Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Embedding planar graphs on the grid
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Directed edges—A scalable representation for triangle meshes
Journal of Graphics Tools
On topological aspects of orientations
Discrete Mathematics
Succinct Representation of Balanced Parentheses and Static Trees
SIAM Journal on Computing
Star-vertices: a compact representation for planar meshes with adjacency information
Journal of Graphics Tools
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Compact representations of separable graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Compact Encodings of Planar Graphs via Canonical Orderings and Multiple Parentheses
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Winged edge polyhedron representation.
Winged edge polyhedron representation.
Representing Trees of Higher Degree
Algorithmica
Optimal Coding and Sampling of Triangulations
Algorithmica
Succinct representations of planar maps
Theoretical Computer Science
A polyhedron representation for computer vision
AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition
Schnyder Woods for Higher Genus Triangulated Surfaces, with Applications to Encoding
Discrete & Computational Geometry - Special Issue: 24th Annual Symposium on Computational Geometry
SOT: compact representation for tetrahedral meshes
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Succinct representation of labeled graphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A compact encoding of plane triangulations with efficient query supports
Information Processing Letters
LR: compact connectivity representation for triangle meshes
ACM SIGGRAPH 2011 papers
Succinct representation of triangulations with a boundary
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Computational Geometry: Theory and Applications
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We consider the problem of designing space efficient solutions for representing triangle meshes. Our main result is a new explicit data structure for compactly representing planar triangulations: if one is allowed to permute input vertices, then a triangulation with n vertices requires at most 4n references (5n references if vertex permutations are not allowed). Our solution combines existing techniques from mesh encoding with a novel use of minimal Schnyder woods. Our approach extends to higher genus triangulations and could be applied to other families of meshes (such as quadrangular or polygonal meshes). As far as we know, our solution provides the most parsimonious data structures for triangulations, allowing constant time navigation in the worst case. Our data structures require linear construction time, and all space bounds hold in the worst case. We have implemented and tested our results, and experiments confirm the practical interest of compact data structures.