An optimal bound for high-quality conforming triangulations

Abstract

This paper shows that, for any plane geometric graph $$\mathcal{G}$$ withn vertices, there is a triangulation $$\mathcal{T}$$ that conforms to $$\mathcal{G}$$ , i.e., each edge of $$\mathcal{G}$$ is the union of some edges of $$\mathcal{T}$$ , where $$\mathcal{T}$$ hasO(n2) vertices with each angle of its triangles measuring no more than 11/15ź. Additionally, $$\mathcal{T}$$ can be computed inO(n2 logn) time.