How much geometry it takes to reconstruct a 2-manifold in R3

Authors:
Daniel Dumitriu;Stefan Funke;Martin Kutz;Nikola Milosavljević
Affiliations:
Johannes Gutenberg University, Mainz, Germany;Ernst Moritz Arndt University, Greifswald, Germany;Stanford University, Stanford, CA, USA;Stanford University, Stanford, CA, USA
Venue:
Journal of Experimental Algorithmics (JEA)
Year:
2010

Citing 7
Cited 2

Surface reconstruction by Voronoi filtering

Proceedings of the fourteenth annual symposium on Computational geometry
A core library for robust numeric and geometric computation

SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A simple algorithm for homeomorphic surface reconstruction

Proceedings of the sixteenth annual symposium on Computational geometry
Smooth-surface reconstruction in near-linear time

SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The LEDA Platform of Combinatorial and Geometric Computing

ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Network sketching or: "How Much Geometry Hides in Connectivity?--Part II"

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the Locality of Extracting a 2-Manifold in

SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory

SMI 2011: Full Paper: Localized Cocone surface reconstruction

Computers and Graphics
A fast and simple surface reconstruction algorithm

Proceedings of the twenty-eighth annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

Known algorithms for reconstructing a 2-manifold from a point sample in R3 are naturally based on decisions/predicates that take the geometry of the point sample into account. Facing the always present problem of round-off errors that easily compromise the exactness of those predicate decisions, an exact and robust implementation of these algorithms is far from being trivial and typically requires employment of advanced datatypes for exact arithmetic, as provided by libraries like CORE, LEDA, or GMP. In this article, we present a new reconstruction algorithm, one whose main novelties is to throw away geometry information early on in the reconstruction process and to mainly operate combinatorially on a graph structure. More precisely, our algorithm only requires distances between the sample points and not the actual embedding in R3. As such, it is less susceptible to robustness problems due to round-off errors and also benefits from not requiring expensive exact arithmetic by faster running times. A more theoretical view on our algorithm including correctness proofs under suitable sampling conditions can be found in a companion article.