1. Graphics Programming 2006, Choi Nam-Seok, Dongseo Univ., E-mail:d8003150@dongseo.ac.kr Voronoi diagrams and Delaunay Triangulations 2006. 03. 20 Choi Nam-Seok kowon.dongseo.ac.kr/~d8003150

2. Graphics Programming 2006, Choi Nam-Seok, Dongseo Univ., E-mail:d8003150@dongseo.ac.kr Voronoi diagrams 임의의 공간을 site 를 기준으로 여러 개의 영역으로 구분하는 것 The Voronoi diagrams of a set S of points in the plane, called site, is a partitioning of the plane into n convex regions, one per site.

3. Graphics Programming 2006, Choi Nam-Seok, Dongseo Univ., E-mail:d8003150@dongseo.ac.kr Delaunay Triangulation Voronoi diagrams 내의 3 개의 사이트의 외접원 안에 다른 사이트 가 존재하지 않는다면, 그 다이어그램 내의 사이트들을 인접한 영 역의 사이트 들과 직선으로 연결함으로 삼각영역을 형성한다.

4. Computer Graphics Lab 2006, Choi Nam-Seok, Dongseo Univ., E-mail:d8003150@dongseo.ac.kr Delaunay Triangulation How to Triangulate p1 p2

5. Computer Graphics Lab 2006, Choi Nam-Seok, Dongseo Univ., E-mail:d8003150@dongseo.ac.kr Delaunay Triangulation The Guibas-Stolfi Algorithm –Improving Worst-Case Optimal Delaunay Triangulation Algorithms (Geoff Leach) –Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams.(L.Guibas, J.Stolfi) divide-and-conquer partition two halves remove and new L-R cross edges add

6. Graphics Programming 2006, Choi Nam-Seok, Dongseo Univ., E-mail:d8003150@dongseo.ac.kr Delaunay Triangulation Improving Worst-Case Optimal Delaunay Triangulation Algorithms (Geoff Leach) –divide-and-conquer –partition two halves –remove and new L-R cross edges add

7. Graphics Programming 2006, Choi Nam-Seok, Dongseo Univ., E-mail:d8003150@dongseo.ac.kr Programming result face_only_vertex.obj g v -1.5 -6 -1 v 1.5 -6 -1 v -3 -4 -2 v -1.5 -3 -1.5 v 0 -4 -2 v 1.5 -3 -1.5 v 3 -4 -2 v -4 -2 -1 v -1.5 -1.8 -2 v 0 -2.5 -1 v 1.5 -1.8 -2 v 4 -2 -1 v -2 0.5 -1 v 0 0 0 v 2 0.5 -1 v -4 2 -1.5 v -1 2.5 0 v 1 2.5 0 v 4 2 -1.5 v -2 4 -2 v 0 4.5 0 v 2 4 -2

8. Graphics Programming 2006, Choi Nam-Seok, Dongseo Univ., E-mail:d8003150@dongseo.ac.kr Reference [1] Geoff Leach. Improving Worst-Case Optimal Delaunay Triangulation Algorithms [2]http://goanna.cs.rmit.edu.au/~gl/research/comp_geom/delaunay/dela unay.htmlhttp://goanna.cs.rmit.edu.au/~gl/research/comp_geom/delaunay/dela unay.html