# Our Division Algorithm

The problem with Weil's algorithm is that once the cloth is approximated using catenary points, the triangles that result are very "coherent" and are extremely difficult to cover with polygons. Weil himself mentions this in his paper and proposes a few methods for solving it (all of which are quite difficult).

We decided to attempt to cover the cloth by means of stopping at the Weil stage #0, and then throw catenaries in between the main triangle catenary threads. As you notice in the image below, the lattice thus produced is much more coherent and can be (relatively) easily covered with triangles in a hash pattern.

 Catenary interpolation with 8 point skip. The 8 point skip refers to the amount of data points we skipped when crossing the edge catenaries. The "inbetween" catenaries have much less skip (since we want better resolution on them). Plain old wireframe of the cloth. The natural crease formed in the cloth. We were quite excited when this actually came up : our representation follows Weil's algorithm in that the catenary representation is actually accurate physically ! The crease formed in the cloth witnesses that. The cloth approximated with faceted polygons (10,000 of them). Phong polygons (a bit too shiny -- we didn't set the parameters carefully enough for the Phong shader).

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