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""" | ||
2D Convex Hull Code from Wikibooks | ||
https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain | ||
""" | ||
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class hull2D: | ||
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def convex_hull(self,points): | ||
"""Computes the convex hull of a set of 2D points. | ||
Input: an iterable sequence of (x, y) pairs representing the points. | ||
Output: a list of vertices of the convex hull in counter-clockwise order, | ||
starting from the vertex with the lexicographically smallest coordinates. | ||
Implements Andrew's monotone chain algorithm. O(n log n) complexity. | ||
""" | ||
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# Sort the points lexicographically (tuples are compared lexicographically). | ||
# Remove duplicates to detect the case we have just one unique point. | ||
points = sorted(set(points)) | ||
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# Boring case: no points or a single point, possibly repeated multiple times. | ||
if len(points) <= 1: | ||
return points | ||
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# 2D cross product of OA and OB vectors, i.e. z-component of their 3D cross product. | ||
# Returns a positive value, if OAB makes a counter-clockwise turn, | ||
# negative for clockwise turn, and zero if the points are collinear. | ||
def cross(o, a, b): | ||
return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0]) | ||
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# Build lower hull | ||
lower = [] | ||
for p in points: | ||
while len(lower) >= 2 and cross(lower[-2], lower[-1], p) <= 0: | ||
lower.pop() | ||
lower.append(p) | ||
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# Build upper hull | ||
upper = [] | ||
for p in reversed(points): | ||
while len(upper) >= 2 and cross(upper[-2], upper[-1], p) <= 0: | ||
upper.pop() | ||
upper.append(p) | ||
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# Concatenation of the lower and upper hulls gives the convex hull. | ||
# Last point of each list is omitted because it is repeated at the beginning of the other list. | ||
return lower[:-1] + upper[:-1] | ||
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def convexHullecoords(self,ecoords): | ||
p=[] | ||
for line in ecoords: | ||
p.append((line[0],line[1])) | ||
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hull_data = self.convex_hull(p) | ||
ecoords=[] | ||
for i in range(0,len(hull_data)): | ||
ecoords.append([hull_data[i][0],hull_data[i][1],1]) | ||
ecoords.append(ecoords[0]) | ||
return ecoords | ||
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###################################################################### | ||
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if __name__ == '__main__': | ||
my_hull=hull2D() | ||
p = [(1,1),(0,3),(0,0),(4,5),(10,10)] | ||
c = my_hull.convex_hull(p) | ||
print(p) | ||
print(c) |
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