96 lines
3 KiB
Python
96 lines
3 KiB
Python
# Example from http://wiki.scipy.org/Cookbook/Finding_Convex_Hull
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import numpy as n
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import pylab as p
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import time
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def _angle_to_point(point, centre):
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'''calculate angle in 2-D between points and x axis'''
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delta = point - centre
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res = n.arctan(delta[1] / delta[0])
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if delta[0] < 0:
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res += n.pi
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return res
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def _draw_triangle(p1, p2, p3, **kwargs):
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tmp = n.vstack((p1, p2, p3))
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x, y = [x[0] for x in zip(tmp.transpose())]
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p.fill(x, y, **kwargs)
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# XXX time.sleep(0.2)
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def area_of_triangle(p1, p2, p3):
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'''calculate area of any triangle given co-ordinates of the corners'''
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return n.linalg.norm(n.cross((p2 - p1), (p3 - p1)))/2.
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def convex_hull(points, graphic=True, smidgen=0.0075):
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'''Calculate subset of points that make a convex hull around points
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Recursively eliminates points that lie inside two neighbouring points until
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only convex hull is remaining.
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:Parameters:
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points : ndarray (2 x m)
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array of points for which to find hull
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graphic : bool
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use pylab to show progress?
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smidgen : float
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offset for graphic number labels - useful values depend on your data
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range
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:Returns:
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hull_points : ndarray (2 x n)
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convex hull surrounding points
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'''
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if graphic:
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p.clf()
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p.plot(points[0], points[1], 'ro')
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n_pts = points.shape[1]
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assert(n_pts > 5)
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centre = points.mean(1)
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if graphic:
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p.plot((centre[0], ), (centre[1], ), 'bo')
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angles = n.apply_along_axis(_angle_to_point, 0, points, centre)
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pts_ord = points[:, angles.argsort()]
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if graphic:
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for i in xrange(n_pts):
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p.text(pts_ord[0, i] + smidgen, pts_ord[1, i] + smidgen,
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'%d' % i)
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pts = [x[0] for x in zip(pts_ord.transpose())]
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prev_pts = len(pts) + 1
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k = 0
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while prev_pts > n_pts:
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prev_pts = n_pts
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n_pts = len(pts)
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if graphic:
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p.gca().patches = []
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i = -2
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while i < (n_pts - 2):
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Aij = area_of_triangle(centre, pts[i], pts[(i + 1) % n_pts])
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Ajk = area_of_triangle(centre, pts[(i + 1) % n_pts],
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pts[(i + 2) % n_pts])
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Aik = area_of_triangle(centre, pts[i], pts[(i + 2) % n_pts])
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if graphic:
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_draw_triangle(centre, pts[i], pts[(i + 1) % n_pts],
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facecolor='blue', alpha=0.2)
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_draw_triangle(centre, pts[(i + 1) % n_pts],
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pts[(i + 2) % n_pts],
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facecolor='green', alpha=0.2)
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_draw_triangle(centre, pts[i], pts[(i + 2) % n_pts],
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facecolor='red', alpha=0.2)
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if Aij + Ajk < Aik:
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if graphic:
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p.plot((pts[i + 1][0], ), (pts[i + 1][1], ), 'go')
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del pts[i+1]
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i += 1
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n_pts = len(pts)
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k += 1
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return n.asarray(pts)
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if __name__ == "__main__":
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points = n.random.random_sample((2, 40))
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hull_pts = convex_hull(points)
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p.show()
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