ESQ: Editable SQuad representation for triangle meshes

We consider the problem of designing space efficient solutions for representing the connectivity information of manifold triangle meshes. Most mesh data structures are quite redundant, storing a large amount of information in order to efficiently support mesh traversal operators. Several compact data structures have been proposed to reduce storage cost while supporting constant-time mesh traversal. Some recent solutions are based on a global re-ordering approach, which allows to implicitly encode a map between vertices and faces. Unfortunately, these compact representations do not support efficient updates, because local connectivity changes (such as edge-contractions, edge-flips or vertex insertions) require re-ordering the entire mesh. Our main contribution is to propose a new way of designing compact data structures which can be dynamically maintained. In our solution, we push further the limits of the re-ordering approaches: the main novelty is to allow to re-order vertex data (such as vertex coordinates), and to exploit this vertex permutation to easily maintain the connectivity under local changes. We describe a new class of data structures, called Editable SQuad (ESQ), offering the same navigational and storage performance as previous works, while supporting local editing in amortized constant time. As far as we know, our solution provides the most compact dynamic data structure for triangle meshes. We propose a linear-time and linear-space construction algorithm, and provide worst-case bounds for storage and time cost.Cet article traite de la conception de structure de données usant peu de mémoire pour représenter des surfaces manifold triangulées. La plupart des structures utilisées sont largement redondantes pour permettre un parcours efficace des adjacences entre triangles. Par ailleurs il existe des structures compactes, basées sur une renumérotation qui code de manière implicite une correspondance entre faces et sommets. Malheureusement, ces structures ne permettent pas de modifier la triangulation car des opérations telles que insertion suppression ou bascule d'arête nécessite de renuméroter toute la triangulation. Nous proposons une nouvelle méthode de conception de structures de données compactes permettant une mise à jour dynamique en adaptant l'idée de renumérotation. Nous introduisons Editab SQuad (ESQ), une nouvelle famille de structures de données qui a les mêmes performances de stockage et de temps d'accés que les précédents travaux tout en permettant des modifications locales en temps constant amorti