# Intersection Free Simplification

## Abstract

Triangle mesh decimation and multi-resolution techniques are widely used in visualization applications for huge scenes. A large collection of different simplification algorithms exists in order to build a multi-resolution model from a given triangle mesh. All of the existing approaches focus on the creation of a geometrically close approximation of the original model. In order to produce a simplified version of a model with close layers - such as dressed humans - self-intersections result in intolerable results. Even methods that allow the sewing of close surface parts lead to unpleasant self-intersections. Only the simplification envelops allow to completely prevent them.

In this work we focus on the prevention and avoidance of self-intersection during simplication with vertex pair contractions. We examine the geomorph9 of the parametrized vertex pair contraction and detect collisions of the affected simplices. If no collision arises the operation cannot cause any new self-intersection. Otherwise we can simply discard the operation to prevent self-intersections as is done in the approach of simplification envelops. Our approach goes even further and tries to avoid the self-intersection by testing different target locations. This leads to better approximations as exhibited by a lower RMS and Hausdorff-distance. Furthermore our approach allows for arbitrary changes in the topology and garantees that geomorphs during progressive reception cannot cause self-intersections.

Stichwörter: collision detection, intersection-free simplification, pair contraction

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## Bibtex

@ARTICLE{gumhold-2003-intersection-2, author = {Gumhold, S. and Borodin, Pavel and Klein, Reinhard}, pages = {155--176}, title = {Intersection Free Simplification}, journal = {International Journal of Shape Modeling (IJSM)}, volume = {9}, number = {2}, year = {2003}, month = dec, keywords = {collision detection, intersection-free simplification, pair contraction}, abstract = {Triangle mesh decimation and multi-resolution techniques are widely used in visualization applications for huge scenes. A large collection of different simplification algorithms exists in order to build a multi-resolution model from a given triangle mesh. All of the existing approaches focus on the creation of a geometrically close approximation of the original model. In order to produce a simplified version of a model with close layers - such as dressed humans - self-intersections result in intolerable results. Even methods that allow the sewing of close surface parts lead to unpleasant self-intersections. Only the simplification envelops allow to completely prevent them. In this work we focus on the prevention and avoidance of self-intersection during simplication with vertex pair contractions. We examine the geomorph9 of the parametrized vertex pair contraction and detect collisions of the affected simplices. If no collision arises the operation cannot cause any new self-intersection. Otherwise we can simply discard the operation to prevent self-intersections as is done in the approach of simplification envelops. Our approach goes even further and tries to avoid the self-intersection by testing different target locations. This leads to better approximations as exhibited by a lower RMS and Hausdorff-distance. Furthermore our approach allows for arbitrary changes in the topology and garantees that geomorphs during progressive reception cannot cause self-intersections.}, issn = {0218-6543} }