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. An online algorithm for constrained delaunay triangulation article pdf available in cvgip graphical models and image processing 544. A direct algorithm for computing constrained delaunay triangulation in 2d is presented. Sweepline algorithm for constrained delaunay triangulation. If the delaunay triangulation is calculated using the bowyer watson algorithm. This paper discusses the definitions and basic properties of the standard and constrained delaunay triangulations. Zaliks 39 sweepline algorithm which is based on legalization 4, and the sweepcircle algorithm proposed by adam et. Since many different insertions are possible, the algorithm computes only those that are on the delaunay circles of each intersected triangle. Lewis and robinson 25 describe an 0n1 algorithm based on a divideandconquer approach for triangulating a simple polygon with internal points. In mathematics and computational geometry, a delaunay triangulation for a given set p of. The sweepline status is represented by a socalled advancing front, which is implemented as a hashtable. Constrained delaunay triangulations jhu computer science. It is based on a sweepline paradigm, which is combined with a local optimization criteriona characteristic of incremental insertion algorithms.
The algorithm inserts points along the constrained edges break lines to maintain the delaunay criterion. 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 article in international journal of geographical information science 224. This paper introduces a new algorithm for constructing a 2d delaunay triangulation. Fortunes 18 sweepline algorithm which adds a delaunay triangle to the triangulation at some event points. Previously, the fastest algorithm for constructing the cdt. An efficient sweepline delaunay triangulation algorithm. For a set of points on the same line there is no delaunay triangulation the notion. It has various applications in geographical information system gis, for example, isolines triangulation or the triangulation of polygons in land cadastre. A faster circlesweep delaunay triangulation algorithm.
On constructing delaunay triangulations for sets constrained by line. Each voronoi polygon is constructed by drawing perpendicular bisectors. An online algorithm for constrained delaunay triangulation. 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. This algorithm constructs first a delaunay triangulation for the set. Fast segment insertion and incremental construction of constrained. Delaunay triangulation and the time required to build an arbitrary constrained. Constrained delaunay triangulation of a simple polygon algorithms for constructing the constrained delaunay triangulation of a simple polygon are described in 25, 24. A constrained triangulation is a triangulation that enforces the presence of specified edgesfor example, the.
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