Cylindrical and Toroidal Parameterizations Without Vertex Seams

Abstract

A simple rendering method to avoid vertex seams in cylindrical and toroidal UV mappings used for texture mapping is presented. (A vertex seam is a vertex duplication of a polygonal mesh with different texture coordinates assigned to the two geometrically coinciding copies.) As a result, the method leads to simpler, leaner, replication-free data structures. Is also allows for a higher degree of proceduralism in generation of texture coordinates.

The method is general, trivial to implement (exhaustive pseudocode is provided), very low in cost on resources (with a virtually null impact on performance), and it leverages only basic mechanisms widely available in most GPU implementations. An open-source implementation is available at the address provided at the end of this article.

Notes

¹Data structures for meshes can be designed to deal with jumps in texture coordinates in ways other than vertex duplication: texture coordinates can be indexed per face separately from vertex-position data, or, they can be embedded as a per-wedge attribute (thus replicating UV positions). None of these alternatives bypasses the problems discussed here.

²In GLSL, function d is directly available as fwidth.