## Sunday, 19 February 2012

### 3D Convex hull in Python

In this article I present a present a reimplementation in pure Python of Joseph O'Rourke's incremental 3D convex hull algorithm from his book Computational Geometry in C.

## A convex hull in pure Python

This is the second, rather off topic, article on computational geometry in this blog. The previous article presented an implementation of the marching tetrahedrons algorithm.
The goal of this article is to provide object oriented, pythonic code to compute the convex hull of a collection of 3D points. The code is contained in a single Python module that may be downloaded from GitHub.
A sample of how to use this module is shown below, where we create a a roughly spherical cloud of points, calculate its convex hull and print this hull in STL format to stdout. The resulting object is shown in the image (as seen in Blender).
```from random import random
from chull import Vector,Hull

sphere=[]
for i in range(2000):
x,y,z = 2*random()-1,2*random()-1,2*random()-1
if x*x+y*y+z*z < 1.0:
sphere.append(Vector(x,y,z))
h=Hull(sphere)
h.Print()
```

## Difference from the original implementation

The original code restricted the coordinates of points to integers, here there is no such restriction. This might result in errors if the coordinates are large.

1. When I try to open ti with the GNU Meshlab I get an error saying "Premature end of file". What is that supposed to mean?

2. Hi,
thank you very much for this piece of code! I am using it succesfully.
There is only one strange behaviour I couldnt yet figure out why it happens: Sometimes the code doesnt finish saying

338 # e interior: mark for deletion
339 e.delete = REMOVED;
341 # e border: make a new face
342 e.newface = self.MakeConeFace( e, p )

AttributeError: 'NoneType' object has no attribute 'visible'

in the constructor when calling (Hull(myvectors)).

Do you have an idea about how I could avoid this? For a some selection of my data points the code works, for some this error occurs and I cant figure out what the pattern is.

Thanks again!

3. Thank you for sharing your code!
it would be great if there was an easy build-in method available, which can calculate the surface area of the resulting convex polyhedron.

4. Great code! I've used it to create an STL file for a 3D shape that contains concavities and convexity. Unfortunately, the code seems to fill in those concavities to create a convex shape. I'm not a Python expert - is there a (simple?) way to modify this code to not get rid of the concavities?

5. Thank you very much, this code was very useful for me to represent some data :)

I added a little function:

def PrintFile(self, filename='tmpshape.stl'):
f1 = open(filename, 'w+')
f1.write("solid points\n")
for f in self.faces:
f1.write(str(f) + '\n')
f1.write("endsolid points\n")
f1.close()

to print directly to a stl file which was handy for me.