PreprintCC BY 4.0arXiv
Rational barycentric coordinates and low degree adjoints
Abstract
We study rational generalized barycentric coordinates (rational GBCs) on polytopes. We recall their essential theory and clarify some statements from the literature. We study polytopes that admit GBCs with low degree denominators (and hence, low degree (affine) adjoint polynomials). We give a full classification of polytopes that admit polynomial barycentric coordinates (i.e. constant adjoints).
Related
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BibTeX
@misc{winter2026rational,
title = {{Rational barycentric coordinates and low degree adjoints}},
author = {Martin Winter and Tom Baumbach},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02110},
eprint = {2611.02110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02110},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rational barycentric coordinates and low degree adjoints
AU - Martin Winter
AU - Tom Baumbach
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02110
UR - https://arxiv.org/abs/2611.02110
AB - We study rational generalized barycentric coordinates (rational GBCs) on polytopes. We recall their essential theory and clarify some statements from the literature. We study polytopes that admit GBCs with low degree denominators (and hence, low degree (affine) adjoint polynomials). We give a full classification of polytopes that admit polynomial barycentric coordinates (i.e. constant adjoints).
ER -