Hull 3D via gift wrapping

Implement the gift wrapping algorithm for finding the convex hull of a set of points in 3D.

The skeleton

To start, sketch high-level pseudocode for gift wrapping and express it terms of generic functions, such as:

a queue/stack that stores all the edges that are on the frontier of the search (in other words: all edges that have found only one adjacent face so far);
a generic function that takes an edge as an argument and returns TRUE if the edge is on the frontier: edgeOnFrontier(edge e): return TRUE if precisely one face adjacent to edge e has been discovered so far.

Representing the hull

For this assignment you do need to store the topology of the hull. You’ll want to keep track of the vertices, edges and faces that are on the convex hull, and their adjacencies. Basically a 3d hull consists of:

An array/vector/list of the vertices on the hull (ideally pointers to points in P so that coordinates are not duplicated)
[ An array/vector/list of edges on the hull (edges may be inferred from the faces so perhaps they dont need to be stored explicitly) ]

An array/vector/list of faces on the hull, where each face stores pointers to its vertices and its neighbor faces.

    struct _face3 {
         point3 *p1, *p2, *p3;  //the vertices on this face (in ccw as looking from outside)
         face3d *f12; //face to the left of p1p2
         face3d *f23; //face to the left of p2p3
         face3d *f31; //face to the left of p3p1
    } face3;

Dealing with degeneracies

If there exist sets of 4 or more points that are co-planar, it is possible that faces in the hull are not triangular. It would be nice to triangulate the faces that are not triangular, so that the hull is a list of triangles.

Extra features

Some ideas:

Draw the hull transparent
Use a timerfunc() to make an animation

Submitting your work

Make a folder called giftwrapping3d in your svn folder on microwave. I will have access to this svn, so no need to submit anything --- just make sure everything is checked in.

Enjoy!