Conformal flattening of non-planar surface

Abstract

This paper presents an approach that uses conformal mapping to flattening a 3D surface to 2D plane. We propose an algorithm by traversing the mesh in a region growing way. The algorithm is greedy and begins with a seed triangle which can be chosen freely. In each operation, we develop a piecewise linear mapping function that is conformal. In addition, at first step, we initialize the planar triangle which corresponding to the seed triangle. The initialization ensures that the seed triangle flattening process produce no distortion. And in other steps, we reduce the distortion by unifying the vertices in the plane. Our approach is efficient and fast enough.