TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.5.1.011
TI  - Coarse-grained curvature tensor on polygonal surfaces
PY  - 2022/03/11
UR  - https://scipost.org/SciPostPhysCore.5.1.011
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 5
IS  - 1
SP  - 011
A1  - Duclut, Charlie
AU  - Amiri, Aboutaleb
AU  - Paijmans, Joris
AU  - Jülicher, Frank
AB  - Using concepts from integral geometry, we propose a definition for a local coarse-grained curvature tensor that is well-defined on polygonal surfaces. This coarse-grained curvature tensor shows fast convergence to the curvature tensor of smooth surfaces, capturing with accuracy not only the principal curvatures but also the principal directions of curvature. Thanks to the additivity of the integrated curvature tensor, coarse-graining procedures can be implemented to compute it over arbitrary patches of polygons. When computed for a closed surface, the integrated curvature tensor is identical to a rank-2 Minkowski tensor. We also provide an algorithm to extend an existing C++ package, that can be used to compute efficiently local curvature tensors on triangulated surfaces.
ER  -

@Article{10.21468/SciPostPhysCore.5.1.011,
	title={{Coarse-grained curvature tensor on polygonal surfaces}},
	author={Charlie Duclut and Aboutaleb Amiri and Joris Paijmans and Frank Jülicher},
	journal={SciPost Phys. Core},
	volume={5},
	pages={011},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.5.1.011},
	url={https://scipost.org/10.21468/SciPostPhysCore.5.1.011},
}