X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/ae3c7cc888444a66597e093ea0b1fd83f521f0a6..cc6c00616ffb4e7bdf81d5d186ea91b61b304ff1:/pypol/geometry.py

diff --git a/pypol/geometry.py b/pypol/geometry.py
index d0146cf..1db5710 100644
--- a/pypol/geometry.py
+++ b/pypol/geometry.py
@@ -1,8 +1,17 @@
-from abc import ABC, abstractmethod, abstractproperty
+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',
 ]
 
 
@@ -22,3 +31,262 @@ class GeometricObject(ABC):
 
     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):
+        """
+        Adds a Point to a Vector and returns the result as a Point.
+        """
+        if not isinstance(other, Vector):
+            return NotImplemented
+        coordinates = self._map2(other, operator.add)
+        return Point(coordinates)
+
+    def __sub__(self, other):
+        """
+        Returns the difference between two Points as a Vector.
+        """
+        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