@techreport{a-vdsfg-90 , author = "F. Aurenhammer" , title = "Voronoi diagrams: a survey of a fundamental geometric data structure" , type = "Report" , number = "B-90-09" , institution = "Fachber. Math., Free Univ. Berlin" , address = "Berlin, West Germany" , year = 1990 , keywords = "survey paper, Voronoi diagrams, Delaunay triangulations, arrangements, hyperplanes, plane sweep, divide-and-conquer, parallel computation, minimum spanning trees, cluster analysis, motion planning" , succeeds = "a-vds-88" , precedes = "a-vdsfg-91" , update = "93.09 aurenhammer" } @article{a-vdsfg-91 , author = "F. Aurenhammer" , title = "Voronoi diagrams: A survey of a fundamental geometric data structure" , journal = "ACM Comput. Surv." , volume = 23 , year = 1991 , pages = "345--405" , keywords = "survey paper, Voronoi diagrams, Delaunay triangulations, arrangements, hyperplanes, plane sweep, divide-and-conquer, parallel computation, minimum spanning trees, cluster analysis, motion planning" , succeeds = "a-vdsfg-90" , update = "95.09 agarwal" } @inproceedings{bb-dvddt-90 , author = "C. L. Bajaj and W. J. Bouma" , title = "Dynamic {Voronoi} diagrams and {Delaunay} triangulations" , booktitle = "Proc. 2nd Canad. Conf. Comput. Geom." , year = 1990 , pages = "273--277" } @techreport{b-cdtsc-88 , author = "J. Bernal" , title = "Constructing {Delaunay} Triangulations For Sets Constrained By Line Segments" , number = "NIST/TN-1252" , institution = "Mathematical Analysis Div., National Inst. of Standards and Technology (NEL)" , address = "Gaithersburg, MD" , month = sep , year = 1988 , keywords = "Delaunay triangulations, ntiscomnbs" , abstract = "In the paper, the authors propose a simple algorithm for constructing a Delaunay triangulation for a finite set of points in the plane constrained by a finite collection of line segments. The algorithm constructs first a Delaunay triangulation for the set, and then generates from it a sequence of triangulations as each line segment is incorporated into the previously obtained triangulation. An expected time analysis shows the algorithm to be linear if the number of line segments is kept constant." } @article{b-srpcs-88 , author = "J.-D. Boissonnat" , title = "Shape Reconstruction From Planar Cross-Sections" , journal = "Comput. Vision Graph. Image Process." , volume = 44 , number = 1 , month = oct , year = 1988 , pages = "1--29" , keywords = "shape reconstruction, planar cross sections, Delaunay triangulation, computational geometry" , update = "93.09 devillers" , annote = "Computes the 3D DT between two contours (extra points are added to force the boundary---by repeatedly adding midpoints to edges not in DT) by merging DTs of each contour. Then tetras are eliminated so that each point is on the surface." , abstract = "We propose a new solution to the problem of constructing a shape over a set of cross-sectional contours. We construct a volume whose boundary is a polyhedron with triangular faces intersecting the cutting planes along the given contours. This volume is obtained, slice by slice, by pruning the Delaunay triangulations formed between two adjacent cross sections. The Delaunay triangulation can be computed efficiently in this specific situation: an algorithm is presented that is optimal with respect to the input size and the output size and that only uses 2-dimensional operations. The shape reconstruction method extracts, from that triangulation, a maximum solid with no singularity. It can handle the case where the number of contours varies from one cross section to the other and thus, can handle contour-defined objects which are branched and have holes. This algorithm has been fully implemented and tested on various examples; results on medical images are presented. (Author ." , year = 1992 , pages = "170--175" } @techreport{kln-edtur-89 , author = "M. Karasick and D. Lieber and L. R. Nackman" , title = "Efficient {Delaunay} triangulations using rational arithmetic" , type = "Report" , number = "RC 14455" , institution = "IBM T. J. Watson Res. Center" , address = "Yorktown Heights, NY" , month = mar , year = 1989 , precedes = "kln-edtur-91" } @article{b-srpcs-88 , author = "J.-D. Boissonnat" , title = "Shape Reconstruction From Planar Cross-Sections" , journal = "Comput. Vision Graph. Image Process." , volume = 44 , number = 1 , month = oct , year = 1988 , pages = "1--29" , keywords = "shape reconstruction, planar cross sections, Delaunay triangulation, computational geometry" , update = "93.09 devillers" , annote = "Computes the 3D DT between two contours (extra points are added to force the boundary---by repeatedly adding midpoints to edges not in DT) by merging DTs of each contour. Then tetras are eliminated so that each point is on the surface." , abstract = "We propose a new solution to the problem of constructing a shape over a set of cross-sectional contours. We construct a volume whose boundary is a polyhedron with triangular faces intersecting the cutting planes along the given contours. This volume is obtained, slice by slice, by pruning the Delaunay triangulations formed between two adjacent cross sections. The Delaunay triangulation can be computed efficiently in this specific situation: an algorithm is presented that is optimal with respect to the input size and the output size and that only uses 2-dimensional operations. The shape reconstruction method extracts, from that triangulation, a maximum solid with no singularity. It can handle the case where the number of contours varies from one cross section to the other and thus, can handle contour-defined objects which are branched and have holes. This algorithm has been fully implemented and tested on various examples; results on medical images are presented. (Author abstract) 28 Refs." } @article{b-gdtnd-90 , author = "C. Borgers" , title = "Generalized {Delaunay} Triangulations of Nonconvex Domains" , journal = "Comput. Math. Appl." , volume = 20 , number = 7 , year = 1990 , pages =@article{cl-aldt-84 , author = "R. C. Chang and R. C. T. Lee" , title = "On the average length of {Delaunay} triangulations" , journal = "BIT" , volume = 24 , year = 1984 , pages = "269--273" } @article{ch-dspc2-90 , author = "C. Cherfils and F. Hermeline" , title = "Diagonal Swap Procedures and Characterizations of 2{D}-{Delaunay} Triangulations" , journal = "RAIRO-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique" , volume = 24 , number = 5 , year = 1990 , pages = "613--625" , annote = "Proves that Delaunay switchings converge to DT." } @inproceedings{c-cdt-87 , author = "L. P. Chew" , title = "Constrained {Delaunay} triangulations" , booktitle = "Proc. 3rd Annu. ACM Sympos. Comput. Geom." , year = 1987 , pages = "215--222" , precedes = "c-cdt-89" } @article{c-cdt-89 , author = "L. P. Chew" , title = "Constrained {Delaunay} triangulations" , journal = "Algorithmica" , volume = 4 , year = 1989 , pages = "97--108" , succeeds = "c-cdt-87" } @article{cc-fcdt-87 , author = "Y. Correc and E. Chapuis" , title = "Fast Computation of {Delaunay} Triangulations" , journal = "Adv. Eng. Softw." , volume = 9 , number = 2 , year = 1987 , pages = "77--83" , annote = "Claims $O(n \log n)$ measured performance. Points are sorted by one coordinate and a Lawson style incremental algorithm is used. Triangle list is maintained in sorted by one coordinate of barycentre." } @inproceedings{msz-frplw-96 , author = "Ernst P. M{\"u}cke and Isaac Saias and Binhai Zhu" , title = "Fast Randomized Point Location Without Preprocessing in Two- and Three-Dimensional {Delaunay} Triangulations" , booktitle = "Proc. 12th Annu. ACM Sympos. Comput. Geom." , year = 1996 , pages = "274--283" , update = "96.05 efrat" } @article{o-cg-88 , author = "J. O'Rourke" , title = "Computational geometry" , journal = "Annu. Rev. Comput. Sci." , volume = 3 , year = 1988 , pages = "389--411" , keywords = "survey paper, convex hull, Voronoi diagrams, Delaunay triangulations, arrangements, polygons, triangulation, range search, point location, motion planning, Davenport-Schinzel sequences, parallel computation" } @article{o-cgc4-88 , author = "J. O'Rourke" , title = "Computational geometry column ~4" , journal = "SIGACT News" , volume = 19 , number = 2 , year = 1988 , pages = "22--24" , note = "Also in Computer Graphics 22(1988), 111--112." , keywords = "hidden line elimination, Delaunay triangulations, link distance, stabbing" , annote = "Old and new problems" } @article{o-cgc12-91 , author = "J. O'Rourke" , title = "Computational geometry column 12" , journal = "Internat. J. Comput. Geom. Appl." , volume = 1 , number = 2 , year = 1991 , pages = "197--200" , note = "Also in SIGACT News 22:2 (1991), 26--29" , keywords = "Voronoi diagrams, arrangements, visibility, Delaunay triangulations, path planning, shortest paths, separation" , annote = "Seven open problems from various sources" } @article{obw-cdnh-87 , author = "J. O'Rourke and H. Booth and R. Washington" , title = "Connect-the-dots: a new heuristic" , journal = "Comput. Vision Graph. Image Process." , volume = 39 , year = 1987 , pages = "258--266" , keywords = "pattern recognition, Delaunay triangulations, Hamiltonian cycles" } @article{pr-dhsac-9@inproceedings{pm-dtcfd-92 , author = "M.-A. K. Posenau and D. M. Mount" , title = "Delaunay triangulations and computational fluid dynamics meshes" , booktitle = "Proc. 4th Canad. Conf. Comput. Geom." , year = 1992 , pages = "316--321" }