Multiresolution Representations for Surfaces Meshes

We describe a method for constructing multi resolution models (MRM) of complex triangle meshes and show how these representations can be used to create view dependent adaptive approximations of triangle meshes on the y with guaranteed approximation error. We use a modiied one-sided Hausdorr distance as a geometrically meaningful error value between the original and the simpliied mesh. Since this distance is parameterization-independent, its use as error measure is superior to the use of the L 1-Norm between parameterized surfaces. The proposed multi-resolution model supports progressive transmission, smooth geomorphing of diierent levels of detail approximations, mesh compression and selective error tolerance editing. Various examples demonstrate the excellent results that were achieved by this new method with triangle meshes from diierent application areas such as volume rendering, terrain modeling and the approximations of parameterized surfaces.