An interactive algorithm for quality constraint Delaunay triangulation

• Main Authors: Chu-Sheng Wang, 王竹生
• Other Authors: Jen-Ing Huang
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/56653118684171414614

碩士 === 輔仁大學 === 資訊工程學系 === 87 === Abstract A constrained Delaunay triangulation (CDT) is a Delaunay triangulation of a set of points and constraint lines. It is required in several applications, such as computer graphics, computational geometric, and geographic information system. In this paper, an improved on-line CDT algorithm faster than De Floriani’s[DFP92] method is proposed. The algorithm solves the CDT problems by updating an initial CDT through stepwise insertion of points and constraint lines. The modified algorithm is then combined with Ruppert’s[Rup94] Delaunay refinement algorithm to have guaranteed quality triangulations (no small angles in triangulations). This refinement is obtained to enhance the convergence and stability in the running time. The hybrid algorithm is also implemented for computational experiments. Several key implementation decisions are considered carefully , including the choice of programming language, the representation of data structures, the improvement of algorithms, the steps taken to refine an existing triangulation by the incremental insertion of points and constraint lines. Both the original on-line CDT algorithm and the improved version are coded and a comparison of their running times is reported. Through the process of computational experiment, the efficiency of the improved version is assessed, with quite good results. A computational experiment is also proceeded to demonstrate the quality refinement. An example is given to show the whole process of the hybrid algorithm, from the construction of a CDT to the refinement of the triangulation. The results are presented for different constraints of angles and triangle areas. We expect the interactive algorithm for quality CDT could be applied to the problem of approximating a surface as a basis of a multiresolution triangle-based surface model.