YF Xu, WQ Dai, N Katoh, M Ohsaki
COMPUTING AND COMBINATORICS, PROCEEDINGS 3595 481-489 2005年
For a given convex polygon with inner angle no less than 2/3 pi and boundary edge bounded by [1, alpha l] for 1 <= alpha <= 1.4, where 1 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 [beta l, 2l], where beta is a given constant and meets 0 < beta < 1, and (ii) the number of non-standard bars in the triangulation 2 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.