filename : vis95
title : Fast Multiresolution Surface Meshing
author : M. H. Gross, R. Gatti and O. Staadt
type : inproceedings
organization : Institute for Information Systems, ETH Zürich
month : July
year : 1995
booktitle : Proceedings of the IEEE Visualization '95 (to appear)
keywords : Surface Meshing, Polygonal Approximations,
Level-of-Detail, Quadtrees, Wavelet Transforms,
Wavelet Space Filtering, Biorthogonal Wavelets,
Mean-Square Error, Digital Terrain Modeling
language : English
pages : 8
abstract:
We present a new method for adaptive surface meshing
and triangulation which controls the local level-of-detail
of the surface approximation by local spectral estimates.
These estimates are determined by a wavelet representation of the
surface data. The basic idea is to decompose the initial
data set by means of an orthogonal or semi-orthogonal tensor
product wavelet transform (WT) and to analyze the resulting
coefficients. In surface regions, where the partial
energy of the resulting coefficients is low, the polygonal
approximation of the surface can be performed with larger
triangles without loosing too much fine grain details. However,
since the localization of the WT is bound by the Heisenberg
principle the meshing method has to be controlled by the detail
signals rather than directly by the coefficients. The dyadic
scaling of the WT stimulated us to build an hierarchical meshing
algorithm which transforms the initially regular data grid into a
quadtree representation by rejection of unimportant mesh vertices.
The optimum triangulation of the resulting quadtree cells is carried
out by selection from a look-up table. The tree grows recursively
as controlled by detail signals which are computed from a modified
inverse WT.