convex_hull.py

import numpy as n, pylab as p, time

def _angle_to_point(point, centre):
    '''calculate angle in 2-D between points and x axis'''
    delta = point - centre
    res = n.arctan(delta[1] / delta[0])
    if delta[0] < 0:
        res += n.pi
    return res


def _draw_triangle(p1, p2, p3, **kwargs):
    tmp = n.vstack((p1,p2,p3))
    x,y = [x[0] for x in zip(tmp.transpose())]
    p.fill(x,y, **kwargs)
    #time.sleep(0.2)


def area_of_triangle(p1, p2, p3):
    '''calculate area of any triangle given co-ordinates of the corners'''
    return n.linalg.norm(n.cross((p2 - p1), (p3 - p1)))/2.


def convex_hull(points, graphic=True, smidgen=0.0075):
    '''Calculate subset of points that make a convex hull around points

    Recursively eliminates points that lie inside two neighbouring points until only convex hull is remaining.

    :Parameters:
        points : ndarray (2 x m)
            array of points for which to find hull
        graphic : bool
            use pylab to show progress?
        smidgen : float
            offset for graphic number labels - useful values depend on your data range

    :Returns:
        hull_points : ndarray (2 x n)
            convex hull surrounding points
    '''
    if graphic:
        p.clf()
        p.plot(points[0], points[1], 'ro')
    n_pts = points.shape[1]
    assert(n_pts > 5)
    centre = points.mean(1)
    if graphic: p.plot((centre[0],),(centre[1],),'bo')
    angles = n.apply_along_axis(_angle_to_point, 0, points, centre)
    pts_ord = points[:,angles.argsort()]
    if graphic:
        for i in xrange(n_pts):
            p.text(pts_ord[0,i] + smidgen, pts_ord[1,i] + smidgen, \
                   '%d' % i)
    pts = [x[0] for x in zip(pts_ord.transpose())]
    prev_pts = len(pts) + 1
    k = 0
    while prev_pts > n_pts:
        prev_pts = n_pts
        n_pts = len(pts)
        if graphic: p.gca().patches = []
        i = -2
        while i < (n_pts - 2):
            Aij = area_of_triangle(centre, pts[i],     pts[(i + 1) % n_pts])
            Ajk = area_of_triangle(centre, pts[(i + 1) % n_pts], \
                                   pts[(i + 2) % n_pts])
            Aik = area_of_triangle(centre, pts[i],     pts[(i + 2) % n_pts])
            if graphic:
                _draw_triangle(centre, pts[i], pts[(i + 1) % n_pts], \
                               facecolor='blue', alpha = 0.2)
                _draw_triangle(centre, pts[(i + 1) % n_pts], \
                               pts[(i + 2) % n_pts], \
                               facecolor='green', alpha = 0.2)
                _draw_triangle(centre, pts[i], pts[(i + 2) % n_pts], \
                               facecolor='red', alpha = 0.2)
            if Aij + Ajk < Aik:
                if graphic: p.plot((pts[i + 1][0],),(pts[i + 1][1],),'go')
                del pts[i+1]
            i += 1
            n_pts = len(pts)
        k += 1
    if graphic: p.show()
    return n.asarray(pts)

if __name__ == "__main__":
    points = n.random.random_sample((2,40))
    hull_pts = convex_hull(points)