Weil's Division Algorithm

[Jerry Weil, AT&T Bell Labs]

The crux of this algorithm is to split the cloth in two "catenary" triangles (in stage #0). Afterwards, inside each triangle we consider the "median" catenaries and pick the highest one (yielding two more triangles from the original one). The algorithm continues recursively from here.

The algorithm is quite difficult in that in order to correctly find the length of the median threads inside each triangle, a two step line integral followed by interpolation is necessary. At each stage, we represented the catenaries and then chose a certain step at which we evaluate them and produce a point. The points are then fed to the projective renderer who know how to display them.

Here are images of the cloth in various stages :

Subdivision stage #0
Subdivision stage #1
Subdivision stage #2
Subdivision stage #5

The last subdivision stage above consists of 40,000 catenary points and took in excess of .5 hr to render on a Pentium 75 (running Linux). The renderer script file was 500k.

Last modified: February 4, 2003
Copyright 2003 Razvan Surdulescu
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