Triangulating a Convex Polygon with Small Number of Non-standard Bars

For a given convex polygon with inner angle no less than $\frac{2}{3}\pi$ and boundary edge bounded by [l, αl] for 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 $0 < \beta <\frac{1}{2}$, 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.