from sympy.core.basic import Basic
from sympy.vector.vector import Vector
from sympy.vector.coordsysrect import CoordSysCartesian
from sympy.vector.functions import express, _path
from sympy.simplify import trigsimp
from sympy import Symbol
from sympy.core.cache import cacheit


class Point(Basic):
    """
    Represents a point in 3-D space.
    """

    def __new__(cls, name, position=Vector.zero, parent_point=None):
        #Check the args first
        if not isinstance(position, Vector):
            raise TypeError("position should be a Vector instance")
        if (not isinstance(parent_point, Point)
                and parent_point is not None):
            raise TypeError("parent_point should be a Point instance")
        #Create an object
        if parent_point is None:
            arg_parent = Symbol('default')
            arg_self = Symbol(name)
        else:
            arg_parent = parent_point
            arg_self = Symbol('default')
        #All points that are defined as 'roots' are unequal.
        #Points defined at same position wrt the same
        #'parent' are equal, irrespective of the names.
        obj = super(Point, cls).__new__(cls, arg_self,
                                        position, arg_parent)
        #Decide the object parameters
        obj._name = name
        obj._pos = position
        if parent_point is None:
            obj._parent = None
            obj._root = obj
        else:
            obj._parent = parent_point
            obj._root = parent_point._root
        #Return object
        return obj

    @cacheit
    def position_wrt(self, other):
        """
        Returns the position vector of this Point with respect to
        another Point/CoordSysCartesian.

        Parameters
        ==========

        other : Point/CoordSysCartesian
            If other is a Point, the position of this Point wrt it is
            returned. If its an instance of CoordSyRect, the position
            wrt its origin is returned.

        Examples
        ========

        >>> from sympy.vector import Point, CoordSysCartesian
        >>> N = CoordSysCartesian('N')
        >>> p1 = N.origin.locate_new('p1', 10 * N.i)
        >>> N.origin.position_wrt(p1)
        (-10)*N.i

        """

        if (not isinstance(other, Point)
                and not isinstance(other, CoordSysCartesian)):
            raise TypeError(str(other) +
                            "is not a Point or CoordSysCartesian")
        if isinstance(other, CoordSysCartesian):
            other = other.origin
        #Handle special cases
        if other == self:
            return Vector.zero
        elif other == self._parent:
            return self._pos
        elif other._parent == self:
            return -1 * other._pos
        #Else, use point tree to calculate position
        rootindex, path = _path(self, other)
        result = Vector.zero
        i = -1
        for i in range(rootindex):
            result += path[i]._pos
        i += 2
        while i < len(path):
            result -= path[i]._pos
            i += 1
        return result

    def locate_new(self, name, position):
        """
        Returns a new Point located at the given position wrt this
        Point.
        Thus, the position vector of the new Point wrt this one will
        be equal to the given 'position' parameter.

        Parameters
        ==========

        name : str
            Name of the new point

        position : Vector
            The position vector of the new Point wrt this one

        Examples
        ========

        >>> from sympy.vector import Point, CoordSysCartesian
        >>> N = CoordSysCartesian('N')
        >>> p1 = N.origin.locate_new('p1', 10 * N.i)
        >>> p1.position_wrt(N.origin)
        10*N.i

        """
        return Point(name, position, self)

    def express_coordinates(self, coordinate_system):
        """
        Returns the Cartesian/rectangular coordinates of this point
        wrt the origin of the given CoordSysCartesian instance.

        Parameters
        ==========

        coordinate_system : CoordSysCartesian
            The coordinate system to express the coordinates of this
            Point in.

        Examples
        ========

        >>> from sympy.vector import Point, CoordSysCartesian
        >>> N = CoordSysCartesian('N')
        >>> p1 = N.origin.locate_new('p1', 10 * N.i)
        >>> p2 = p1.locate_new('p2', 5 * N.j)
        >>> p2.express_coordinates(N)
        (10, 5, 0)

        """

        #Determine the position vector
        pos_vect = self.position_wrt(coordinate_system.origin)
        #Express it in the given coordinate system
        return tuple(pos_vect.to_matrix(coordinate_system))

    def __str__(self, printer=None):
        return self._name

    __repr__ = __str__
    _sympystr = __str__
