Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
A quadratic time algorithm for the minmax length triangulation
SIAM Journal on Computing
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
The greedy triangulation can be computed from the Delaunay triangulation in linear time
Computational Geometry: Theory and Applications
Higher order Delaunay triangulations
Computational Geometry: Theory and Applications
Minimum weight triangulation is NP-hard
Proceedings of the twenty-second annual symposium on Computational geometry
Generating realistic terrains with higher-order Delaunay triangulations
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Constrained higher order Delaunay triangulations
Computational Geometry: Theory and Applications
Algorithms for optimal area triangulations of a convex polygon
Computational Geometry: Theory and Applications
Constructing interference-minimal networks
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Optimization for first order delaunay triangulations
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Towards a definition of higher order constrained Delaunay triangulations
Computational Geometry: Theory and Applications
Optimization for first order Delaunay triangulations
Computational Geometry: Theory and Applications
Hi-index | 0.00 |
This paper presents an algorithm to triangulate polygons optimally using order-k Delaunay triangulations, for a number of quality measures. The algorithm uses properties of higher order Delaunay triangulations to improve the O(n3) running time required for normal triangulations to O(k2n log k + kn log n) expected time, where n is the number of vertices of the polygon. An extension to polygons with points inside is also presented, allowing to compute an optimal triangulation of a polygon with h ≥ 1 components inside in O(kn log n) + O(k)h+2n expected time. Furthermore, through experimental results we show that, in practice, it can be used to triangulate point sets optimally for small values of k. This represents the first practical result on optimization of higher order Delaunay triangulations for k 1.