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This recipe implements vectors in pure Python and does not use "C" for speed enhancements. As a result, much effort has gone towards optimizing the instructions for the class methods. There are a few things that have yet to be improved, but it is being posted as an RFC. Comments on the structure, method names, and coding technique are requested for change. Once this code is standardized, work may commence on writing Vector3, Vector4, and VectorX. Please note that there is a difference between the "direction" and "degrees" properties.

Python, 482 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):
        temp = hypot(self.x, self.y)
        self.x, self.y = sin(radians(value)) * temp, cos(radians(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, self.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

    # Synonymous Definitions

    copy = __pos__

    inverse = __neg__

    unit = unit_vector

    dot = dot_product

    cross = cross_product

    lerp = interpolate

    perp = perpendicular

4 comments

Stephen Chappell (author) 12 years, 2 months ago  # | flag

Would someone mind testing the following code for their respective speeds?

timeit.Timer('test1(1.2, 4.3)', 'def test1(a, b): return (a * a + b * b) ** 0.5').timeit()

timeit.Timer('test2(1.2, 4.3)', 'import math\ndef test2(a, b, h=math.hypot): return h(a, b)').timeit()

Gabriel Genellina pointed out that the second should be faster, but the opposite appears to be true while running on my computer.

Scott Lyons 12 years, 2 months ago  # | flag

Here's what I get for those lines:

>>> import timeit
>>> timeit.Timer('test1(1.2, 4.3)', 'def test1(a, b): return (a * a + b * b) ** 0.5').timeit()
0.41190791130065918
>>> timeit.Timer('test2(1.2, 4.3)', 'import math\ndef test2(a, b, h=math.hypot): return h(a, b)').timeit()
0.3513648509979248

MacBook Pro (Core2Duo 2.6) running 10.6

Stephen Chappell (author) 12 years, 2 months ago  # | flag

Compaq Presario CQ60

Genuine Intel(R) CPU - 585 @ 2.16GHz, 2161 Mhz, 1 Core(s), 1 Logical Processor(s)

Microsoft(R) Windows Vista(TM) Home Basic

Python 3.1.1 (r311:74483, Aug 17 2009, 17:02:12) [MSC v.1500 32 bit (Intel)] on win32

>>> import timeit

>>> timeit.Timer('test1(1.2, 4.3)', 'def test1(a, b): return (a * a + b * b) ** 0.5').timeit()

0.5237614696839962

>>> timeit.Timer('test2(1.2, 4.3)', 'import math\ndef test2(a, b, h=math.hypot): return h(a, b)').timeit()

0.8653614495697077

Can anyone explain the difference in time (or the "correct" syntax for post code block in the comments)?

Those numbers are mostly consistent at a ratio of difference at about 1.6; the second is never faster here.

Are most of you running on Linux kernels? Many people run Python in Linux, and I have heard that Mac uses it now.

Scott Lyons 12 years, 2 months ago  # | flag

OSX 10.5 came with 2.4 and 2.5, 10.6 comes with 2.4, 2.5 and 2.6 (which is what I ran my tests on).

To get the code blocks working, you have to either indent 4 spaces, or replace the ">>>" (just re-type it, copying and pasting doesn't work for some reason).