Academic Journal
Tangent Blow‐Ups for Processing Non‐Manifold Geometry.
| Τίτλος: | Tangent Blow‐Ups for Processing Non‐Manifold Geometry. |
|---|---|
| Συγγραφείς: | Petrov, Alice1 (AUTHOR), Nabizadeh, Mohammad Sina1 (AUTHOR), Dodik, Ana1 (AUTHOR), Solomon, Justin1 (AUTHOR) |
| Πηγή: | Computer Graphics Forum. Aug2026, p1. 19p. 24 Illustrations. |
| Θεματικοί όροι: | Blowing up (Algebraic geometry), Mathematical singularities, Computational geometry, Differential operators, Geometry, Parameterization, Curvature measurements, Geodesics |
| Περίληψη: | Many geometry processing pipelines implicitly assume their input data is a manifold, or is sampled from one, with a unique tangent plane at every point. Geometric data, however, routinely contains sharp features like edges, corners, self‐intersections, branching junctions, and other singularities, rendering standard methods ill‐defined at these points. To bring geometry processing to these and other singular spaces, we introduce the “tangent blow‐up,” a representation inspired by algebraic geometry that restores structure at singularities by lifting to the product of the ambient space and the Grassmannian of tangent planes. After iterating this construction, points that coincide in position but differ in tangent direction, curvature, or higher‐order contact become well‐separated. We equip the tangent blow‐up with a product metric and define discretized differential operators, such as the gradient, divergence, and Laplacian, directly in the lifted domain. We demonstrate our framework across geodesic computation, segmentation, surface parameterization, and curvature estimation. [ABSTRACT FROM AUTHOR] |
| Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Tangent Blow‐Ups for Processing Non‐Manifold Geometry. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Petrov%2C+Alice%22">Petrov, Alice</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Nabizadeh%2C+Mohammad+Sina%22">Nabizadeh, Mohammad Sina</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Dodik%2C+Ana%22">Dodik, Ana</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Solomon%2C+Justin%22">Solomon, Justin</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Computer+Graphics+Forum%22">Computer Graphics Forum</searchLink>. Aug2026, p1. 19p. 24 Illustrations. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Blowing+up+%28Algebraic+geometry%29%22">Blowing up (Algebraic geometry)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+geometry%22">Computational geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+operators%22">Differential operators</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Parameterization%22">Parameterization</searchLink><br /><searchLink fieldCode="DE" term="%22Curvature+measurements%22">Curvature measurements</searchLink><br /><searchLink fieldCode="DE" term="%22Geodesics%22">Geodesics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Many geometry processing pipelines implicitly assume their input data is a manifold, or is sampled from one, with a unique tangent plane at every point. Geometric data, however, routinely contains sharp features like edges, corners, self‐intersections, branching junctions, and other singularities, rendering standard methods ill‐defined at these points. To bring geometry processing to these and other singular spaces, we introduce the “tangent blow‐up,” a representation inspired by algebraic geometry that restores structure at singularities by lifting to the product of the ambient space and the Grassmannian of tangent planes. After iterating this construction, points that coincide in position but differ in tangent direction, curvature, or higher‐order contact become well‐separated. We equip the tangent blow‐up with a product metric and define discretized differential operators, such as the gradient, divergence, and Laplacian, directly in the lifted domain. We demonstrate our framework across geodesic computation, segmentation, surface parameterization, and curvature estimation. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1111/cgf.70527 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 1 Subjects: – SubjectFull: Blowing up (Algebraic geometry) Type: general – SubjectFull: Mathematical singularities Type: general – SubjectFull: Computational geometry Type: general – SubjectFull: Differential operators Type: general – SubjectFull: Geometry Type: general – SubjectFull: Parameterization Type: general – SubjectFull: Curvature measurements Type: general – SubjectFull: Geodesics Type: general Titles: – TitleFull: Tangent Blow‐Ups for Processing Non‐Manifold Geometry. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Petrov, Alice – PersonEntity: Name: NameFull: Nabizadeh, Mohammad Sina – PersonEntity: Name: NameFull: Dodik, Ana – PersonEntity: Name: NameFull: Solomon, Justin IsPartOfRelationships: – BibEntity: Dates: – D: 13 M: 08 Text: Aug2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 01677055 Titles: – TitleFull: Computer Graphics Forum Type: main |
| ResultId | 1 |