Generation of Solid Multiresolution Models

Abstract

We present an automatic simplification algorithm that produces multiresolution models with piecewise algebraic implicit surfaces. The method is based on a spatial decomposition —initial voxelization of the model— and wavelet simplification. Like other spatial decomposition simplification schemes (MDCO, BSpline filtering) it simplifies geometry and topology It can be used for navigation with LOD models in virtual environments or for approximate collision detection. The implicit simplified surface is defined as the zero-valued algebraic isosurface of a 4D functional tensor-product unform cubic BSpline. A wavelet multiresolution scheme that deals with uniform cubic BSplines on bounded domains has been constructed. One dimensional wavelet analysis and synthesis are defined on intervals with an even number (2n) of coefficient data, instead of 2ⁿ. Storage requirements for coefficients are of the order of number of initial voxels (surface area of the object). A suitable data structure and a way to estimate / reject data coefficients at each multiresolution step is also proposed.