Optimal quadtree construction algorithms
Computer Vision, Graphics, and Image Processing
Construction of three-dimensional Delaunay triangulations using local transformations
Computer Aided Geometric Design
A comparison of sequential Delaunay triangulation algorithms
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
SIAM Journal on Computing
Expected time analysis for Delaunay point location
Computational Geometry: Theory and Applications
Incremental construction of the delaunay triangulation and the delaunay graph in medium dimension
Proceedings of the twenty-fifth annual symposium on Computational geometry
HCPO: an efficient insertion order for incremental Delaunay triangulation
Information Processing Letters
Data-Parallel Octrees for Surface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Dynamic grid for mesh generation by the advancing front method
Computers and Structures
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In the light of the simplicity and the linearity of regular grid insertion, a multi-grid insertion scheme is proposed for the Delaunay triangulation of uniform and non-uniform point distributions by recursive application of the regular grid insertion to an arbitrary subset of the original point set. The fundamentals and difficulties of Delaunay triangulation of highly non-uniformly distributed points by the insertion method are discussed. Current strategies and methods of point insertions for non-uniformly distributed points are reviewed. An enhanced kd-tree insertion scheme with specified number of points in a cell and its natural sequence of insertion are presented. The regular grid insertion, the enhanced kd-tree insertion and the multi-grid insertion have been thoroughly tested with benchmark non-uniform distributions of 1-100million points. It is found that the kd-tree insertion is very sensitive to the triangulation of non-uniform point distributions with a large amount of conflicting elongated triangles. Multi-grid insertion is the most stable and efficient for all the uniform and non-uniform point distributions tested.