Conformal mapping
Introduction
Conformal mapping is a branch within the field of differential geometry characterized by its preservation of local angles on surfaces after mapping, maintaining a one-to-one correspondence between the surfaces before and after mapping. Similar to this method is the area-preserving mapping, which conserves local surface areas post-mapping and also upholds a one-to-one correspondence property. The development by Yueh et al. of Conformal Energy Minimization (CEM) and Stretch Energy Minimization (SEM) theories has expedited the realization of conformal mapping and area-preserving mapping.
There are three primary application domains for conformal mapping: remeshing, surface registration, and surface deformation. Remeshing aims to enhance the quality of surface meshes. Surface registration is utilized to establish correspondences between two distinct surfaces. Surface deformation, an extension of surface registration, involves altering one surface by controlling the changes based on the correspondences found between two distinct surfaces.