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Communication Dans Un Congrès Année : 2024

SCARST: Schnyder Compact and Regularity Sensitive Triangulation Data Structure

Résumé

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.
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hal-04618429 , version 1 (20-06-2024)

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Luca Castelli Aleardi, Olivier Devillers. SCARST: Schnyder Compact and Regularity Sensitive Triangulation Data Structure. 40th International Symposium on Computational Geometry (SoCG 2024), Jun 2024, Athens, Greece. ⟨10.4230/LIPIcs.SoCG.2024.32⟩. ⟨hal-04618429⟩
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