Geometric Illumination of Implicit Surfaces
Computational Geometry
2026-04-03 v1
Abstract
Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we provide a semi-algebraic representation of each part of the construction. To solve polynomial condition systems and find constrained regions, we apply algebraic computational algorithms for computing the Gr{\" o}bner basis and cylindrical algebraic decomposition. The final selection of illuminated and self-shaded components for polynomial surfaces of a degree higher than three is discussed. The text is accompanied by visualizations of illumination of surfaces up to degree eight.
Cite
@article{arxiv.2403.19679,
title = {Geometric Illumination of Implicit Surfaces},
author = {Michal Zamboj and Jakub Řada},
journal= {arXiv preprint arXiv:2403.19679},
year = {2026}
}