BPM: Blended Piecewise Möbius Maps

Rorberg, Shir; Vaxman, Amir; Ben-Chen, Mirela

BPM: Blended Piecewise Möbius Maps

Files

v42i5_18_14914.pdf (19.26 MB)

Date

2023

Authors

Rorberg, Shir
Vaxman, Amir
Ben-Chen, Mirela

Publisher

The Eurographics Association and John Wiley & Sons Ltd.

Abstract

We propose a novel Möbius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a continuous 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 results, and lower quasi-conformal errors.

        @article{10.1111:cgf.14914
,
journal = {Computer Graphics Forum},
title = {{BPM: Blended Piecewise Möbius Maps
}},
author = {Rorberg, Shir and 
Vaxman, Amir and 
Ben-Chen, Mirela
},
year = {2023
},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.
},
ISSN = {1467-8659
},
DOI = {10.1111/cgf.14914
}
}