On the randomized construction of the Delaunay tree
Theoretical Computer Science
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Geometric compression through topological surgery
ACM Transactions on Graphics (TOG)
Progressive forest split compression
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Real time compression of triangle mesh connectivity
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Progressive compression of arbitrary triangular meshes
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Efficient compression of non-manifold polygonal meshes
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Optimal bit allocation in compressed 3D models
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
WRAP&Zip decompression of the connectivity of triangle meshes compressed with edgebreaker
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Face fixer: compressing polygon meshes with properties
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Spectral compression of mesh geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Geometric compression for interactive transmission
Proceedings of the conference on Visualization '00
Compressing large polygonal models
Proceedings of the conference on Visualization '01
Compressing polygon mesh geometry with parallelogram prediction
Proceedings of the conference on Visualization '02
Edgebreaker: Connectivity Compression for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
Near-optimal connectivity encoding of 2-manifold polygon meshes
Graphical Models - Special issue: Processing on large polygonal meshes
Linear-Time Reconstruction of Delaunay Triangulations with Applications
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Single Resolution Compression of Arbitrary Triangular Meshes with Properties
DCC '99 Proceedings of the Conference on Data Compression
| Hi-index | 0.00 |
We present a new linear time algorithm to compute a good order for the point set of a Delaunay triangulation in the plane. Such a good order makes reconstruction in linear time with a simple algorithm possible. Similarly to the algorithm of Snoeyink and van Kreveld [Proceedings of 5th European Symposium on Algorithms (ESA), 1997, pp. 459-471], our algorithm constructs such orders in O(logn) phases by repeatedly removing a constant fraction of vertices from the current triangulation. Compared to [Proceedings of 5th European Symposium on Algorithms (ESA), 1997, pp. 459-471] we improve the guarantee on the number of removed vertices in each such phase. If we restrict the degree of the points (at the time they are removed) to 6, our algorithm removes at least 1/3 of the points while the algorithm from [Proceedings of 5th European Symposium on Algorithms (ESA), 1997, pp. 459-471] gives a guarantee of 1/10. We achieve this improvement by removing the points sequentially using a breadth first search (BFS) based procedure that-in contrast to [Proceedings of 5th European Symposium on Algorithms (ESA), 1997, pp. 459-471]-does not (necessarily) remove an independent set. Besides speeding up the algorithm, removing more points in a single phase has the advantage that two consecutive points in the computed order are usually closer to each other. For this reason, we believe that our approach is better suited for vertex coordinate compression. We implemented prototypes of both algorithms and compared their running time on point sets uniformly distributed in the unit cube. Our algorithm is slightly faster. To compare the vertex coordinate compression capabilities of both algorithms we round the resulting sequences of vertex coordinates to 16-bit integers and compress them with a simple variable length code. Our algorithm achieves about 14% better vertex data compression than the algorithm from [Proceedings of 5th European Symposium on Algorithms (ESA), 1997, pp. 459-471].