Geometric Illumination of Implicit Surfaces
<|reference_start|>Geometric Illumination of Implicit Surfaces: 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.<|reference_end|>
@article{zamboj2024geometric,
    title={Geometric Illumination of Implicit Surfaces},
    author={Michal Zamboj, Jakub v{R}ada},
    journal={arXiv preprint arXiv:2403.19679},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19679},
    primaryClass={cs.CG}
}