Uniform Pattern Mapping for Freeform Surface

Abstract

This study proposes a new pattern mapping method that enables keeping isometric and conformal conditions between 2D patterns and mapped patterns on freeform surfaces. Although the established method called parameterization is widely used in the CG field, there is no critical method in the manufacturing field. In this paper, a differential equation of conformal condition around an arbitrary point on the freeform surface is formulated, and uniform pattern mapping with less distortion on the freeform surface is enabled by combining the equation of the isometric condition proposed by the previous report. Moreover, the effectiveness of the proposed method is confirmed through some case studies.