| Title | Research and Implementation of Triangulation Algorithm with Constraints |
| Abstract | In geoscientific field, terrain data contains massive terrain features, for instance surficial ridge line, valley line, fracture line, islands, etc. The GIS workers gave full consideration to the case of terrain features, then developed the theory and algorithm of Delaunay triangulation with the constraints. The triangulation basing on constrained data set) which takes terrain features into consideration, is foundation of establishing the high precision Digital Terrain Models. It plays a crucial role on the establishment of high-quality DEM, and is widely applied in Geographic Information Systems, geoscience analysis, Computer Graphics, Multi-resolution DTM, etc.This paper elaborates classical algorithms of Delaunay Triangulation with constraints, in which two-step method is elaborated detailedly. In the first step of two-step method, incremental insertion algorithm is used for constructing Delaunay Triangulation. In incremental insertion algorithm, Convex Hull is used as the bounding box, and an algorithm for computing the convex hull of scattered plane point set through the extreme points on the boundary of plane is proposed. According to the extreme points, the plane point set is divided into five zones. The four zones on the boundary contain all convex vertexes. By computing extreme points of subsets in the four marginal zones, a polygon that contains all convex vertexes is obtained. After eliminating the concave vertexes, the convex hull of plane point set is obtained.The second step of two-step method is embedding constraints, in which the embedding process of the constrained line is classified detailedly, and realizes inserting the constrained edge into Delaunay Triangulation network.The Delaunay Triangulation algorithm of constrained data set with islands is studied. Based on the results of previous research, a general triangulation algorithm for constrained data set with islands is proposed. The algorithm firstly constructs Constrained Delaunay Triangulation with constraint polygons which are inner boundary of islands, then according to topological relations within edge, surface, arc segment, applies bidirectional search to find the triangle in island, lastly carries on certain corresponding processing to complete the Delaunay Triangulation algorithm with islands. By comparison and analysis of experimental results, the improved algorithm has better efficiency in the implementation.Experiments show that convex hull algorithm for computing the convex hull of scattered plane point set through the extreme points on the boundary of plane and improved triangulation algorithm for constrained data set with islands can effectively improve efficiency of constructing network. |
| Category | Internet |
| Keywords | Constraint, convex hull, Delaunay, Islands, TIN, |
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| Pages | 180 |
| Price | US$48.00 |
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Research and Implementation of Triangulation Algorithm with Constraints
Billy HU, Ph.D
E-Mail:itpaper@hotmail.com
TEL:1-888-786-998A
