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