Geometric Illumination of Implicit Surfaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914437898698752 |
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| author | Zamboj, Michal Řada, Jakub |
| author_facet | Zamboj, Michal Řada, Jakub |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric Illumination of Implicit Surfaces Zamboj, Michal Řada, Jakub Computational Geometry 68U05, 14J70, 51N15 I.3.5; J.6 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. |
| title | Geometric Illumination of Implicit Surfaces |
| topic | Computational Geometry 68U05, 14J70, 51N15 I.3.5; J.6 |
| url | https://arxiv.org/abs/2403.19679 |