interpolate a terrain surface from scattered data using heat equation

Question

Hi This is my first question in this forum, so please bear with me and I hope I'm not violating any rules. I am looking at different ways to model scattered 3d data as a gridded function (over xy support, z=z(x,y)).

Answering another question, coryan was so nice as to mention the method using heat equation to interpolate (approximate) a terrain surface which I've heard about and been eager to learn, or even find a parallel implementation? Could please coryan or anybody else point me to such an implementation, if it's in public domain, or at least to explain a bit further how it is done.

Answer 1

Not sure about heat eqautions, but the way that I solve this problem is via TIN modelling. Check out Herbert Edelsbrunners book on the topic, Geometry and Topology for Mesh Generation. I would have it down as a must read. Also well worthwhile is Joeseph O'Rourkes Computational Geometry in C which while more general does include worked examples and makes a useful cookbook.

In terms of open source, check the following Code Guru link and have a look at Paul Bourkes work.