Finding a Triangular Mesh with a Constant Number of Different Edge Lengths
Shin‐ichi Tanigawa · IEICE Transactions on Information and Systems · 2006
We consider the problem of triangulating an x-monotone polygon with a small number of different edge lengths using Steiner points. Given a parameter α, where 0 < α < 1, we shall present an algorithm for finding an almost uniform triangular mesh with 3π/8α2 + o(1/α2) different edge lengths such that every edge length is between l and (2 + √2α)l. Experiments demonstrate the effectiveness of this algorithm.