Properties of n-dimensional triangulations
Computer Aided Geometric Design
Construction of three-dimensional Delaunay triangulations using local transformations
Computer Aided Geometric Design
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Implementation of a randomized algorithm for Delaunay and regular triangulations in three dimensions
Computer Aided Geometric Design
Perturbations and vertex removal in a 3D delaunay triangulation
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Updating and constructing constrained delaunay and constrained regular triangulations by flips
Proceedings of the nineteenth annual symposium on Computational geometry
Flipping to robustly delete a vertex in a delaunay tetrahedralization
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
| Hi-index | 0.00 |
In this paper, we propose a randomized algorithm that allows to delete a point in three--dimensional regular or Delaunay triangulation by a sequence of flips. All the previous algorithms check regularity of each new tetrahedron globally, i.e. with respect to all vertices of tetrahedra incident to the point, which is being deleted. In contrast, the proposed hybrid algorithm uses a combination of local and global regularity tests. First, the proposed algorithm tries to delete a point by a randomized sequence of flips of faces satisfying a certain local condition. This simple approach will always delete the point successfully, but theoretically in an unbounded time in the worst case. Therefore we combine it with the global regularity tests -- if the point is not deleted after a certain number of flips, the proposed algorithm replaces the local regularity test by the global regularity test. In practice, the local regularity tests are sufficient in most cases and the global regularity tests are used only rarely. In consequence, the proposed algorithm needs less tests of regularity in average than the previous algorithms.