## Succinct representation of triangulations with a boundary. WADS (2005)

Citations: | 13 - 5 self |

### BibTeX

@MISC{Aleardi05succinctrepresentation,

author = {L. Castelli Aleardi and Olivier Devillers and Gilles Schaeffer},

title = {Succinct representation of triangulations with a boundary. WADS},

year = {2005}

}

### OpenURL

### Abstract

Abstract. We consider the problem of designing succinct geometric data structures while maintaining efficient navigation operations. A data structure is said succinct if the asymptotic amount of space it uses matches the entropy of the class of structures represented. For the case of planar triangulations with a boundary we propose a succinct representation of the combinatorial information that improves to 2.175 bits per triangle the asymptotic amount of space required and that supports the navigation between adjacent triangles in constant time (as well as other standard operations). For triangulations with m faces of a surface with genus g, our representation requires asymptotically an extra amount of 36(g − 1) lg m bits (which is negligible as long as g ≪ m / lg m). 1

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Citation Context ...x.polytechnique.fr/~schaeffe/GeoComp/[12] for a recent optimal encoding). Similarly, 2.175 bits per triangle are needed to code triangulations when a larger boundary of arbitrary size is allowed (in =-=[1]-=- the entropy of this class of triangulations is computed). In this paper, our purpose is not to compress the data for storage or network transmission, but to design a compact representation that can b... |