Abstract
The Constrained Delaunay Triangulation (CDT) is the basis for building surface models in a variety of applications. The paper introduces the notion of constrained Delaunay triangulation and presents its fundamental properties. The basic algorithms proposed in the literature for building a CDT are classified and briefly described.
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References
Barnhill, R.E.: Representation and Approximation of Surfaces, in: Mathematical Software III, (Ed. J.R. Rice), Academic Press Inc., 1977, 69–120.
Boissonnat, J.D.: Geometric Structures for Three Dimensional Shape Representation, ACM Transactions on Graphics, 3, 4 (1984) 266–286.
Boissonnat, J.D., Faugeras, O.D., Le Bras-Mehlman, E.: Representing Stereo Data with the Delaunay Triangulation, in: Proceedings IEEE Robotics and Automation, Philadelphia, April 1988.
De Fioriani, L.: A Triangle Based Data Structure For Multiresolution Surface Representation, in: Image Analysis and Processing, (Ed. S. Levialdi, A. Restivo and V. Di Gesu’), Plenum Press, 1987 (in print).
Lawson, C.L.: Software for Cl surface interpolation, in: Mathematical Software III, (Ed. J.R. Rice), Academic Press Inc., 1977, 161–164.
Samet, H.: The Quadtree and Related Hierarchical Data Structures, Computing Surveys, 16,2 (1984), 187–260.
Babuska, I., Aziz, A.K.: On the Angle Condition in the Finite Element Method, SIAM J. Num. Anal., 13, 2 (1976), 214–226.
De Fioriani, L., Falcidieno, B., Pienovi, C., Allen, D., Nagy, G.: A visibility-based model for terrain features, in: Proc. 2nd Int. Symp. on Spatial Data Handling, Seattle, July 1986, 235–250.
LLoyd, E.L.: On triangulations on a set of points in the plane, in: Proceedings IEEE 18th Annual Symposium on the Foundations of Computer Science, 1977, 228–240.
Lee, D.T.: Proximity and reachability in the plane, Ph.D. Dissertation, Coordinated Science Laboratory Report ACT-12, University of Illinois, Urbana, 1978.
De Floriani, L., Falcidieno, B., Pienovi, C.: A Delaunay-based representation of surfaces defined over arbitrarily-shaped domains, Computer Vision, Graphics and Image Processing, 32 (1985), 127–140.
Lee, D.T., Lin, A.K.: Generalized Delaunay Triangulation for Planar Graphs, Discrete and Computational Geometry, 1 (1986), 201–217.
Preparata, F.P., Shamos, M.I.: Computational Geometry: an Introduction, Springer Verlag, 1985.
Wang, C.A., Schubert, L.: An optimal algorithm for constricting the Delaunay triangulation of a set of line segments, in: Proceedings Third ACM Symposium on Computational Geometry, Waterloo, June 1987, 223–232.
Garey, M.R., Johnson, D.S., Preparata, F.P., Tarjan, R.E.: Triangulating a simple polygon, Information Processing Letters, 7, 4 (1978), 175–179.
Lee, D.T., Preparata, F.P.: Location of a point in a planar subdivision and its applications, SIAM. J. Computing, 6, 3 (1977), 594–606.
Tarjan, R.E., Van Wyk, C.J.: An O(n log log n) time algorithm for triangulating a simple polygon, SIAM Journal on Computing, 17 (1988), 143–178.
Chazelle, B.M., A Theorem on Polygon Cutting with Applications, in: Proceedings 23rd IEEE Annual Symp. on the Foundations of Computer Science, 1982, 339–349.
Lewis, B.A., Robinson, J.S.: Triangulation of planar regions with applications, The Computer Journal, 21, 4 (1979), 324–332.
Chazelle, B.M., Incerpi, J.: Triangulating a Polygon by Divide-and-conquer, in: Proceedings 21st Allerton Conf. Commun. Control Comput., 1983, 447–456.
Lee, D.T., Schacter, B.J.: Two algorithms for constructing a Delaunay Triangulation, Int. Journal of Computer and Information Sciences, 9, 3 (1980), 219–242.
Bernai, J.: On Constructing Delaunay triangulations for sets Constrained by Line Segments, Tech. Rep. National Bureau of Standards, 1988.
Chew, L.P.: Constrained Delaunay Triangulations, in: Proceedings Third ACM Symposium on Computational Geometry, Waterloo, June 1987, 216–222.
De Floriani, L., Puppo, E.: Constrained Delaunay Triangulation for Multiresolution Surface Description, in: Proceedings Ninth International Conference on Pattern Recognition, Rome, November 1988, (in print).
De Floriani, L.: Surface Representation Based on Triangular Grids, The Visual Computer, 1987, 27–50.
Asano, T., Asano, T., Guibas, L., Hershberger, J., Imei, H.: Visibility of Disjoint Polygons, Algorithmica, 1 (1986), 45–63.
Watson, D.F.: Computing the n-dimensional Delaunay tesselation with application to Voronoi polytopes, The Computer Journal, 24 (1981), 167–171.
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© 1989 Springer-Verlag Wien
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Floriani, L.D., Puppo, E. (1989). A Survey of Constrained Delaunay Triangulation Algorithms for Surface Representation. In: Pieroni, G.G. (eds) Issues on Machine Vision. International Centre for Mechanical Sciences, vol 307. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2830-5_7
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DOI: https://doi.org/10.1007/978-3-7091-2830-5_7
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82148-0
Online ISBN: 978-3-7091-2830-5
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