BPM: Blended Piecewise Moebius Maps
Shir Rorberg, Amir Vaxman, Mirela Ben-Chen

TL;DR
This paper introduces a new Moebius-based interpolator for discrete maps between triangle meshes, producing smooth, low-distortion mappings suitable for texture transfer and surface parameterization.
Contribution
The paper presents a closed-form, local Moebius interpolator that improves smoothness and reduces distortion in discrete mesh mappings, applicable to various mesh types.
Findings
Produces smoother texture transfer than existing methods
Achieves lower quasi-conformal distortion
Works effectively even on coarse triangulations
Abstract
We propose a novel Moebius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a smooth map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi-conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed-form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer…
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Taxonomy
Topics3D Shape Modeling and Analysis · Advanced Numerical Analysis Techniques · Computer Graphics and Visualization Techniques
