Sweep‐line algorithm for constrained Delaunay triangulation

Abstract

This paper introduces a new algorithm for constrained Delaunay triangulation, which is built upon sets of points and constraining edges. It has various applications in geographical information system (GIS), for example, iso‐lines triangulation or the triangulation of polygons in land cadastre. The presented algorithm uses a sweep‐line paradigm combined with Lawson's legalisation. An advancing front moves by following the sweep‐line. It separates the triangulated and non‐triangulated regions of interest. Our algorithm simultaneously triangulates points and constraining edges and thus avoids consuming location of those triangles containing constraining edges, as used by other approaches. The implementation of the algorithm is also considerably simplified by introducing two additional artificial points. Experiments show that the presented algorithm is among the fastest constrained Delaunay triangulation algorithms available at the moment.

Keywords:

• Algorithm
• Constrained Delaunay triangulation
• Sweep‐line approach

Acknowledgements

We would like to thank Dr Ivana Kolingerova and Dr Josef Kohout from West Bohemia University in the Czech Republic for their help and motivation when preparing this algorithm. We would also like to thank the Slovenian Research Agency for supporting this research under project P2‐0041.