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A RESEARCH OF AMELIORATING ARITHMETIC ABOUT DELAUNAY TRANGULATION

Huang Di-long

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Abstract

Delaunay triangulation has been widely used in manifold fields and is long researched content in computer Graphics Image and visualization in scientific computing.This paper introduces a fast algorithm for generating 2D constrained Delaunay triangulation.In this method,a ring-shaped rectangle is applied to separate 2D disheveled points at first,and then,according to the property of Delaunay triangulation,new points are inserted from outside ring to inside ring,step by step.And then the effective Delaunay triangulation is found out by the end of every ring.So that the 2D Delaunay triangular grid is formed quickly.This algorithm is very simple and efficient and there is no recursive computation in it.Moreover,the 2D constrained Delaunay triangulation is solved by a new technique.The algorithm is approved by its applications in engineering.

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What this paper is about

Delaunay triangulation has been widely used in manifold fields and is long researched content in computer Graphics Image and visualization in scientific computing.This paper introduces a fast algorithm for generating 2D constrained Delaunay triangulation.In this method,a ring-shaped rectangle is applied to separate 2D disheveled points at first,and then,according to the property of Delaunay triangulation,new points are inserted from outside ring to inside ring,step by step.And then the effective Delaunay triangulation is found out by the end of every ring.So that the 2D Delaunay triangular grid is formed quickly.This algorithm is very simple and efficient and there is no recursive computation in it.Moreover,the 2D constrained Delaunay triangulation is solved by a new technique.The algorithm is approved by its applications in engineering.

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Available abstract

Delaunay triangulation has been widely used in manifold fields and is long researched content in computer Graphics Image and visualization in scientific computing.This paper introduces a fast algorithm for generating 2D constrained Delaunay triangulation.In this method,a ring-shaped rectangle is applied to separate 2D disheveled points at first,and then,according to the property of Delaunay triangulation,new points are inserted from outside ring to inside ring,step by step.And then the effective Delaunay triangulation is found out by the end of every ring.So that the 2D Delaunay triangular grid is formed quickly.This algorithm is very simple and efficient and there is no recursive computation in it.Moreover,the 2D constrained Delaunay triangulation is solved by a new technique.The algorithm is approved by its applications in engineering.

Key concepts: Delaunay triangulation, Bowyer–Watson algorithm, Chew's second algorithm, Constrained Delaunay triangulation, Pitteway triangulation, Ruppert's algorithm, Surface triangulation, Mathematics

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