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413 lines (350 loc) · 12.6 KB
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# Copyright (c) 2008 Peter Shinners
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
from operator import isNumberType
from math import hypot, sin, cos, atan2
getattr = getattr # copy builtin to global for speed
__all__ = ["Vec2"]
class Vec2(object):
"""Immutable floating point 2D vector class.
The vector acts as an indexable
and iterable pair of floating point numbers. Operators are
overridden to perform elemntwise operations. The length related
methods are safe against zero length vectors, and will not
raise division exceptions. All vector arguments accept any number
or object with a pair of numbers."""
__slots__ = ("__vec2__")
def __init__(self, x, y=None):
"""Initialize a new vector from any number or pair of numbers."""
_none = None
if y is _none:
if isNumberType(x):
x += 0.0
self.__vec2__ = (x, x)
else:
x, y = x
self.__vec2__ = (x + 0.0, y + 0.0)
elif x is _none:
self.__vec2__ = y
else:
self.__vec2__ = (x + 0.0, y + 0.0)
@property
def x(self):
return self.__vec2__[0]
@property
def y(self):
return self.__vec2__[1]
def __repr__(self):
return "Vec2(%f, %f)" % self.__vec2__
def __iter__(self):
return self.__vec2__.__iter__()
def __len__(self):
"""The number of dimensions for the vector, always two."""
return 2
def __getitem__(self, key):
"""Index the vector as a two item container"""
return self.__vec2__[key]
def length(self):
"""Length of the vector"""
return hypot(*self.__vec2__)
def length2(self):
"""Squared length of the vector"""
vx, vy = self.__vec2__
return vx * vx + vy * vy
def setlength(self, value):
"""Assign the length of the vector. If the vector
currently has a zero length vector, it is moved only
in positive y."""
vx, vy = self.__vec2__
l = hypot(vx, vy)
if l:
l = value / l
return Vec2((vx * l, vy * l))
return Vec2(None, (0.0, l))
def normalize(self):
"""Set the length of the vector to exactly one, in place,
unless the vector has zero length."""
vx, vy = self.__vec2__
l = hypot(vx, vy)
if l:
return Vec2(None, (vx / l, vy / l))
return self
def distance(self, other):
"""The distance between two vectors."""
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return hypot(vx - ox, vy - oy)
def distance2(self, other):
"""The squared distance between two vectors."""
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return (vx - ox) ** 2.0 + (vy - oy) ** 2.0
def setdistance(self, other, distance):
"""Set the distance to another vector, in place. If the
two vectors are in the same position, the vector is moved
in positive y."""
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
dx = vx - ox
dy = vy - oy
l = hypot(dx, dy)
if l:
l = distance / l
return Vec2((ox + vx * l, oy + vy * l))
return Vec2(None, (ox, oy + distance))
def perp(self):
"""Make the vector a perpendicular, and keep the same length.
The perpendicular will be rotated 90 degrees clockwise."""
vx, vy = self.__vec2__
return Vec2(None, (vy, -vx))
def rotate(self, degrees, pivot=None):
radians = degrees * -0.017453292519943295 # pi/180
c = cos(radians)
s = sin(radians)
vx, vy = self.__vec2__
if pivot is None:
return Vec2(None, (vx*c - vy*s, vx*s + vy*c))
if isNumberType(pivot):
ox = oy = pivot
else:
ox, oy = getattr(pivot, "__vec2__", pivot)
vx -= ox
vy -= oy
x = vx*c - vy*s
y = vx*s + vy*c
return Vec2(None, (x + ox, y + oy))
def angle(self, other=None):
vx, vy = self.__vec2__
if not vx or not vy:
return 0.0
if other is None:
return atan2(vx, vy) * 57.295779513082323 # 180/pi
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
cross = vx * oy - vy * ox
dot = vx * ox + vy * oy
return atan2(cross, dot) * 57.295779513082323 # 180/pi
def setangle(self, degrees, other=None):
radians = degrees * 0.017453292519943295 # pi/180
c = cos(radians)
s = sin(radians)
vx, vy = self.__vec2__
if other is None:
l = hypot(vx, vy)
return Vec2(None, (l*s, l*c))
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
l = hypot(vx - ox, vy - oy)
return Vec2(None, (ox + l*s, oy + l*c))
def cross(self, other):
"""Cross multiplication with another vector."""
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return vx * oy - vy * ox
def dot(self, other):
"""Dot product with another vector."""
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return vx * ox + vy * oy
def atan2(self):
"""Pass the coordinates to the atan2 function"""
return atan2(*self.__vec2__)
def project(self, other):
"""Project onto another vector. The other vector does not
need to be normalized."""
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
length2 = other ** 2
length2 += length2
else:
ox, oy = getattr(other, "__vec2__", other)
length2 = ox ** 2 + oy ** 2
if not length2:
return self
dot = vx * ox + vy * oy
length = dot / length2
return Vec2(None, (ox * length, oy * length))
def reflect(self, other):
"""Reflect the direction of the vector based on the direction
of another. The other vector does not need to be normalized."""
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
length2 = other ** 2
length2 += length2
else:
ox, oy = getattr(other, "__vec2__", other)
length2 = ox ** 2 + oy ** 2
if not length2:
return self
dot = vx * ox + vy * oy
length = dot / length2 * 2
return Vec2(None, (ox * length - vx, oy * length - vy))
def almost(self, other, epsilon=1e-7):
"""Compare if two vectors are almost equal."""
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
dx = vx - ox
dy = vy - oy
nepsilon = -epsilon
return (dx < epsilon and dy > nepsilon
and dy < epsilon and dy > nepsilon)
def floor(self):
"""Create a pair of integers of the floor from each value."""
vx, vy = self.__vec2__
_i = int
return (_i(vx // 1.0), _i(vy // 1.0)) # NOTE, not a vec
def ceil(self):
"""Create a pair of integers of the ceil from each value."""
vx, vy = self.__vec2__
_i = int
return (_i(vx // 1.0) + 1, _i(vy // 1.0) + 1) # NOTE, not a vec
def __complex__(self):
return complex(*self.__vec2__)
def __neg__(self):
vx, vy = self.__vec2__
return Vec2(None, (-vx, -vy))
def __pos__(self):
return self
def __abs__(self):
vx, vy = self.__vec2__
_a = abs
return Vec2(None, (_a(vx + 0.0), _a(vy + 0.0)))
def __invert__(self):
vx, vy = self.__vec2__
return Vec2(None, (vy, -vx))
def __cmp__(self, other):
if isNumberType(other):
ovec = other, other
else:
ovec = getattr(other, "__vec2__", None)
if ovec is None:
ovec = tuple(other)
return cmp(self.__vec2__, ovec)
def __nonzero__(self):
vx, vy = self.__vec2__
return bool(vx or vy)
def __add__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (vx + ox, vy + oy))
__radd__ = __add__
def __sub__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (vx - ox, vy - oy))
def __rsub__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (ox - vx, oy - vy))
def __mul__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (vx * ox, vy * oy))
__rmul__ = __mul__
def __div__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (vx / ox, vy / oy))
def __rdiv__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (ox / vx, oy / vy))
__truediv__ = __div__
__rtruediv__ = __rdiv__
def __floordiv__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (vx // ox, vy // oy))
def __rfloordiv__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (ox // vx, oy // vy))
__xor__ = dot
__rxor__ = dot
__mod__ = cross
def __rmod__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return ox * vy - oy * vx
def __pow__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
return Vec2(None, (vx * other, vy * other))
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (vx ** ox, vy ** oy))
def __rpow__(self, other):
vx, vy = self.__vec2__
if isNumberType(other):
ox = oy = other
else:
ox, oy = getattr(other, "__vec2__", other)
return Vec2(None, (ox ** vx, oy ** vy))
def __getstate__(self):
return self.__vec2__
def __setstate__(self, value):
self.__vec2__ = value