105 lines
2.8 KiB
Python
105 lines
2.8 KiB
Python
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from math import *
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def inner_product(a, b):
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return a.x * b.x + a.y * b.y
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class Coordinate(object):
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"""
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Basic (x, y) coordinate class (or should it be called vector?) which allows some simple operations.
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"""
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def __init__(self, x, y):
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self.x = float(x)
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self.y = float(y)
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#polar coordinates
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@property
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def t(self):
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angle = atan2(self.y, self.x)
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if angle < 0:
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angle += pi * 2
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return angle
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@t.setter
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def t(self, value):
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length = self.r
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self.x = cos(value) * length
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self.y = sin(value) * length
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@property
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def r(self):
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return hypot(self.x, self.y)
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@r.setter
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def r(self, value):
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angle = self.t
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self.x = cos(angle) * value
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self.y = sin(angle) * value
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def __repr__(self):
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return self.__str__()
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def __str__(self):
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return "(%f, %f)" % (self.x, self.y)
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def __eq__(self, other):
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return self.x == other.x and self.y == other.y
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def __add__(self, other):
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return Coordinate(self.x + other.x, self.y + other.y)
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def __sub__(self, other):
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return Coordinate(self.x - other.x, self.y - other.y)
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def __mul__(self, factor):
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return Coordinate(self.x * factor, self.y * factor)
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def __neg__(self):
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return Coordinate(-self.x, -self.y)
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def __rmul__(self, other):
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return self * other
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def __div__(self, quotient):
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return Coordinate(self.x / quotient, self.y / quotient)
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def __truediv__(self, quotient):
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return self.__div__(quotient)
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def dot(self, other):
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"""dot product"""
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return self.x * other.x + self.y * other.y
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def cross_norm(self, other):
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""""the norm of the cross product"""
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self.x * other.y - self.y * other.x
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def close_enough_to(self, other, limit=1E-9):
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return (self - other).r < limit
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class IntersectionError(ValueError):
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"""Raised when two lines do not intersect."""
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def on_segment(pt, start, end):
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"""Check if pt is between start and end. The three points are presumed to be collinear."""
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pt -= start
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end -= start
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ex, ey = end.x, end.y
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px, py = pt.x, pt.y
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px *= cmp(ex, 0)
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py *= cmp(ey, 0)
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return px >= 0 and px <= abs(ex) and py >= 0 and py <= abs(ey)
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def intersection (s1, e1, s2, e2, on_segments = True):
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D = (s1.x - e1.x) * (s2.y - e2.y) - (s1.y - e1.y) * (s2.x - e2.x)
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if D == 0:
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raise IntersectionError("Lines from {s1} to {e1} and {s2} to {e2} are parallel")
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N1 = s1.x * e1.y - s1.y * e1.x
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N2 = s2.x * e2.y - s2.y * e2.x
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I = ((s2 - e2) * N1 - (s1 - e1) * N2) / D
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if on_segments and not (on_segment(I, s1, e1) and on_segment(I, s2, e2)):
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raise IntersectionError("Intersection {0} is not on line segments [{1} -> {2}] [{3} -> {4}]".format(I, s1, e1, s2, e2))
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return I
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