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.

本文提出了一种新的计算二维多边形细分的准保形直线映射的方法，该方法通过曲线驱动的准保形映射来保留原始拓扑并在弹性意义上最好地保留原始输入的形状。我们首先自动计算细分曲线的矫直样式，然后将其用于生成具有最小谐波能量的最佳直线图。准保形直线图在美学上使人感觉愉悦，并且在空间数据结构设计上具有层次性和渐进性。基于准保形直线图，给出了一种计算多米诺图的方法。我们在数据可视化应用程序中评估建议的结构图。