Thought I'd share this library for anyone doing work with convex hulls in 3 dimensions.  

Link to more info:  http://benatwork.cc/newhull-library-v1-0/

Note: this is really just an implementation of the quickhull3d package from John Lloyd, with a few minor tweaks.  Much props to Mr. Lloyd for the heavy lifting.  

A simple example below:

2. /* Simple NewHull Library Example
3.  * by Ben Leduc-Mills
4.  * 2.02.11
5.  */
6. 
   
7. import newhull.*;
8. 
   
9. QuickHull3D hull = new QuickHull3D(); //init quickhull
10. Point3d[] points; //init Point3d array
11. 
    
12. void setup() {
13. 
    
14.   size(200,200,P3D);
15.   background(255); 
16. 
    
17.   //point array
18.   points = new Point3d[] { 
19.     new Point3d (0.0,  0.0,  0.0),
20.     new Point3d (0.0,  0.0,  50.0),
21.     new Point3d (0.0,  50.0,  0.0),
22.     new Point3d (0.0,  50.0,  50.0),
23.     new Point3d (50.0,  0.0,  0.0),
24.     new Point3d (50.0,  0.0,  50.0),
25.     new Point3d (50.0,  50.0,  50.0),
26.     new Point3d (50.0,  50.0,  0.0),
27.   };
28. }  
29. 
    
30. void draw() {
31.   background(255);
32.   smooth(); 
33.   translate(width/2, height/2);
34.   rotateY(frameCount * 0.01); 
35. 
    
36.   int numPoints = points.length; 
37. 
    
38.   //check that our hull is valid
39.   if (hull.myCheck(points, numPoints) == true) {
40. 
    
41.     hull.build(points);  //build hull
42.     hull.triangulate();  //triangulate faces
43.     Point3d[] vertices = hull.getVertices();  //get vertices
44. 
    
45.     beginShape(TRIANGLE_STRIP);
46.     int[][] faceIndices = hull.getFaces();
47.     //run through faces (each point on each face), and draw them
48.     for (int i = 0; i < faceIndices.length; i++) {  
49.       for (int k = 0; k < faceIndices[i].length; k++) {
50. 
    
51.         //get points that correspond to each face
52.         Point3d pnt2 = vertices[faceIndices[i][k]];
53.         float x = (float)pnt2.x;
54.         float y = (float)pnt2.y;
55.         float z = (float)pnt2.z;
56.         vertex(x,y,z);
57.       }
58.     }
59.     endShape(CLOSE);
60.   }
61. }