Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation
Proceedings of the nineteenth annual symposium on Computational geometry
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Let $F$ and $G$ be two collections of a total of $n$ bivariate algebraic functions of constant maximum degree. The minimization diagrams of $F$, $G$ are the planar maps obtained by the $xy$-projections of the lower envelopes of $F$, $G$, respectively. We show that the combinatorial complexity of the overlay of the minimization diagrams of $F$ and of $G$ is $O(n^{2+\varepsilon})$, for any $\varepsilon