Constructing Piecewise Linear Homeomorphisms of Simple Polygons
✍ Scribed by Himanshu Gupta; Rephael Wenger
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 336 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0196-6774
No coin nor oath required. For personal study only.
✦ Synopsis
respectively. We present an algorithm to construct a piecewise linear homeomorphism between P and Q mapping each vertex p g P to q g Q by constructing i i isomorphic triangulations of P and Q. These isomorphic triangulations consist of Ž 2 . Ž . O M log n q n log n triangles where M is the size of the optimal minimum size Ž 2 . solution. The algorithm runs in O M log n q n log n time. We also give an Ž . O n q L q k log k algorithm for constructing k pairwise disjoint interior paths Ž . between k pairs of vertices in a simple polygon on n vertices using O L q k log k links. The number L is the sum of the interior link distances between the k pairs of vertices.