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# Copyright 2008 by Peter Moxhay and Wade Brainerd.
# This file is part of Math.
#
# Math is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Math is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Math. If not, see <http://www.gnu.org/licenses/>.
import math
class Vector:
def __init__(self, x=0, y=0):
self.x = x
self.y = y
# Binary operators.
def __add__(self, v):
return Vector(self.x + v.x, self.y + v.y)
def __sub__(self, v):
return Vector(self.x - v.x, self.y - v.y)
def __mul__(self, n):
return Vector(self.x * n, self.y * n)
def __div__(self, n):
return Vector(self.x / n, self.y / n)
# In-place operators.
def __iadd__(self, v):
self.x += v.x
self.y += v.y
return self
def __isub__(self, v):
self.x -= v.x
self.y -= v.y
return self
def __imul__(self, n):
self.x *= n
self.y *= n
return self
def __idiv__(self, n):
self.x /= n
self.y /= n
return self
# Unary operators
def __neg__(self):
return Vector(-self.x, -self.y)
def __abs__(self):
return Vector(abs(self.x), abs(self.y))
def __repr__(self):
return "x=%f y=%f" % (self.x, self.y)
# Methods
def dot(self, v):
"""Returns the dot product with v as a scalar."""
return self.x*v.x + self.y*v.y
def length(self):
"""Returns the vector length."""
return math.sqrt(self.x*self.x + self.y*self.y)
def scaled(self, factor):
"""Returns the vector scaled by a given factor."""
return Vector(self.x * factor, self.y * factor)
def theta(self):
"""Returns the vector's angle with respect to the x-axis."""
return math.atan2(self.y, self.x)
def normalize(self):
"""Returns the vector normalized, or else a zero vector if the vector has zero length."""
l = self.length()
if l > 0:
return self / l
else:
return Vector(0, 0)
def max(self, v):
"""Returns the componentwise maximum of the vector with v."""
return Vector(max(self.x, v.x), max(self.y, v.y))
def min(self, v):
"""Returns the componentwise minimum of the vector with v."""
return Vector(min(self.x, v.x), min(self.y, v.y))
def clamp(self, mn, mx):
"""Returns the vector clamped componentwise between mn and mx."""
return self.max(mx).min(mn)
def rotate(self, a):
"""Returns the vector rotated about the origin by a radians."""
sa, ca, = math.sin(a), math.cos(a)
return Vector(self.x*ca - self.y*sa, self.x*sa + self.y*ca)
def approx_equal(self, a, tolerance=5):
"""Returns True if the vector is within tolerance of equaling a."""
return (self - a).length() < tolerance
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