3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917378661548032 |
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| author | Řada, Jakub Zamboj, Michal |
| author_facet | Řada, Jakub Zamboj, Michal |
| contents | The paper is focused on the four-dimensional visualization of hypersurfaces represented by implicit equations without their parametrization. We describe a general method to find shadow boundaries in an arbitrary dimension and apply it in a three- and four-dimensional space. Furthermore, we design a system of polynomial equations to construct occluding contours of algebraic surfaces in a 4-D perspective. The method is presented on a composed 3-D scene and three 4-D cases with gradual complexity. In general, our goal is to improve the understanding of spatial properties in a four-dimensional space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12986 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective Řada, Jakub Zamboj, Michal General Mathematics 51N15 (Primary) 68U05, 14J70 (Secondary) I.3.5; J.6 The paper is focused on the four-dimensional visualization of hypersurfaces represented by implicit equations without their parametrization. We describe a general method to find shadow boundaries in an arbitrary dimension and apply it in a three- and four-dimensional space. Furthermore, we design a system of polynomial equations to construct occluding contours of algebraic surfaces in a 4-D perspective. The method is presented on a composed 3-D scene and three 4-D cases with gradual complexity. In general, our goal is to improve the understanding of spatial properties in a four-dimensional space. |
| title | 3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective |
| topic | General Mathematics 51N15 (Primary) 68U05, 14J70 (Secondary) I.3.5; J.6 |
| url | https://arxiv.org/abs/2307.12986 |