Since many different insertions are possible, the algorithm computes only those that are on the delaunay circles of each intersected triangle. The delaunay triangulation is commonly used to generate triangulated irregular network tin models for a best description of the surface morphology in a variety of applications in geographic information systems gis. In mathematics and computational geometry, a delaunay triangulation for a given set p of. Zaliks 39 sweepline algorithm which is based on legalization 4, and the sweepcircle algorithm proposed by adam et. Constrained delaunay triangulations jhu computer science. Previously, the fastest algorithm for constructing the cdt. This paper discusses the definitions and basic properties of the standard and constrained delaunay triangulations. If the delaunay triangulation is calculated using the bowyer watson algorithm. Fast segment insertion and incremental construction of constrained.
A faster circlesweep delaunay triangulation algorithm. Lewis and robinson 25 describe an 0n1 algorithm based on a divideandconquer approach for triangulating a simple polygon with internal points. For a set of points on the same line there is no delaunay triangulation the notion. This paper introduces a new algorithm for constrained delaunay triangulation, which is built upon sets of points and constraining edges.
Sweepline algorithm for constrained delaunay triangulation. A direct algorithm for computing constrained delaunay triangulation in 2d is presented. A constrained triangulation is a triangulation that enforces the presence of specified edgesfor example, the. An efficient sweepline delaunay triangulation algorithm. The algorithm inserts points along the constrained edges break lines to maintain the delaunay criterion. It is based on a sweepline paradigm, which is combined with a local optimization criteriona characteristic of incremental insertion algorithms. It has various applications in geographical information system gis, for example, iso. Fortunes 18 sweepline algorithm which adds a delaunay triangle to the triangulation at some event points. The voronoi diagram for seven points in the plane is shown by the dotted lines in fig. Compare this defintion with the definition of the unconstrained delaunay triangulation given above. Constrained delaunay triangulation of a simple polygon algorithms for constructing the constrained delaunay triangulation of a simple polygon are described in 25, 24. This algorithm constructs first a delaunay triangulation for the set. A planar straight line graph and its constrained delaunay triangulation.
An online algorithm for constrained delaunay triangulation. It has various applications in geographical information system gis, for example, isolines triangulation or the triangulation of polygons in land cadastre. On constructing delaunay triangulations for sets constrained by line. Each voronoi polygon is constructed by drawing perpendicular bisectors. Sweepline algorithm for constrained delaunay triangulation article in international journal of geographical information science 224. A triangulation t is a constrained delaunay triangulation cdt of g if each edge of g is an edge of t and for each remaining edge e. The sweepline status is represented by a socalled advancing front, which is implemented as a hashtable.
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