One-Shot Method for Computing Generalized Winding Numbers
| dc.contributor.author | Martens, Cedric | en_US |
| dc.contributor.author | Bessmeltsev, Mikhail | en_US |
| dc.contributor.editor | Attene, Marco | en_US |
| dc.contributor.editor | Sellán, Silvia | en_US |
| dc.date.accessioned | 2025-06-20T07:40:05Z | |
| dc.date.available | 2025-06-20T07:40:05Z | |
| dc.date.issued | 2025 | |
| dc.description.abstract | The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to compute a generalized winding number, based only on the surface boundary and the intersections of a single ray with the surface, supporting any oriented surface representations that support a ray intersection query. Due to the focus on the boundary, our algorithm has a unique set of properties. For 2D parametric curves, on a regular grid of query points, our method is up to 4× faster than the current state of the art, maintaining the same precision. In 3D, our method can compute a winding number of a surface without discretizing it, including parametric surfaces. For some meshes with many triangles and a simple boundary, our method is faster than the hierarchical evaluation of the generalized winding number while still being precise. Similarly, on some parametric surfaces with a simple boundary, our method can be faster than adaptive quadrature. We validate our algorithms theoretically, numerically, and by demonstrating a gallery of results on a variety of parametric surfaces and meshes, as well uses in a variety of applications, including voxelizations and boolean operations. | en_US |
| dc.description.number | 5 | |
| dc.description.sectionheaders | Implicit Representations | |
| dc.description.seriesinformation | Computer Graphics Forum | |
| dc.description.volume | 44 | |
| dc.identifier.doi | 10.1111/cgf.70194 | |
| dc.identifier.issn | 1467-8659 | |
| dc.identifier.pages | 15 pages | |
| dc.identifier.uri | https://doi.org/10.1111/cgf.70194 | |
| dc.identifier.uri | https://diglib.eg.org/handle/10.1111/cgf70194 | |
| dc.publisher | The Eurographics Association and John Wiley & Sons Ltd. | en_US |
| dc.rights | Attribution 4.0 International License | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | CCS Concepts: Computing methodologies → Shape analysis; Parametric curve and surface models | |
| dc.subject | Computing methodologies → Shape analysis | |
| dc.subject | Parametric curve and surface models | |
| dc.title | One-Shot Method for Computing Generalized Winding Numbers | en_US |
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