Exact and Efficient Mesh-Kernel Generation

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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
The mesh kernel for a star-shaped mesh is a convex polyhedron given by the intersection of all half-spaces defined by the faces of the input mesh. For all non-star-shaped meshes, the kernel is empty. We present a method to robustly and efficiently compute the kernel of an input triangle mesh by using exact plane-based integer arithmetic to compute the mesh kernel. We make use of several ways to accelerate the computation time. Since many applications just require information if a non-empty mesh kernel exists, we also propose a method to efficiently determine whether a kernel exists by developing an exact plane-based linear program solver. We evaluate our method on a large dataset of triangle meshes and show that in contrast to previous methods, our approach is exact and robust while maintaining a high performance. It is on average two orders of magnitude faster than other exact state-of-the-art methods and often about one order of magnitude faster than non-exact methods.
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@article{
10.1111:cgf.70187
, journal = {Computer Graphics Forum}, title = {{
Exact and Efficient Mesh-Kernel Generation
}}, author = {
Nehring-Wirxel, Julius
and
Kern, Paul
and
Trettner, Philip
and
Kobbelt, Leif
}, year = {
2025
}, publisher = {
The Eurographics Association and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.70187
} }
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