A Modified de Casteljau Subdivision that Supports Smooth Stitching with Hierarchically Organized Bicubic Bezier Patches
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911772562161664 |
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| author | Zarrinmehr, Saied Akleman, Ergun Chen, Jianer |
| author_facet | Zarrinmehr, Saied Akleman, Ergun Chen, Jianer |
| contents | One of the theoretically intriguing problems in computer-aided geometric modeling comes from the stitching of the tensor product Bezier patches. When they share an extraordinary vertex, it is not possible to obtain continuity C1 or G1 along the edges emanating from that extraordinary vertex. Unfortunately, this stitching problem cannot be solved by using higher degree or rational polynomials. In this paper, we present a modified de Casteljau subdivision algorithm that can provide a solution to this problem. Our modified de Casteljau subdivision, when combined with topological modeling, provides a framework for interactive real-time modeling of piecewise smooth manifold meshes with arbitrary topology. The main advantage of the modified subdivision is that the continuity C1 on a given boundary edge does not depend on the positions of the control points on other boundary edges. The modified subdivision allows us to obtain the desired C1 continuity along the edges emanating from the extraordinary vertices along with the desired G1 continuity in the extraordinary vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Modified de Casteljau Subdivision that Supports Smooth Stitching with Hierarchically Organized Bicubic Bezier Patches Zarrinmehr, Saied Akleman, Ergun Chen, Jianer Computational Geometry Graphics Human-Computer Interaction Algebraic Geometry Algebraic Topology One of the theoretically intriguing problems in computer-aided geometric modeling comes from the stitching of the tensor product Bezier patches. When they share an extraordinary vertex, it is not possible to obtain continuity C1 or G1 along the edges emanating from that extraordinary vertex. Unfortunately, this stitching problem cannot be solved by using higher degree or rational polynomials. In this paper, we present a modified de Casteljau subdivision algorithm that can provide a solution to this problem. Our modified de Casteljau subdivision, when combined with topological modeling, provides a framework for interactive real-time modeling of piecewise smooth manifold meshes with arbitrary topology. The main advantage of the modified subdivision is that the continuity C1 on a given boundary edge does not depend on the positions of the control points on other boundary edges. The modified subdivision allows us to obtain the desired C1 continuity along the edges emanating from the extraordinary vertices along with the desired G1 continuity in the extraordinary vertices. |
| title | A Modified de Casteljau Subdivision that Supports Smooth Stitching with Hierarchically Organized Bicubic Bezier Patches |
| topic | Computational Geometry Graphics Human-Computer Interaction Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2402.04319 |