# Source code for pymunk.vec2d

    # ----------------------------------------------------------------------------
    # pymunk
    # Copyright (c) 2007-2011 Victor Blomqvist
    #
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    # of this software and associated documentation files (the "Software"), to deal
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    """This module contain the Vec2d class that is used in all of pymunk when a
    vector is needed.

    The Vec2d class is used almost everywhere in pymunk for 2d coordinates and
    vectors, for example to define gravity vector in a space. However, pymunk is
    smart enough to convert tuples or tuple like objects to Vec2ds so you usually
    do not need to explicitly do conversions if you happen to have a tuple::

        >>> import pymunk
        >>> space = pymunk.Space()
        >>> space.gravity
        Vec2d(0.0, 0.0)
        >>> space.gravity = 3,5
        >>> space.gravity
        Vec2d(3.0, 5.0)
        >>> space.gravity += 2,6
        >>> space.gravity
        Vec2d(5.0, 11.0)

    More examples::

        >>> from pymunk.vec2d import Vec2d
        >>> Vec2d(7.3, 4.2)
        Vec2d(7.3, 4.2)
        >>> Vec2d((7.3, 4.2))
        Vec2d(7.3, 4.2)
        >>> Vec2d(7.3, 4.2) + Vec2d((1,2))
        Vec2d(8.3, 6.2)

    """
    __docformat__ = "reStructuredText"

    import operator
    import math

    __all__ = ["Vec2d"]

    class Vec2d(object):
        """2d vector class, supports vector and scalar operators, and also
        provides some high level functions.
        """
        __slots__ = ("x", "y")

        @staticmethod
        def _fromcffi(p):
            """Used as a speedy way to create Vec2ds internally in pymunk."""
            v = Vec2d.__new__(Vec2d)
            v.x = p.x
            v.y = p.y
            return v

        def __init__(self, x_or_pair=None, y = None):
            if x_or_pair != None:
                if y == None:
                    if hasattr(x_or_pair, "x") and hasattr(x_or_pair, "y"):
                        self.x = x_or_pair.x
                        self.y = x_or_pair.y
                    else:
                        self.x = x_or_pair[0]
                        self.y = x_or_pair[1]
                else:
                    self.x = x_or_pair
                    self.y = y
            else:
                self.x = 0
                self.y = 0

        def __getitem__(self, i):
            if i == 0:
                return self.x
            elif i == 1:
                return self.y
            raise IndexError()

        def __iter__(self):
            yield self.x
            yield self.y

        def __len__(self):
            return 2

        def __setitem__(self, i, value):
            if i == 0:
                self.x = value
            elif i == 1:
                self.y = value
            else:
                raise IndexError()

        # String representaion (for debugging)
        def __repr__(self):
            return 'Vec2d(%s, %s)' % (self.x, self.y)

        # Comparison
        def __eq__(self, other):
            if hasattr(other, "__getitem__") and len(other) == 2:
                return self.x == other[0] and self.y == other[1]
            else:
                return False

        def __ne__(self, other):
            if hasattr(other, "__getitem__") and len(other) == 2:
                return self.x != other[0] or self.y != other[1]
            else:
                return True

        def __nonzero__(self):
            return self.x != 0.0 or self.y != 0.0

        # Generic operator handlers
        def _o2(self, other, f):
            "Any two-operator operation where the left operand is a Vec2d"
            if isinstance(other, Vec2d):
                return Vec2d(f(self.x, other.x),
                             f(self.y, other.y))
            elif (hasattr(other, "__getitem__")):
                return Vec2d(f(self.x, other[0]),
                             f(self.y, other[1]))
            else:
                return Vec2d(f(self.x, other),
                             f(self.y, other))

        def _r_o2(self, other, f):
            "Any two-operator operation where the right operand is a Vec2d"
            if (hasattr(other, "__getitem__")):
                return Vec2d(f(other[0], self.x),
                             f(other[1], self.y))
            else:
                return Vec2d(f(other, self.x),
                             f(other, self.y))

        def _io(self, other, f):
            "inplace operator"
            if (hasattr(other, "__getitem__")):
                self.x = f(self.x, other[0])
                self.y = f(self.y, other[1])
            else:
                self.x = f(self.x, other)
                self.y = f(self.y, other)
            return self

        # Addition
        def __add__(self, other):
            if isinstance(other, Vec2d):
                return Vec2d(self.x + other.x, self.y + other.y)
            elif hasattr(other, "__getitem__"):
                return Vec2d(self.x + other[0], self.y + other[1])
            else:
                return Vec2d(self.x + other, self.y + other)
        __radd__ = __add__

        def __iadd__(self, other):
            if isinstance(other, Vec2d):
                self.x += other.x
                self.y += other.y
            elif hasattr(other, "__getitem__"):
                self.x += other[0]
                self.y += other[1]
            else:
                self.x += other
                self.y += other
            return self

        # Subtraction
        def __sub__(self, other):
            if isinstance(other, Vec2d):
                return Vec2d(self.x - other.x, self.y - other.y)
            elif (hasattr(other, "__getitem__")):
                return Vec2d(self.x - other[0], self.y - other[1])
            else:
                return Vec2d(self.x - other, self.y - other)
        def __rsub__(self, other):
            if isinstance(other, Vec2d):
                return Vec2d(other.x - self.x, other.y - self.y)
            if (hasattr(other, "__getitem__")):
                return Vec2d(other[0] - self.x, other[1] - self.y)
            else:
                return Vec2d(other - self.x, other - self.y)
        def __isub__(self, other):
            if isinstance(other, Vec2d):
                self.x -= other.x
                self.y -= other.y
            elif (hasattr(other, "__getitem__")):
                self.x -= other[0]
                self.y -= other[1]
            else:
                self.x -= other
                self.y -= other
            return self

        # Multiplication
        def __mul__(self, other):
            if isinstance(other, Vec2d):
                return Vec2d(self.x*other.x, self.y*other.y)
            if (hasattr(other, "__getitem__")):
                return Vec2d(self.x*other[0], self.y*other[1])
            else:
                return Vec2d(self.x*other, self.y*other)
        __rmul__ = __mul__

        def __imul__(self, other):
            if isinstance(other, Vec2d):
                self.x *= other.x
                self.y *= other.y
            elif (hasattr(other, "__getitem__")):
                self.x *= other[0]
                self.y *= other[1]
            else:
                self.x *= other
                self.y *= other
            return self

        # Division
        def __div__(self, other):
            return self._o2(other, operator.div)
        def __rdiv__(self, other):
            return self._r_o2(other, operator.div)
        def __idiv__(self, other):
            return self._io(other, operator.div)

        def __floordiv__(self, other):
            return self._o2(other, operator.floordiv)
        def __rfloordiv__(self, other):
            return self._r_o2(other, operator.floordiv)
        def __ifloordiv__(self, other):
            return self._io(other, operator.floordiv)

        def __truediv__(self, other):
            return self._o2(other, operator.truediv)
        def __rtruediv__(self, other):
            return self._r_o2(other, operator.truediv)
        def __itruediv__(self, other):
            return self._io(other, operator.truediv)

        # Modulo
        def __mod__(self, other):
            return self._o2(other, operator.mod)
        def __rmod__(self, other):
            return self._r_o2(other, operator.mod)

        def __divmod__(self, other):
            return self._o2(other, divmod)
        def __rdivmod__(self, other):
            return self._r_o2(other, divmod)

        # Exponentation
        def __pow__(self, other):
            return self._o2(other, operator.pow)
        def __rpow__(self, other):
            return self._r_o2(other, operator.pow)

        # Bitwise operators
        def __lshift__(self, other):
            return self._o2(other, operator.lshift)
        def __rlshift__(self, other):
            return self._r_o2(other, operator.lshift)

        def __rshift__(self, other):
            return self._o2(other, operator.rshift)
        def __rrshift__(self, other):
            return self._r_o2(other, operator.rshift)

        def __and__(self, other):
            return self._o2(other, operator.and_)
        __rand__ = __and__

        def __or__(self, other):
            return self._o2(other, operator.or_)
        __ror__ = __or__

        def __xor__(self, other):
            return self._o2(other, operator.xor)
        __rxor__ = __xor__

        # Unary operations
        def __neg__(self):
            return Vec2d(operator.neg(self.x), operator.neg(self.y))

        def __pos__(self):
            return Vec2d(operator.pos(self.x), operator.pos(self.y))

        def __abs__(self):
            return Vec2d(abs(self.x), abs(self.y))

        def __invert__(self):
            return Vec2d(-self.x, -self.y)

        # vectory functions
        def get_length_sqrd(self):
            """Get the squared length of the vector.
            It is more efficient to use this method instead of first call
            get_length() or access .length and then do a sqrt().

            :return: The squared length
            """
            return self.x**2 + self.y**2

        def get_length(self):
            """Get the length of the vector.

            :return: The length
            """
            return math.sqrt(self.x**2 + self.y**2)
        def __setlength(self, value):
            length = self.get_length()
            self.x *= value/length
            self.y *= value/length
        length = property(get_length, __setlength,
            doc = """Gets or sets the magnitude of the vector""")

        def rotate(self, angle_radians):
            """Rotate the vector by angle_radians radians."""
            cos = math.cos(angle_radians)
            sin = math.sin(angle_radians)
            x = self.x*cos - self.y*sin
            y = self.x*sin + self.y*cos
            self.x = x
            self.y = y

        def rotated(self, angle_radians):
            """Create and return a new vector by rotating this vector by
            angle_radians radians.

            :return: Rotated vector
            """
            cos = math.cos(angle_radians)
            sin = math.sin(angle_radians)
            x = self.x*cos - self.y*sin
            y = self.x*sin + self.y*cos
            return Vec2d(x, y)

        def rotate_degrees(self, angle_degrees):
            """Rotate the vector by angle_degrees degrees."""
            self.rotate(math.radians(angle_degrees))

        def rotated_degrees(self, angle_degrees):
            """Create and return a new vector by rotating this vector by
            angle_degrees degrees.

            :return: Rotade vector
            """
            return self.rotated(math.radians(angle_degrees))

        def get_angle(self):
            if (self.get_length_sqrd() == 0):
                return 0
            return math.atan2(self.y, self.x)
        def __setangle(self, angle):
            self.x = self.length
            self.y = 0
            self.rotate(angle)
        angle = property(get_angle, __setangle,
            doc="""Gets or sets the angle (in radians) of a vector""")

        def get_angle_degrees(self):
            return math.degrees(self.get_angle())
        def __set_angle_degrees(self, angle_degrees):
            self.__setangle(math.radians(angle_degrees))
        angle_degrees = property(get_angle_degrees, __set_angle_degrees,
            doc="""Gets or sets the angle (in degrees) of a vector""")

        def get_angle_between(self, other):
            """Get the angle between the vector and the other in radians

            :return: The angle
            """
            cross = self.x*other[1] - self.y*other[0]
            dot = self.x*other[0] + self.y*other[1]
            return math.atan2(cross, dot)

        def get_angle_degrees_between(self, other):
            """Get the angle between the vector and the other in degrees

            :return: The angle (in degrees)
            """
            return math.degrees(self.get_angle_between(other))

        def normalized(self):
            """Get a normalized copy of the vector
            Note: This function will return 0 if the length of the vector is 0.

            :return: A normalized vector
            """
            length = self.length
            if length != 0:
                return self/length
            return Vec2d(self)

        def normalize_return_length(self):
            """Normalize the vector and return its length before the normalization

            :return: The length before the normalization
            """
            length = self.length
            if length != 0:
                self.x /= length
                self.y /= length
            return length

        def perpendicular(self):
            return Vec2d(-self.y, self.x)

        def perpendicular_normal(self):
            length = self.length
            if length != 0:
                return Vec2d(-self.y/length, self.x/length)
            return Vec2d(self)

        def dot(self, other):
            """The dot product between the vector and other vector
                v1.dot(v2) -> v1.x*v2.x + v1.y*v2.y

            :return: The dot product
            """
            return float(self.x*other[0] + self.y*other[1])

        def get_distance(self, other):
            """The distance between the vector and other vector

            :return: The distance
            """
            return math.sqrt((self.x - other[0])**2 + (self.y - other[1])**2)

        def get_dist_sqrd(self, other):
            """The squared distance between the vector and other vector
            It is more efficent to use this method than to call get_distance()
            first and then do a sqrt() on the result.

            :return: The squared distance
            """
            return (self.x - other[0])**2 + (self.y - other[1])**2

        def projection(self, other):
            other_length_sqrd = other[0]*other[0] + other[1]*other[1]
            projected_length_times_other_length = self.dot(other)
            return other*(projected_length_times_other_length/other_length_sqrd)

        def cross(self, other):
            """The cross product between the vector and other vector
                v1.cross(v2) -> v1.x*v2.y - v1.y*v2.x

            :return: The cross product
            """
            return self.x*other[1] - self.y*other[0]

        def interpolate_to(self, other, range):
            return Vec2d(self.x + (other[0] - self.x)*range, self.y + (other[1] - self.y)*range)

        def convert_to_basis(self, x_vector, y_vector):
            x = self.dot(x_vector)/x_vector.get_length_sqrd()
            y = self.dot(y_vector)/y_vector.get_length_sqrd()
            return Vec2d(x, y)

        def __get_int_xy(self):
            return int(self.x), int(self.y)
        int_tuple = property(__get_int_xy,
            doc="""Return the x and y values of this vector as ints""")

        @staticmethod
        def zero():
            """A vector of zero length"""
            return Vec2d(0, 0)

        @staticmethod
        def unit():
            """A unit vector pointing up"""
            return Vec2d(0, 1)

        @staticmethod
        def ones():
            """A vector where both x and y is 1"""
            return Vec2d(1, 1)

        # Extra functions, mainly for chipmunk
        def cpvrotate(self, other):
            """Uses complex multiplication to rotate this vector by the other. """
            return Vec2d(self.x*other.x - self.y*other.y, self.x*other.y + self.y*other.x)
        def cpvunrotate(self, other):
            """The inverse of cpvrotate"""
            return Vec2d(self.x*other.x + self.y*other.y, self.y*other.x - self.x*other.y)

        # Pickle
        def __reduce__(self):
            callable = Vec2d
            args = (self.x, self.y)
            return (callable, args)