Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Higher-dimensional Voronoi diagrams in linear expected time
Discrete & Computational Geometry
Computational Geometry: Theory and Applications
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
On the maximum degree of minimum spanning trees
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Journal of Combinatorial Theory Series B
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computing a canonical polygonal schema of an orientable triangulated surface
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Nice point sets can have nasty Delaunay triangulations
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Delaunay triangulation programs on surface data
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Ball-Pivoting Algorithm for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Four Results on Randomized Incremental Constructions
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
ICIAP '99 Proceedings of the 10th International Conference on Image Analysis and Processing
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Given a surface mesh F in R 3 with vertex set S and consisting of Delaunay triangles, we want to construct the Delaunay tetrahedralization of S.We present an algorithm which constructs the Delaunay tetrahedralization of S given a bounded degree spanning subgraph T of F. It accelerates the incremental Delaunay triangulation construction by exploiting the connectivity of the points on the surface. If the expected size of the Delaunay triangulation is linear, we prove that our algorithm runs in O(n log* n) expected time, speeding up the standard randomized incremental Delaunay triangulation algorithm, which is O(n log n) expected time in this case.We discuss how to find a bounded degree spanning subgraph T from surface mesh F and give a linear time algorithm which obtains a spanning subgraph from any triangulated surface with genus g with maximum degree at most 12g for g0 or three for g=0.