A Survey of Constrained Delaunay Triangulation Algorithms for Surface Representation

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.

[1]  Bernard Chazelle,et al.  A theorem on polygon cutting with applications , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[2]  Der-Tsai Lee.  Proximity and reachability in the plane. , 1978 .

[3]  C. Lawson.  Software for C1 Surface Interpolation , 1977 .

[4]  Jean-Daniel Boissonnat,et al.  Geometric structures for three-dimensional shape representation , 1984, TOGS.

[5]  Leila De Floriani,et al.  Constrained Delaunay triangulation for multiresolution surface description , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[6]  B. A. Lewis,et al.  Triangulation of Planar Regions with Applications , 1978, Comput. J..

[7]  D. T. Lee,et al.  Generalized delaunay triangulation for planar graphs , 1986, Discret. Comput. Geom..

[8]  Robert E. Tarjan,et al.  Triangulating a Simple Polygon , 1978, Inf. Process. Lett..

[9]  Errol L. Lloyd.  On triangulations of a set of points in the plane , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[10]  Robert E. Barnhill,et al.  Representation and Approximation of Surfaces , 1977 .

[11]  Robert E. Tarjan,et al.  An O(n log log n)-Time Algorithm for Triangulating a Simple Polygon , 1988, SIAM J. Comput..

[12]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[13]  Olivier D. Faugeras,et al.  Representing stereo data with the Delaunay triangulation , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[14]  Lenhart K. Schubert,et al.  An optimal algorithm for constructing the Delaunay triangulation of a set of line segments , 1987, SCG '87.

[15]  Stefano Levialdi,et al.  Image Analysis and Processing , 1987 .

[16]  Olivier D. Faugeras,et al.  Representing Stereo Data with the Delaunay Triangulation , 1990, Artif. Intell..

[17]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[18]  Leila De Floriani,et al.  Delaunay-based representation of surfaces defined over arbitrarily shaped domains , 1985, Comput. Vis. Graph. Image Process..

[19]  Franco P. Preparata,et al.  Location of a Point in a Planar Subdivision and Its Applications , 1977, SIAM J. Comput..

[20]  I. Babuska,et al.  ON THE ANGLE CONDITION IN THE FINITE ELEMENT METHOD , 1976 .

[21]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.