Conformal Mesh Deformations with Möbius Transformations

摘要

We establish a framework to design triangular and circular polygonalrnmeshes by using face-based compatible M¨obius transformations.rnEmbracing the viewpoint of surfaces from circles, we characterizerndiscrete conformality for such meshes, in which the invariants arerncircles, cross-ratios, and mutual intersection angles. Such transformationsrnare important in practice for editing meshes withoutrndistortions or loss of details. In addition, they are of substantialrntheoretical interest in discrete differential geometry. Our frameworkrnallows for handle-based deformations, and interpolation betweenrngiven meshes with controlled conformal error.