Triangulating a Convex Polygon with Small Number of Non-standard Bars Extended Abstract
Yinfeng Xu, Wenqiang Dai, Naoki Katoh, Makoto Ohsaki · 2005
For a given convex polygon with inner angle no less than 2 π and boundary edge bounded by (l, αl )f or 1≤ α ≤ 1.4, where l is a given standard bar's length, we investigate the problem of triangulating the polygon using some Steiner points such that (i) the length of each edge in triangulation is bounded by (βl,2l), where β is a given constant and meets 0 <β< 1 , and (ii) the number of non-standard bars in the triangulation is minimum. This problem is motivated by practical applications and has not been studied previously. In this paper, we present a heuristic to solve the above problem, which is based on the heuristic to generate a triangular mesh with more number of standard bars and shorter maximal edge length, and a process to make the length of each edge lower bounded. Our procedure is simple and easily implemented for this problem, and we prove that it has good performance guaranteed.