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#!/usr/bin/python 

 

# Compute the convex hull of a set of 2D points 

# A Python implementation of the qhull algorithm 

#  

# Tested with Python 2.6.5 on Ubuntu 10.04.4 

 

# Copyright (c) 2008 Dave (www.literateprograms.org) 

# 

# Permission is hereby granted, free of charge, to any person obtaining a copy  

# of this software and associated documentation files (the "Software"), to deal  

# in the Software without restriction, including without limitation the rights  

# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell  

# copies of the Software, and to permit persons to whom the Software is  

# furnished to do so, subject to the following conditions: 

# 

# The above copyright notice and this permission notice shall be included in  

# all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR  

# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,  

# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE  

# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER  

# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING  

# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS  

# IN THE SOFTWARE. 

 

from __future__ import division 

from numpy import * 

 

link = lambda a,b: concatenate((a,b[1:])) 

edge = lambda a,b: concatenate(([a],[b])) 

 

def qhull2D(sample): 

    def dome(sample,base): 

        h, t = base 

        dists = dot(sample-h, dot(((0,-1),(1,0)),(t-h))) 

        outer = repeat(sample, dists>0, 0) 

        if len(outer): 

            pivot = sample[argmax(dists)] 

            return link(dome(outer, edge(h, pivot)), 

                    dome(outer, edge(pivot, t))) 

        else: 

            return base 

    if len(sample) > 2: 

        axis = sample[:,0] 

        base = take(sample, [argmin(axis), argmax(axis)], 0) 

        return link(dome(sample, base), dome(sample, base[::-1])) 

    else: 

        return sample