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.
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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
|
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.
Here's what I get for those lines:
MacBook Pro (Core2Duo 2.6) running 10.6
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()0.8653614495697077Can 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.
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).