
 275         result = 0
 276         for coordinate in self._coordinates.values():
 277             result += coordinate ** 2
 278         return result
 279
 280     def asunit(self):
 281         return self / self.norm()
 282
 283     def __sub__(self, other):
 284     """
 285     Subtract a Point or Vector from a Vector.
 286     """
 287         if isinstance(other, (Point, Vector)):
 288             coordinates = self._map2(other, operator.sub)
 289             return other.__class__(coordinates)
 290         return NotImplemented