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Voronoi Diagrams of Set-Theoretic solid Models
September/October 1992 (vol. 12 no. 5)
pp. 69-77

The definition of a Voronoi diagram is extended to arbitrary set-theoretic solid models. A method for approximating such diagrams using recursive subdivision is described. The method relies on octrees, which have been used for computing the distances between whole solid models. Two- and three-dimensional images generated using the algorithm are presented.

1. J.F. Canny,The Complexity of Robot Motion Planning, PhD thesis, MIT Press, Cambridge, Mass., 1987.
2. C.M. Hoffmann, "How to Construct the Skeleton of CSG Objects,"Proc. 3rd IMA Conf. Muthematics of Surfaces, Oxford Univ. Press, Oxford, UK. 1990.
3. D.F. Watson, "Computing then-Dimensional Delaunay Tessellation with Application to Voronoi Polytopes,"Computer J., Vol. 24, No. 2, 1981, pp. 167-172.
4. A. Bowyer, "Computing Dirichlet Tessellations,"Computer J., Vol. 24, No. 2, 1981, pp. 162-166.
5. H. Samet,The Design and Analysis of Spatial Data Structures. Reading, MA: Addison-Wesley, 1990.
6. H. Samet,Applications of Spatial Data Structures, Addison-Wesley, Reading, Mass., 1989.
7. H. Blum, "A Transformation for Extracting New Descriptors of Shape," inModels for the Perception of Speech and Visual Form, W. Whaten-Dunn, ed., MIT Press, Cambridge, Mass., 1967, pp. 362-380.
8. U. Montanari, "Continuous skeletons from digitized images,"J. Assoc. Comput. Machinery, vol. 16, pp. 534-549, Oct. 1969.
9. D.G. Kirkpatrick, "Efficient Computation of Continuous Skeletons,"Proc. 20th Ann. Symp. Foundutions of Computer Science, IEEE Computer Society Press, Los Alamitos, Calif., 1979, pp. 18-27.
10. D.T. Lee, "Medial Axis Transformation of a Planar Shape,"IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 4, No. 4, July 1982, pp. 363-369.
11. S. Fortune, "A Sweepline Algorithm for Voronoi Diagrams,"Proc. 2nd ACM Symp. Computational Geometry, ACM, New York, 1986, pp. 313-322.
12. V. Srinivasan and L.R. Nackman, "Voronoi Diagram of Multiply Connected Polygonal Domains,"IBM J. Research and Development, Vol. 31, No. 3, May 1987, pp. 373-381.
13. R. Klein,Concrete and Abstract Voronoi Diagrams, Lecture Notes in Computer Science, Vol. 400, Springer-Verlag, Berlin, 1989.
14. D.T. Lee and R.L. Drysdale, "Generalization of Voronoi Diagrams in the Plane,"SIAM J. Computing, Vol. 10, No. 1, Feb. 1081, pp. 73-87.
15. J. Woodwark and A. Bowyer, "Better and Faster Pictures from Solid Models,"Computer-Aided Eng. J., Vol. 3, No. 1, Feb. 1986, pp. 17-24.
16. P.S. Milne and D.A. Lavender, "GAS--The Manual," tech. report, School of Mathematical Sciences, Bath Univ., Bath, UK, 1991.

Citation:
David Lavender, Adrian Bowyer, James Davenport, Andrew Wallis, John Woodwark, "Voronoi Diagrams of Set-Theoretic solid Models," IEEE Computer Graphics and Applications, vol. 12, no. 5, pp. 69-77, Sept.-Oct. 1992, doi:10.1109/38.156016
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