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Needed by recipe 578004, this is meant to be a power pure-python-based module for running optimized 2D vector operations with a few possibilities not seen in most vector libraries. Many of the methods are overloaded to provide great versitility in what operations can be performed. To allow for even greater operations, the many methods mays be wrapped with the included autocast method so that even more datatypes can be used in whatever calculations the programmer may desire.

Python, 510 lines
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from math import *
from functools import wraps

################################################################################

def autocast(method): # Optional method decorator
    @wraps(method)
    def wrapper(self, obj):
        try:
            return method(self, self.__class__(*obj))
        except TypeError:
            return method(self, obj)
    return wrapper

################################################################################

def Polar2(magnitude, degrees):
    x = magnitude * sin(radians(degrees))
    y = magnitude * cos(radians(degrees))
    return Vector2(x, y)

################################################################################

class Vector2:

    __slots__ = 'x', 'y'

    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __repr__(self):
        return 'Vector2({!r}, {!r})'.format(self.x, self.y)

    def polar_repr(self):
        x, y = self.x, self.y
        magnitude = hypot(x, y)
        angle = degrees(atan2(x, y)) % 360
        return 'Polar2({!r}, {!r})'.format(magnitude, angle)

    # Rich Comparison Methods

    def __lt__(self, obj):
        if isinstance(obj, Vector2):
            x1, y1, x2, y2 = self.x, self.y, obj.x, obj.y
            return x1 * x1 + y1 * y1 < x2 * x2 + y2 * y2
        return hypot(self.x, self.y) < obj

    def __le__(self, obj):
        if isinstance(obj, Vector2):
            x1, y1, x2, y2 = self.x, self.y, obj.x, obj.y
            return x1 * x1 + y1 * y1 <= x2 * x2 + y2 * y2
        return hypot(self.x, self.y) <= obj

    def __eq__(self, obj):
        if isinstance(obj, Vector2):
            return self.x == obj.x and self.y == obj.y
        return hypot(self.x, self.y) == obj

    def __ne__(self, obj):
        if isinstance(obj, Vector2):
            return self.x != obj.x or self.y != obj.y
        return hypot(self.x, self.y) != obj

    def __gt__(self, obj):
        if isinstance(obj, Vector2):
            x1, y1, x2, y2 = self.x, self.y, obj.x, obj.y
            return x1 * x1 + y1 * y1 > x2 * x2 + y2 * y2
        return hypot(self.x, self.y) > obj

    def __ge__(self, obj):
        if isinstance(obj, Vector2):
            x1, y1, x2, y2 = self.x, self.y, obj.x, obj.y
            return x1 * x1 + y1 * y1 >= x2 * x2 + y2 * y2
        return hypot(self.x, self.y) >= obj

    # Boolean Operation

    def __bool__(self):
        return self.x != 0 or self.y != 0

    # Container Methods

    def __len__(self):
        return 2

    def __getitem__(self, index):
        return (self.x, self.y)[index]

    def __setitem__(self, index, value):
        temp = [self.x, self.y]
        temp[index] = value
        self.x, self.y = temp

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

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

    def __contains__(self, obj):
        return obj in (self.x, self.y)

    # Binary Arithmetic Operations

    def __add__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x + obj.x, self.y + obj.y)
        return Vector2(self.x + obj, self.y + obj)

    def __sub__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x - obj.x, self.y - obj.y)
        return Vector2(self.x - obj, self.y - obj)

    def __mul__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x * obj.x, self.y * obj.y)
        return Vector2(self.x * obj, self.y * obj)

    def __truediv__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x / obj.x, self.y / obj.y)
        return Vector2(self.x / obj, self.y / obj)

    def __floordiv__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x // obj.x, self.y // obj.y)
        return Vector2(self.x // obj, self.y // obj)

    def __mod__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x % obj.x, self.y % obj.y)
        return Vector2(self.x % obj, self.y % obj)

    def __divmod__(self, obj):
        if isinstance(obj, Vector2):
            return (Vector2(self.x // obj.x, self.y // obj.y),
                    Vector2(self.x % obj.x, self.y % obj.y))
        return (Vector2(self.x // obj, self.y // obj),
                Vector2(self.x % obj, self.y % obj))

    def __pow__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x ** obj.x, self.y ** obj.y)
        return Vector2(self.x ** obj, self.y ** obj)

    def __lshift__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x << obj.x, self.y << obj.y)
        return Vector2(self.x << obj, self.y << obj)

    def __rshift__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x >> obj.x, self.y >> obj.y)
        return Vector2(self.x >> obj, self.y >> obj)

    def __and__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x & obj.x, self.y & obj.y)
        return Vector2(self.x & obj, self.y & obj)

    def __xor__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x ^ obj.x, self.y ^ obj.y)
        return Vector2(self.x ^ obj, self.y ^ obj)

    def __or__(self, obj):
        if isinstance(obj, Vector2):
            return Vector2(self.x | obj.x, self.y | obj.y)
        return Vector2(self.x | obj, self.y | obj)

    # Binary Arithmetic Operations (with reflected operands)

    def __radd__(self, obj):
        return Vector2(obj + self.x, obj + self.y)

    def __rsub__(self, obj):
        return Vector2(obj - self.x, obj - self.y)

    def __rmul__(self, obj):
        return Vector2(obj * self.x, obj * self.y)

    def __rtruediv__(self, obj):
        return Vector2(obj / self.x, obj / self.y)

    def __rfloordiv__(self, obj):
        return Vector2(obj // self.x, obj // self.y)

    def __rmod__(self, obj):
        return Vector2(obj % self.x, obj % self.y)

    def __rdivmod__(self, obj):
        return (Vector2(obj // self.x, obj // self.y),
                Vector2(obj % self.x, obj % self.y))

    def __rpow__(self, obj):
        return Vector2(obj ** self.x, obj ** self.y)

    def __rlshift__(self, obj):
        return Vector2(obj << self.x, obj << self.y)

    def __rrshift__(self, obj):
        return Vector2(obj >> self.x, obj >> self.y)

    def __rand__(self, obj):
        return Vector2(obj & self.x, obj & self.y)

    def __rxor__(self, obj):
        return Vector2(obj ^ self.x, obj ^ self.y)

    def __ror__(self, obj):
        return Vector2(obj | self.x, obj | self.y)

    # Augmented Arithmetic Assignments

    def __iadd__(self, obj):
        if isinstance(obj, Vector2):
            self.x += obj.x
            self.y += obj.y
        else:
            self.x += obj
            self.y += obj
        return self

    def __isub__(self, obj):
        if isinstance(obj, Vector2):
            self.x -= obj.x
            self.y -= obj.y
        else:
            self.x -= obj
            self.y -= obj
        return self

    def __imul__(self, obj):
        if isinstance(obj, Vector2):
            self.x *= obj.x
            self.y *= obj.y
        else:
            self.x *= obj
            self.y *= obj
        return self

    def __itruediv__(self, obj):
        if isinstance(obj, Vector2):
            self.x /= obj.x
            self.y /= obj.y
        else:
            self.x /= obj
            self.y /= obj
        return self

    def __ifloordiv__(self, obj):
        if isinstance(obj, Vector2):
            self.x //= obj.x
            self.y //= obj.y
        else:
            self.x //= obj
            self.y //= obj
        return self

    def __imod__(self, obj):
        if isinstance(obj, Vector2):
            self.x %= obj.x
            self.y %= obj.y
        else:
            self.x %= obj
            self.y %= obj
        return self

    def __ipow__(self, obj):
        if isinstance(obj, Vector2):
            self.x **= obj.x
            self.y **= obj.y
        else:
            self.x **= obj
            self.y **= obj
        return self

    def __ilshift__(self, obj):
        if isinstance(obj, Vector2):
            self.x <<= obj.x
            self.y <<= obj.y
        else:
            self.x <<= obj
            self.y <<= obj
        return self

    def __irshift__(self, obj):
        if isinstance(obj, Vector2):
            self.x >>= obj.x
            self.y >>= obj.y
        else:
            self.x >>= obj
            self.y >>= obj
        return self

    def __iand__(self, obj):
        if isinstance(obj, Vector2):
            self.x &= obj.x
            self.y &= obj.y
        else:
            self.x &= obj
            self.y &= obj
        return self

    def __ixor__(self, obj):
        if isinstance(obj, Vector2):
            self.x ^= obj.x
            self.y ^= obj.y
        else:
            self.x ^= obj
            self.y ^= obj
        return self

    def __ior__(self, obj):
        if isinstance(obj, Vector2):
            self.x |= obj.x
            self.y |= obj.y
        else:
            self.x |= obj
            self.y |= obj
        return self

    # Unary Arithmetic Operations

    def __pos__(self):
        return Vector2(+self.x, +self.y)

    def __neg__(self):
        return Vector2(-self.x, -self.y)

    def __invert__(self):
        return Vector2(~self.x, ~self.y)

    def __abs__(self):
        return Vector2(abs(self.x), abs(self.y))

    # Virtual "magnitude" Attribute

    def __fg_ma(self):
        return hypot(self.x, self.y)

    def __fs_ma(self, value):
        x, y = self.x, self.y
        temp = value / hypot(x, y)
        self.x, self.y = x * temp, y * temp

    magnitude = property(__fg_ma, __fs_ma, doc='Virtual "magnitude" Attribute')

    # Virtual "direction" Attribute

    def __fg_di(self):
        return atan2(self.y, self.x)

    def __fs_di(self, value):
        temp = hypot(self.x, self.y)
        self.x, self.y = cos(value) * temp, sin(value) * temp

    direction = property(__fg_di, __fs_di, doc='Virtual "direction" Attribute')

    # Virtual "degrees" Attribute

    def __fg_de(self):
        return degrees(atan2(self.x, self.y)) % 360

    def __fs_de(self, value):
        value, temp = radians(value), hypot(self.x, self.y)
        self.x, self.y = sin(value) * temp, cos(value) * temp

    degrees = property(__fg_de, __fs_de, doc='Virtual "degrees" Attribute')

    # Virtual "xy" Attribute

    def __fg_xy(self):
        return self.x, self.y

    def __fs_xy(self, value):
        self.x, self.y = value

    xy = property(__fg_xy, __fs_xy, doc='Virtual "xy" Attribute')

    # Virtual "yx" Attribute

    def __fg_yx(self):
        return self.y, self.x

    def __fs_yx(self, value):
        self.y, self.x = value

    yx = property(__fg_yx, __fs_yx, doc='Virtual "yx" Attribute')

    # Unit Vector Operations

    def unit_vector(self):
        x, y = self.x, self.y
        temp = hypot(x, y)
        return Vector2(x / temp, y / temp)

    def normalize(self):
        x, y = self.x, self.y
        temp = hypot(x, y)
        self.x, self.y = x / temp, y / temp
        return self

    # Vector Multiplication Operations

    def dot_product(self, vec):
        return self.x * vec.x + self.y * vec.y

    def cross_product(self, vec):
        return self.x * vec.y - self.y * vec.x

    # Geometric And Physical Reflections

    def reflect(self, vec):
        x1, y1, x2, y2 = self.x, self.y, vec.x, vec.y
        temp = 2 * (x1 * x2 + y1 * y2) / (x2 * x2 + y2 * y2)
        return Vector2(x2 * temp - x1, y2 * temp - y1)

    def bounce(self, vec):
        x1, y1, x2, y2 = self.x, self.y, +vec.y, -vec.x
        temp = 2 * (x1 * x2 + y1 * y2) / (x2 * x2 + y2 * y2)
        return Vector2(x2 * temp - x1, y2 * temp - y1)

    # Standard Vector Operations

    def project(self, vec):
        x, y = vec.x, vec.y
        temp = (self.x * x + self.y * y) / (x * x + y * y)
        return Vector2(x * temp, y * temp)

    def rotate(self, vec):
        x1, y1, x2, y2 = self.x, self.y, vec.x, vec.y
        return Vector2(x1 * x2 + y1 * y2, y1 * x2 - x1 * y2)

    def interpolate(self, vec, bias):
        a = 1 - bias
        return Vector2(self.x * a + vec.x * bias, self.y * a + vec.y * bias)

    # Other Useful Methods

    def near(self, vec, dist):
        x, y = self.x - vec.x, self.y - vec.y
        return x * x + y * y <= dist * dist

    def perpendicular(self):
        return Vector2(+self.y, -self.x)

    def subset(self, vec1, vec2):
        x1, x2 = vec1.x, vec2.x
        if x1 <= x2:
            if x1 <= self.x <= x2:
                y1, y2 = vec1.y, vec2.y
                if y1 <= y2:
                    return y1 <= self.y <= y2
                return y2 <= self.y <= y1
        else:
            if x2 <= self.x <= x1:
                y1, y2 = vec1.y, vec2.y
                if y1 <= y2:
                    return y1 <= self.y <= y2
                return y2 <= self.y <= y1
        return False

    def distance(self, vec):
        return hypot(self.x - vec.x, self.y - vec.y)

    def limit(self, dist):
        x, y = self.x, self.y
        magnitude = hypot(x, y)
        if magnitude > dist:
            temp = dist / magnitude
            self.x, self.y = x * temp, y * temp
        return self

    def direction_between(self, vec):
        return atan2(self.y, self.x) - atan2(vec.y, vec.x)

    def degrees_between(self, vec):
        diff = degrees(atan2(self.y, self.x) - atan2(vec.y, vec.x)) % 360
        return 360 - diff if diff > 180 else diff

    # Synonymous Definitions

    copy = __pos__

    inverse = __neg__

    unit = unit_vector

    dot = dot_product

    cross = cross_product

    lerp = interpolate

    perp = perpendicular

    dist = distance

    dir_diff = direction_between

    deg_diff = degrees_between

################################################################################

import recipe576904; recipe576904.bind_all(globals())