A Novel 3D Mapping Representation and its Applications

Abstract: The analysis of mapping relationships and distortions in multidimensional data poses a significant challenge in contemporary research. While Beltrami coefficients offer a precise description of distortions in two-dimensional mappings, current tools lack this capability in the context of three-dimensional space. This paper presents a novel approach: a 3D quasiconformal representation that captures the local dilation of 3D mappings, along with a reconstruction algorithm that establishes a connection between this representation and the corresponding mapping. Experimental results showcase the algorithm's effectiveness in mapping reconstruction, keyframe interpolation, and mapping compression. These features bear a resemblance to the 2D Linear Beltrami Solver technique. The work presented in this paper offers a promising solution for the precise analysis and adjustment of distortions in 3D data and mappings.