Memory‐Efficient Bijective Parameterizations of Very‐Large‐Scale Models

Abstract As high‐precision 3D scanners become more and more widespread, it is easy to obtain very‐large‐scale meshes containing at least millions of vertices. However, processing these very‐large‐scale meshes is still a very challenging task due to memory limitations. This paper focuses on a fundamental geometric processing task, i.e., bijective parameterization construction. To this end, we present a spline‐enhanced method to compute bijective and low distortion parameterizations for very‐large‐scale disk topology meshes. Instead of computing descent directions using the mesh vertices as variables, we estimate descent directions for each vertex by optimizing a proxy energy defined in spline spaces. Since the spline functions contain a small set of control points, it significantly decreases memory requirement. Besides, a divide‐and‐conquer method is proposed to obtain bijective initializations, and a submesh‐based optimization strategy is developed to reduce distortion further. The capability and feasibility of our method are demonstrated over various complex models. Compared to the existing methods for bijective parameterizations of very‐large‐scale meshes, our method exhibits better scalability and requires much less memory.