Quasiconformal rectilinear map

Abstract

This paper presents a novel method to compute the quasiconformal rectilinear map for a 2D polygonal subdivision, which keeps the original topology and best preserves the shape of the original input in the elasticity sense by the curve-driven quasiconformal mapping. We first automatically compute the straightening styles of the subdivision curves, which are then utilized to generate the optimal rectilinear map with the minimal harmonic energy. The quasiconformal rectilinear map is aesthetically pleasing for human perception, and hierarchically and progressively flexible for the design of spatial data structures. Based on the quasiconformal rectilinear map, an approach is given to compute the polyomino map. We evaluate the proposed structural maps in the data visualization application.