2026-07-22T10:53:05Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:19977 2024-06-06T06:21:14Z ddc:004 open_access

SCARST: Schnyder Compact and Regularity Sensitive Triangulation Data Structure Castelli Aleardi, Luca Devillers, Olivier Meshes compression triangulations compact representations We consider the design of fast and compact representations of the connectivity information of triangle meshes. Although traditional data structures (Half-Edge, Corner Table) are fast and user-friendly, they tend to be memory-expensive. On the other hand, compression schemes, while meeting information-theoretic lower bounds, do not support navigation within the mesh structure. Compact representations provide an advantageous balance for representing large meshes, enabling a judicious compromise between memory consumption and fast implementation of navigational operations. We propose new representations that are sensitive to the regularity of the graph while still having worst case guarantees. For all our data structures we have both an interesting storage cost, typically 2 or 3 r.p.v. (references per vertex) in the case of very regular triangulations, and provable upper bounds in the worst case scenario. One of our solutions has a worst case cost of 3.33 r.p.v., which is currently the best-known bound improving the previous 4 r.p.v. [Castelli et al. 2018]. Our representations have slightly slower running times (factors 1.5 to 4) than classical data structures. In our experiments we compare on various meshes runtime and memory performance of our representations with those of the most efficient existing solutions. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Luca Castelli Aleardi and Olivier Devillers 2024 Is Part Of LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2024.32 urn:nbn:de:0030-drops-199779 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.32 eng https://creativecommons.org/licenses/by/4.0/legalcode