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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 21
Edited by: M. Papadrakakis and B.H.V. Topping
Paper IV.5

An Algorithm for Automatic Delaunay Triangulation of Planar Arbitrary Domains

C. Du

Institut für Wasserbau und Kulturtechnik, University of Karlsruhe, Karlsruhe, Germany

Full Bibliographic Reference for this paper
C. Du, "An Algorithm for Automatic Delaunay Triangulation of Planar Arbitrary Domains", in M. Papadrakakis, B.H.V. Topping, (Editors), "Advances in Post and Preprocessing for Finite Element Technology", Civil-Comp Press, Edinburgh, UK, pp 187-191, 1994. doi:10.4203/ccp.21.4.5
In this paper an algorithm for automatic Delaunay triangulation of arbitrary planar domains is presented. A new method in which a Delaunay triangle is constructed by computing the angles of points with respect to a baseline in a region instead of checking the empty circumcircle is proposed. The algorithm is based on a working boundary which starts from the original boundary and moves dynamically to the centre of the planar domains. An edge on the working boundary is taken as a baseline, a third point is then searched to form a Delaunay-satisfying triangle. The triangulation is finished when the working boundary is empty. The Algorithm is numerically stable, sufficiently robust to handle irregular region and simple to implement. Several examples and applications are included to demonstrate the validity of the algorithm as well as its effectiveness.

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