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152 lines
4.4 KiB
152 lines
4.4 KiB
from sympy.core.basic import Basic
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from sympy.core.symbol import Str
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from sympy.vector.vector import Vector
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from sympy.vector.coordsysrect import CoordSys3D
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from sympy.vector.functions import _path
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from sympy.core.cache import cacheit
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class Point(Basic):
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"""
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Represents a point in 3-D space.
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"""
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def __new__(cls, name, position=Vector.zero, parent_point=None):
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name = str(name)
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# Check the args first
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if not isinstance(position, Vector):
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raise TypeError(
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"position should be an instance of Vector, not %s" % type(
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position))
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if (not isinstance(parent_point, Point) and
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parent_point is not None):
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raise TypeError(
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"parent_point should be an instance of Point, not %s" % type(
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parent_point))
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# Super class construction
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if parent_point is None:
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obj = super().__new__(cls, Str(name), position)
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else:
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obj = super().__new__(cls, Str(name), position, parent_point)
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# Decide the object parameters
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obj._name = name
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obj._pos = position
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if parent_point is None:
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obj._parent = None
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obj._root = obj
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else:
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obj._parent = parent_point
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obj._root = parent_point._root
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# Return object
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return obj
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@cacheit
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def position_wrt(self, other):
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"""
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Returns the position vector of this Point with respect to
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another Point/CoordSys3D.
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Parameters
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==========
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other : Point/CoordSys3D
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If other is a Point, the position of this Point wrt it is
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returned. If its an instance of CoordSyRect, the position
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wrt its origin is returned.
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Examples
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========
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>>> from sympy.vector import CoordSys3D
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>>> N = CoordSys3D('N')
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>>> p1 = N.origin.locate_new('p1', 10 * N.i)
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>>> N.origin.position_wrt(p1)
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(-10)*N.i
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"""
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if (not isinstance(other, Point) and
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not isinstance(other, CoordSys3D)):
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raise TypeError(str(other) +
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"is not a Point or CoordSys3D")
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if isinstance(other, CoordSys3D):
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other = other.origin
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# Handle special cases
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if other == self:
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return Vector.zero
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elif other == self._parent:
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return self._pos
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elif other._parent == self:
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return -1 * other._pos
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# Else, use point tree to calculate position
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rootindex, path = _path(self, other)
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result = Vector.zero
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i = -1
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for i in range(rootindex):
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result += path[i]._pos
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i += 2
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while i < len(path):
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result -= path[i]._pos
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i += 1
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return result
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def locate_new(self, name, position):
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"""
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Returns a new Point located at the given position wrt this
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Point.
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Thus, the position vector of the new Point wrt this one will
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be equal to the given 'position' parameter.
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Parameters
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==========
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name : str
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Name of the new point
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position : Vector
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The position vector of the new Point wrt this one
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Examples
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========
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>>> from sympy.vector import CoordSys3D
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>>> N = CoordSys3D('N')
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>>> p1 = N.origin.locate_new('p1', 10 * N.i)
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>>> p1.position_wrt(N.origin)
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10*N.i
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"""
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return Point(name, position, self)
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def express_coordinates(self, coordinate_system):
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"""
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Returns the Cartesian/rectangular coordinates of this point
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wrt the origin of the given CoordSys3D instance.
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Parameters
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==========
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coordinate_system : CoordSys3D
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The coordinate system to express the coordinates of this
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Point in.
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Examples
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========
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>>> from sympy.vector import CoordSys3D
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>>> N = CoordSys3D('N')
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>>> p1 = N.origin.locate_new('p1', 10 * N.i)
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>>> p2 = p1.locate_new('p2', 5 * N.j)
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>>> p2.express_coordinates(N)
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(10, 5, 0)
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"""
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# Determine the position vector
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pos_vect = self.position_wrt(coordinate_system.origin)
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# Express it in the given coordinate system
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return tuple(pos_vect.to_matrix(coordinate_system))
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def _sympystr(self, printer):
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return self._name
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