Re-tiling polygonal surfaces

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.