+++ /dev/null
-import math
-import numbers
-import operator
-
-from abc import ABC, abstractproperty, abstractmethod
-from collections import OrderedDict, Mapping
-
-from .linexprs import Symbol
-
-
-__all__ = [
- 'GeometricObject',
- 'Point',
- 'Vector',
-]
-
-
-class GeometricObject(ABC):
-
- @abstractproperty
- def symbols(self):
- pass
-
- @property
- def dimension(self):
- return len(self.symbols)
-
- @abstractmethod
- def aspolyhedron(self):
- pass
-
- def asdomain(self):
- return self.aspolyhedron()
-
-
-class Coordinates:
-
- __slots__ = (
- '_coordinates',
- )
-
- def __new__(cls, coordinates):
- if isinstance(coordinates, Mapping):
- coordinates = coordinates.items()
- self = object().__new__(cls)
- self._coordinates = OrderedDict()
- for symbol, coordinate in sorted(coordinates,
- key=lambda item: item[0].sortkey()):
- if not isinstance(symbol, Symbol):
- raise TypeError('symbols must be Symbol instances')
- if not isinstance(coordinate, numbers.Real):
- raise TypeError('coordinates must be real numbers')
- self._coordinates[symbol] = coordinate
- return self
-
- @property
- def symbols(self):
- return tuple(self._coordinates)
-
- @property
- def dimension(self):
- return len(self.symbols)
-
- def coordinates(self):
- yield from self._coordinates.items()
-
- def coordinate(self, symbol):
- if not isinstance(symbol, Symbol):
- raise TypeError('symbol must be a Symbol instance')
- return self._coordinates[symbol]
-
- __getitem__ = coordinate
-
- def values(self):
- yield from self._coordinates.values()
-
- def __bool__(self):
- return any(self._coordinates.values())
-
- def __hash__(self):
- return hash(tuple(self.coordinates()))
-
- def __repr__(self):
- string = ', '.join(['{!r}: {!r}'.format(symbol, coordinate)
- for symbol, coordinate in self.coordinates()])
- return '{}({{{}}})'.format(self.__class__.__name__, string)
-
- def _map(self, func):
- for symbol, coordinate in self.coordinates():
- yield symbol, func(coordinate)
-
- def _iter2(self, other):
- if self.symbols != other.symbols:
- raise ValueError('arguments must belong to the same space')
- coordinates1 = self._coordinates.values()
- coordinates2 = other._coordinates.values()
- yield from zip(self.symbols, coordinates1, coordinates2)
-
- def _map2(self, other, func):
- for symbol, coordinate1, coordinate2 in self._iter2(other):
- yield symbol, func(coordinate1, coordinate2)
-
-
-class Point(Coordinates, GeometricObject):
- """
- This class represents points in space.
- """
-
- def isorigin(self):
- """
- Return True if a Point is the origin.
- """
- return not bool(self)
-
- def __hash__(self):
- return super().__hash__()
-
- def __add__(self, other):
- if not isinstance(other, Vector):
- return NotImplemented
- coordinates = self._map2(other, operator.add)
- return Point(coordinates)
-
- def __sub__(self, other):
- coordinates = []
- if isinstance(other, Point):
- coordinates = self._map2(other, operator.sub)
- return Vector(coordinates)
- elif isinstance(other, Vector):
- coordinates = self._map2(other, operator.sub)
- return Point(coordinates)
- else:
- return NotImplemented
-
- def __eq__(self, other):
- """
- Compares two Points for equality.
- """
- return isinstance(other, Point) and \
- self._coordinates == other._coordinates
-
- def aspolyhedron(self):
- """
- Return a Point as a polyhedron.
- """
- from .polyhedra import Polyhedron
- equalities = []
- for symbol, coordinate in self.coordinates():
- equalities.append(symbol - coordinate)
- return Polyhedron(equalities)
-
-
-class Vector(Coordinates):
- """
- This class represents displacements in space.
- """
-
- def __new__(cls, initial, terminal=None):
- if not isinstance(initial, Point):
- initial = Point(initial)
- if terminal is None:
- coordinates = initial._coordinates
- else:
- if not isinstance(terminal, Point):
- terminal = Point(terminal)
- coordinates = terminal._map2(initial, operator.sub)
- return super().__new__(cls, coordinates)
-
- def isnull(self):
- """
- Returns true if a Vector is null.
- """
- return not bool(self)
-
- def __hash__(self):
- return super().__hash__()
-
- def __add__(self, other):
- """
- Adds either a Point or Vector to a Vector.
- """
- if isinstance(other, (Point, Vector)):
- coordinates = self._map2(other, operator.add)
- return other.__class__(coordinates)
- return NotImplemented
-
- def angle(self, other):
- """
- 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.
- """
- if not isinstance(other, Vector):
- raise TypeError('argument must be a Vector instance')
- cosinus = self.dot(other) / (self.norm()*other.norm())
- return math.acos(cosinus)
-
- def cross(self, other):
- """
- Calculate the cross product of two Vector3D structures.
- """
- if not isinstance(other, Vector):
- raise TypeError('other must be a Vector instance')
- if self.dimension != 3 or other.dimension != 3:
- raise ValueError('arguments must be three-dimensional vectors')
- if self.symbols != other.symbols:
- raise ValueError('arguments must belong to the same space')
- x, y, z = self.symbols
- coordinates = []
- coordinates.append((x, self[y]*other[z] - self[z]*other[y]))
- coordinates.append((y, self[z]*other[x] - self[x]*other[z]))
- coordinates.append((z, self[x]*other[y] - self[y]*other[x]))
- return Vector(coordinates)
-
- def __truediv__(self, other):
- """
- Divide the vector by the specified scalar and returns the result as a
- vector.
- """
- if not isinstance(other, numbers.Real):
- return NotImplemented
- coordinates = self._map(lambda coordinate: coordinate / other)
- return Vector(coordinates)
-
- def dot(self, other):
- """
- Calculate the dot product of two vectors.
- """
- if not isinstance(other, Vector):
- raise TypeError('argument must be a Vector instance')
- result = 0
- for symbol, coordinate1, coordinate2 in self._iter2(other):
- result += coordinate1 * coordinate2
- return result
-
- def __eq__(self, other):
- """
- Compares two Vectors for equality.
- """
- return isinstance(other, Vector) and \
- self._coordinates == other._coordinates
-
- def __hash__(self):
- return hash(tuple(self.coordinates()))
-
- def __mul__(self, other):
- """
- Multiplies a Vector by a scalar value.
- """
- if not isinstance(other, numbers.Real):
- return NotImplemented
- coordinates = self._map(lambda coordinate: other * coordinate)
- return Vector(coordinates)
-
- __rmul__ = __mul__
-
- def __neg__(self):
- """
- Returns the negated form of a Vector.
- """
- coordinates = self._map(operator.neg)
- return Vector(coordinates)
-
- def norm(self):
- """
- Normalizes a Vector.
- """
- return math.sqrt(self.norm2())
-
- def norm2(self):
- result = 0
- for coordinate in self._coordinates.values():
- result += coordinate ** 2
- return result
-
- def asunit(self):
- return self / self.norm()
-
- def __sub__(self, other):
- """
- Subtract a Point or Vector from a Vector.
- """
- if isinstance(other, (Point, Vector)):
- coordinates = self._map2(other, operator.sub)
- return other.__class__(coordinates)
- return NotImplemented
projects / linpy.git / blobdiff