Towards Voronoi Diagrams of Surface Patches
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912113193123840 |
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| author | Wang, Pengfei Song, Jiantao Wang, Lei Xin, Shiqing Yan, Dongming Chen, Shuangmin Tu, Changhe Wang, Wenping |
| author_facet | Wang, Pengfei Song, Jiantao Wang, Lei Xin, Shiqing Yan, Dongming Chen, Shuangmin Tu, Changhe Wang, Wenping |
| contents | Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface. Commonly, existing approaches yield medial-axis surfaces with various artifacts, including zigzag boundaries, bumpy surfaces, unwanted spikes, and non-smooth stitching curves. Considering that the surface of a CAD model can be easily decomposed into a collection of surface patches, its 3D medial axis can be extracted by computing the Voronoi diagram of these surface patches, where each surface patch serves as a generator. However, no solver currently exists for accurately computing such an extended Voronoi diagram. Under the assumption that each generator defines a linear distance field over a sufficiently small range, our approach operates by tetrahedralizing the region of interest and computing the medial axis within each tetrahedral element. Just as SurfaceVoronoi computes surface-based Voronoi diagrams by cutting a 3D prism with 3D planes (each plane encodes a linear field in a triangle), the key operation in this paper is to conduct the hyperplane cutting process in 4D, where each hyperplane encodes a linear field in a tetrahedron. In comparison with the state-of-the-art, our algorithm produces better outcomes. Furthermore, it can also be used to compute the offset surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards Voronoi Diagrams of Surface Patches Wang, Pengfei Song, Jiantao Wang, Lei Xin, Shiqing Yan, Dongming Chen, Shuangmin Tu, Changhe Wang, Wenping Graphics Extraction of a high-fidelity 3D medial axis is a crucial operation in CAD. When dealing with a polygonal model as input, ensuring accuracy and tidiness becomes challenging due to discretization errors inherent in the mesh surface. Commonly, existing approaches yield medial-axis surfaces with various artifacts, including zigzag boundaries, bumpy surfaces, unwanted spikes, and non-smooth stitching curves. Considering that the surface of a CAD model can be easily decomposed into a collection of surface patches, its 3D medial axis can be extracted by computing the Voronoi diagram of these surface patches, where each surface patch serves as a generator. However, no solver currently exists for accurately computing such an extended Voronoi diagram. Under the assumption that each generator defines a linear distance field over a sufficiently small range, our approach operates by tetrahedralizing the region of interest and computing the medial axis within each tetrahedral element. Just as SurfaceVoronoi computes surface-based Voronoi diagrams by cutting a 3D prism with 3D planes (each plane encodes a linear field in a triangle), the key operation in this paper is to conduct the hyperplane cutting process in 4D, where each hyperplane encodes a linear field in a tetrahedron. In comparison with the state-of-the-art, our algorithm produces better outcomes. Furthermore, it can also be used to compute the offset surface. |
| title | Towards Voronoi Diagrams of Surface Patches |
| topic | Graphics |
| url | https://arxiv.org/abs/2411.06471 |