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.
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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):
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())
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