Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!asuvax!enuxha!nwatson
From: nwatson@enuxha.eas.asu.edu (Nathan F. Watson)
Newsgroups: comp.graphics
Subject: Re: triangulation and contouring
Message-ID: <1317@enuxha.eas.asu.edu>
Date: 15 Aug 90 22:46:27 GMT
References: <1990Aug15.003127.22609@NCoast.ORG>
Organization: Arizona State Univ, Tempe
Lines: 34

In article <1990Aug15.003127.22609@NCoast.ORG>, atul@NCoast.ORG (Atul Parulekar) writes:
> I think there was a discussion some time back about delaunay triangulation of
> random points.  I wrote a program to do this based on a paper by Cavendish JC,

> ...

> Finally, any suggestions on how this triangle network can be used for 
> contouring directly (i.e., without first generating a grid of regularly
> spaced points)?

A student here at Arizona State University recently completed his master's
thesis:  "Contouring Trivariate Surfaces", Brett Keith Bloomquist.  The
thesis describes methods for contouring bivariate and trivariate surfaces
(f(x,y) and f(x,y,z)).  I believe a paper will eventually be published.

For the bivariate case, the scheme boils down to:

   (a) Triangulate the data points, and estimate the gradients of the
       function at each data point.
   (b) Use the stuff obtained in (a) to obtain a Clough-Tocher interpolant
       over each triangle, resulting in a number of triangular Bezier
       patches of degree 3, which you will want to contour.
   (c) Approximate each degree 3 patch with one or more degree 2 patches
       (according to some user-defined tolerance).  The degree 2 patches
       describe quadratic functions, which may be contoured using at most
       six rational quadric bezier curves per patch.

The scheme is too detailed to explain fully here.  I will attempt to
let those interested know when the article appears.


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Nathan F. Watson                             Arizona State University
nwatson@enuxha.eas.asu.edu                Computer Science Department