Make coordinates mandatory in Point constructor
[linpy.git] / pypol / coordinates.py
1 import math
2 import numbers
3 import operator
4
5 from abc import ABC, abstractmethod
6 from collections import OrderedDict, Mapping
7
8 from .linexprs import Symbol
9
10
11 __all__ = [
12 'Point',
13 'Vector',
14 ]
15
16
17 class Coordinates(ABC):
18
19 __slots__ = (
20 '_coordinates',
21 )
22
23 @abstractmethod
24 def __new__(cls):
25 super().__new__(cls)
26
27 @property
28 def symbols(self):
29 return tuple(self._coordinates)
30
31 @property
32 def dimension(self):
33 return len(self.symbols)
34
35 def coordinates(self):
36 yield from self._coordinates.items()
37
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]
42
43 __getitem__ = coordinate
44
45 def __bool__(self):
46 return any(self._coordinates.values())
47
48 def __hash__(self):
49 return hash(tuple(self.coordinates()))
50
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)
55
56 def _map(self, func):
57 for symbol, coordinate in self.coordinates():
58 yield symbol, func(coordinate)
59
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)
66
67 def _map2(self, other, func):
68 for symbol, coordinate1, coordinate2 in self._iter2(other):
69 yield symbol, func(coordinate1, coordinate2)
70
71
72 class Point(Coordinates):
73 """
74 This class represents points in space.
75 """
76
77 def __new__(cls, coordinates):
78 if isinstance(coordinates, Mapping):
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
90
91 def isorigin(self):
92 return not bool(self)
93
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)
99
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
110
111 def __eq__(self, other):
112 return isinstance(other, Point) and \
113 self._coordinates == other._coordinates
114
115 def aspolyhedron(self):
116 from .polyhedra import Polyhedron
117 equalities = []
118 for symbol, coordinate in self.coordinates():
119 equalities.append(symbol - coordinate)
120 return Polyhedron(equalities)
121
122
123 class Vector(Coordinates):
124 """
125 This class represents displacements in space.
126 """
127
128 __slots__ = (
129 '_coordinates',
130 )
131
132 def __new__(cls, initial, terminal=None):
133 self = object().__new__(cls)
134 if not isinstance(initial, Point):
135 initial = Point(initial)
136 if terminal is None:
137 self._coordinates = initial._coordinates
138 elif not isinstance(terminal, Point):
139 terminal = Point(terminal)
140 self._coordinates = terminal._map2(initial, operator.sub)
141 return self
142
143 def isnull(self):
144 return not bool(self)
145
146 def __add__(self, other):
147 if isinstance(other, (Point, Vector)):
148 coordinates = self._map2(other, operator.add)
149 return other.__class__(coordinates)
150 return NotImplemented
151
152 def angle(self, other):
153 """
154 Retrieve the angle required to rotate the vector into the vector passed
155 in argument. The result is an angle in radians, ranging between -pi and
156 pi.
157 """
158 if not isinstance(other, Vector):
159 raise TypeError('argument must be a Vector instance')
160 cosinus = self.dot(other) / (self.norm()*other.norm())
161 return math.acos(cosinus)
162
163 def cross(self, other):
164 """
165 Calculate the cross product of two Vector3D structures.
166 """
167 if not isinstance(other, Vector):
168 raise TypeError('other must be a Vector instance')
169 if self.dimension != 3 or other.dimension != 3:
170 raise ValueError('arguments must be three-dimensional vectors')
171 if self.symbols != other.symbols:
172 raise ValueError('arguments must belong to the same space')
173 x, y, z = self.symbols
174 coordinates = []
175 coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
176 coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
177 coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
178 return Vector(coordinates)
179
180 def __truediv__(self, other):
181 """
182 Divide the vector by the specified scalar and returns the result as a
183 vector.
184 """
185 if not isinstance(other, numbers.Real):
186 return NotImplemented
187 coordinates = self._map(lambda coordinate: coordinate / other)
188 return Vector(coordinates)
189
190 def dot(self, other):
191 """
192 Calculate the dot product of two vectors.
193 """
194 if not isinstance(other, Vector):
195 raise TypeError('argument must be a Vector instance')
196 result = 0
197 for symbol, coordinate1, coordinate2 in self._iter2(other):
198 result += coordinate1 * coordinate2
199 return result
200
201 def __eq__(self, other):
202 return isinstance(other, Vector) and \
203 self._coordinates == other._coordinates
204
205 def __hash__(self):
206 return hash(tuple(self.coordinates()))
207
208 def __mul__(self, other):
209 if not isinstance(other, numbers.Real):
210 return NotImplemented
211 coordinates = self._map(lambda coordinate: other * coordinate)
212 return Vector(coordinates)
213
214 __rmul__ = __mul__
215
216 def __neg__(self):
217 coordinates = self._map(operator.neg)
218 return Vector(coordinates)
219
220 def norm(self):
221 return math.sqrt(self.norm2())
222
223 def norm2(self):
224 result = 0
225 for coordinate in self._coordinates.values():
226 result += coordinate ** 2
227 return result
228
229 def asunit(self):
230 return self / self.norm()
231
232 def __sub__(self, other):
233 if isinstance(other, (Point, Vector)):
234 coordinates = self._map2(other, operator.sub)
235 return other.__class__(coordinates)
236 return NotImplemented