Python implementation: Convex hull + Minimal bounding rectangle

README.md

What is this?

Python proof-of-concept implementation of two geomapping algorithms

Requirements

This code use the following packages:

• numpy
• matplotlib (optional, only for creating graphs)

How to use

$ python ./test.py

min_bounding_rect.py

#!/usr/bin/python

# Find the minimum-area bounding box of a set of 2D points
#
# The input is a 2D convex hull, in an Nx2 numpy array of x-y co-ordinates. 
# The first and last points points must be the same, making a closed polygon.
# This program finds the rotation angles of each edge of the convex polygon,
# then tests the area of a bounding box aligned with the unique angles in
# 90 degrees of the 1st Quadrant.
# Returns the 
#
# Tested with Python 2.6.5 on Ubuntu 10.04.4
# Results verified using Matlab

# Copyright (c) 2013, David Butterworth, University of Queensland
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
#     * Redistributions of source code must retain the above copyright
#       notice, this list of conditions and the following disclaimer.
#     * Redistributions in binary form must reproduce the above copyright
#       notice, this list of conditions and the following disclaimer in the
#       documentation and/or other materials provided with the distribution.
#     * Neither the name of the Willow Garage, Inc. nor the names of its
#       contributors may be used to endorse or promote products derived from
#       this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.

from numpy import *
import sys  # maxint

def minBoundingRect(hull_points_2d):
    #print "Input convex hull points: "
    #print hull_points_2d

    # Compute edges (x2-x1,y2-y1)
    edges = zeros( (len(hull_points_2d)-1,2) ) # empty 2 column array
    for i in range( len(edges) ):
        edge_x = hull_points_2d[i+1,0] - hull_points_2d[i,0]
        edge_y = hull_points_2d[i+1,1] - hull_points_2d[i,1]
        edges[i] = [edge_x,edge_y]
    #print "Edges: \n", edges

    # Calculate edge angles   atan2(y/x)
    edge_angles = zeros( (len(edges)) ) # empty 1 column array
    for i in range( len(edge_angles) ):
        edge_angles[i] = math.atan2( edges[i,1], edges[i,0] )
    #print "Edge angles: \n", edge_angles

    # Check for angles in 1st quadrant
    for i in range( len(edge_angles) ):
        edge_angles[i] = abs( edge_angles[i] % (math.pi/2) ) # want strictly positive answers
    #print "Edge angles in 1st Quadrant: \n", edge_angles

    # Remove duplicate angles
    edge_angles = unique(edge_angles)
    #print "Unique edge angles: \n", edge_angles

    # Test each angle to find bounding box with smallest area
    min_bbox = (0, sys.maxint, 0, 0, 0, 0, 0, 0) # rot_angle, area, width, height, min_x, max_x, min_y, max_y
    print "Testing", len(edge_angles), "possible rotations for bounding box... \n"
    for i in range( len(edge_angles) ):

        # Create rotation matrix to shift points to baseline
        # R = [ cos(theta)      , cos(theta-PI/2)
        #       cos(theta+PI/2) , cos(theta)     ]
        R = array([ [ math.cos(edge_angles[i]), math.cos(edge_angles[i]-(math.pi/2)) ], [ math.cos(edge_angles[i]+(math.pi/2)), math.cos(edge_angles[i]) ] ])
        #print "Rotation matrix for ", edge_angles[i], " is \n", R

        # Apply this rotation to convex hull points
        rot_points = dot(R, transpose(hull_points_2d) ) # 2x2 * 2xn
        #print "Rotated hull points are \n", rot_points

        # Find min/max x,y points
        min_x = nanmin(rot_points[0], axis=0)
        max_x = nanmax(rot_points[0], axis=0)
        min_y = nanmin(rot_points[1], axis=0)
        max_y = nanmax(rot_points[1], axis=0)
        #print "Min x:", min_x, " Max x: ", max_x, "   Min y:", min_y, " Max y: ", max_y

        # Calculate height/width/area of this bounding rectangle
        width = max_x - min_x
        height = max_y - min_y
        area = width*height
        #print "Potential bounding box ", i, ":  width: ", width, " height: ", height, "  area: ", area 

        # Store the smallest rect found first (a simple convex hull might have 2 answers with same area)
        if (area < min_bbox[1]):
            min_bbox = ( edge_angles[i], area, width, height, min_x, max_x, min_y, max_y )
        # Bypass, return the last found rect
        #min_bbox = ( edge_angles[i], area, width, height, min_x, max_x, min_y, max_y )

    # Re-create rotation matrix for smallest rect
    angle = min_bbox[0]   
    R = array([ [ math.cos(angle), math.cos(angle-(math.pi/2)) ], [ math.cos(angle+(math.pi/2)), math.cos(angle) ] ])
    #print "Projection matrix: \n", R

    # Project convex hull points onto rotated frame
    proj_points = dot(R, transpose(hull_points_2d) ) # 2x2 * 2xn
    #print "Project hull points are \n", proj_points

    # min/max x,y points are against baseline
    min_x = min_bbox[4]
    max_x = min_bbox[5]
    min_y = min_bbox[6]
    max_y = min_bbox[7]
    #print "Min x:", min_x, " Max x: ", max_x, "   Min y:", min_y, " Max y: ", max_y

    # Calculate center point and project onto rotated frame
    center_x = (min_x + max_x)/2
    center_y = (min_y + max_y)/2
    center_point = dot( [ center_x, center_y ], R )
    #print "Bounding box center point: \n", center_point

    # Calculate corner points and project onto rotated frame
    corner_points = zeros( (4,2) ) # empty 2 column array
    corner_points[0] = dot( [ max_x, min_y ], R )
    corner_points[1] = dot( [ min_x, min_y ], R )
    corner_points[2] = dot( [ min_x, max_y ], R )
    corner_points[3] = dot( [ max_x, max_y ], R )
    #print "Bounding box corner points: \n", corner_points

    #print "Angle of rotation: ", angle, "rad  ", angle * (180/math.pi), "deg"

    return (angle, min_bbox[1], min_bbox[2], min_bbox[3], center_point, corner_points) # rot_angle, area, width, height, center_point, corner_points

polyplot.py

import math

import numpy as np

import matplotlib.pyplot as plt
from matplotlib.collections import PolyCollection
import matplotlib as mpl

def poly_plot(verts):

    # Generate data. In this case, we'll make a bunch of center-points and generate
    # verticies by subtracting random offsets from those center-points
    numpoly, numverts = 100, 4
    centers = 100 * (np.random.random((numpoly,2)) - 0.5)
    offsets = 10 * (np.random.random((numverts,numpoly,2)) - 0.5)

    #verts = centers + offsets
    #verts = np.swapaxes(verts, 0, 1)

    # In your case, "verts" might be something like:
    # verts = zip(zip(lon1, lat1), zip(lon2, lat2), ...)
    # If "data" in your case is a numpy array, there are cleaner ways to reorder
    # things to suit.

    # Color scalar...
    # If you have rgb values in your "colorval" array, you could just pass them
    # in as "facecolors=colorval" when you create the PolyCollection
    z = np.random.random(numpoly) * 500

    fig, ax = plt.subplots()

    # Make the collection and add it to the plot.
    coll = PolyCollection(verts, array=z, cmap=mpl.cm.jet, edgecolors='none')
    ax.add_collection(coll)
    ax.autoscale_view()

    # Add a colorbar for the PolyCollection
    fig.colorbar(coll, ax=ax)
    plt.show()

qhull_2d.py

#!/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

test.py

import math
import sys

#from barisal_coords import coords
from borgona_coords import coords
#from bhola_coords import coords
#from bangalore_coords import coords

from numpy import *

from qhull_2d import *
from min_bounding_rect import *

from polyplot import poly_plot

grid = []

for lon, lat in coords:

    grid.append([lon, lat])

xy_points = array(grid)

# Find convex hull
hull_points = qhull2D(xy_points)

print len(hull_points)

# Reverse order of points, to match output from other qhull implementations
hull_points = hull_points[::-1]

print 'Convex hull points: \n', hull_points, "\n"

# Find minimum area bounding rectangle
(rot_angle, area, width, height, center_point, corner_points) = minBoundingRect(hull_points)

# Verbose output of return data
print "Minimum area bounding box:"
print "Rotation angle:", rot_angle, "rad  (", rot_angle*(180/math.pi), "deg )"
print "Width:", width, " Height:", height, "  Area:", area
print "Center point: \n", center_point # numpy array
print "Corner points: \n", corner_points, "\n"  # numpy array

# Draw a nice graph with the new shape
poly_plot(array([corner_points]))