Re-tiling polygonal surfaces

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Abstract
This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speeding-up the off-line rendering of complex scenes. Unfortunately, generating these levels of detail is a time-consuming task usually left to a human modeler. This paper shows how a new set of vertices can be distributed over the surface of a model and connected to one anolher to create a re-tiling of a surface that is faithful to both the geometry and the topology of the original surface, The main contributions of this paper are: I ) a robust method of connecting together new vertices over a surface, 2) a way of using an estimate of surface curvature to distribute more new vertices at regions of higher curvature and 3) a method of smoothly interpolating between models that represent the same object at different levels of detail. The key notion in the re-tiling procedure is the creation of an intermediate model called the mufual fessellafion of a surface that contains both the vertices from the original model and the new points that are to become vertices in there-tiled surface. The new model is then created by removing each original vertex and locally re-triangulating the surface in a way that matches the local connectedness of the initial surface. This technique for surface retessellation has been successfully applied to iso-surface models derived from volume data, Connolly surface molecular models and a tessellation of a minimal surface of interest to mathematicians. CR Categories and Subject Descriptors: 1.3.3 [Computer Graphics]: Picture/Image Generation – Display algorithms; 1.3.5 [Computer Graphics]: Computational Geometry and Object Modelling – Curve, surface, solid, and object representations.

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