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About this paper
Leyi Zhu, Michael Tao, Yixin Hu, Daniele Panozzo, Denis Zorin
BijectiveRemesh tracks correspondences through mesh edits so points and embedded curves can retain relationships across remeshing. It maps before- and after-patches into a shared domain and composes maps; for triangle patches, its construction guarantees bijectivity. In isotropic-remeshing tests, 4,998 of 5,139 meshes (97.3%) completed with curve topology verified; 141 timed out, and atlas construction adds about 110× overhead per operation.
Key insights
- Global bijective mappings can be robustly maintained by composing local bijective maps induced by atomic remeshing operations.
- Augmenting local mesh patches with a shared scaffold structure provides a reliable mechanism to enforce bijectivity during 2D parameterization.
- The problem of robustly handling 3D tetrahedral mesh boundary operations can be effectively reduced to constructing convex polyhedra, leveraging graph theory principles for geometric and topological guarantees.
- Preserving the precise topological relationships (e.g., intersection patterns) of complex geometric entities requires careful tracking and, in some cases, the use of exact arithmetic to overcome floating-point inaccuracies.
Summary by alphaXiv.
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