Consistent Volumetric Discretizations Inside Self-Intersecting Surfaces
Decades of research have culminated in a robust geometry processing pipeline for surfaces. Most steps in this pipeline, like deformation, smoothing, subdivision and decimation, may create self‐intersections. Volumetric processing of solid shapes then becomes difficult, because obtaining a correct vo...
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| Vydáno v: | Computer graphics forum Ročník 32; číslo 5; s. 147 - 156 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford, UK
Blackwell Publishing Ltd
01.08.2013
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | Decades of research have culminated in a robust geometry processing pipeline for surfaces. Most steps in this pipeline, like deformation, smoothing, subdivision and decimation, may create self‐intersections. Volumetric processing of solid shapes then becomes difficult, because obtaining a correct volumetric discretization is impossible: existing tet‐meshing methods require watertight input. We propose an algorithm that produces a tetrahedral mesh that overlaps itself consistently with the self‐intersections in the input surface. This enables volumetric processing on self‐intersecting models. We leverage conformalized mean‐curvature flow, which removes self‐intersections, and define an intrinsically similar reverse flow, which prevents them. We tetrahedralize the resulting surface and map the mesh inside the original surface. We demonstrate the effectiveness of our method with applications to automatic skinning weight computation, physically based simulation and geodesic distance computation. |
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| AbstractList | Decades of research have culminated in a robust geometry processing pipeline for surfaces. Most steps in this pipeline, like deformation, smoothing, subdivision and decimation, may create self-intersections. Volumetric processing of solid shapes then becomes difficult, because obtaining a correct volumetric discretization is impossible: existing tet-meshing methods require watertight input. We propose an algorithm that produces a tetrahedral mesh that overlaps itself consistently with the self-intersections in the input surface. This enables volumetric processing on self-intersecting models. We leverage conformalized mean-curvature flow, which removes self-intersections, and define an intrinsically similar reverse flow, which prevents them. We tetrahedralize the resulting surface and map the mesh inside the original surface. We demonstrate the effectiveness of our method with applications to automatic skinning weight computation, physically based simulation and geodesic distance computation. [PUBLICATION ABSTRACT] Decades of research have culminated in a robust geometry processing pipeline for surfaces. Most steps in this pipeline, like deformation, smoothing, subdivision and decimation, may create self‐intersections. Volumetric processing of solid shapes then becomes difficult, because obtaining a correct volumetric discretization is impossible: existing tet‐meshing methods require watertight input. We propose an algorithm that produces a tetrahedral mesh that overlaps itself consistently with the self‐intersections in the input surface. This enables volumetric processing on self‐intersecting models. We leverage conformalized mean‐curvature flow, which removes self‐intersections, and define an intrinsically similar reverse flow, which prevents them. We tetrahedralize the resulting surface and map the mesh inside the original surface. We demonstrate the effectiveness of our method with applications to automatic skinning weight computation, physically based simulation and geodesic distance computation. |
| Author | Jacobson, Alec Schüller, Christian Sorkine-Hornung, Olga Panozzo, Daniele Sacht, Leonardo |
| Author_xml | – sequence: 1 givenname: Leonardo surname: Sacht fullname: Sacht, Leonardo organization: ETH Zurich, Switzerland – sequence: 2 givenname: Alec surname: Jacobson fullname: Jacobson, Alec organization: ETH Zurich, Switzerland – sequence: 3 givenname: Daniele surname: Panozzo fullname: Panozzo, Daniele organization: ETH Zurich, Switzerland – sequence: 4 givenname: Christian surname: Schüller fullname: Schüller, Christian organization: ETH Zurich, Switzerland – sequence: 5 givenname: Olga surname: Sorkine-Hornung fullname: Sorkine-Hornung, Olga organization: IMPA, Brazil |
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| References_xml | – reference: Botsch M., Pauly M., Wicke M., Gross M.: Adaptive space deformations based on rigid cells. Comput. Graph. Forum 26, 3 (2007), 339-347. 2. – reference: Foley J. D., Van Dam A., Feiner S. K., Hughes J. F.: Computer graphics: principles and practice (2nd ed.). Addison-Wesley Longman Publishing Co., Inc., Boston , MA , USA , 1990. 3. – reference: Baraff D., Witkin A., Kass M.: Untangling cloth. ACM Trans. Graph. 22, 3 (2003), 862-870. 3. – reference: Litman R., Bronstein A., Bronstein M.: Stable volumetric features in deformable shapes. Computers & Graphics 36, 5 (2012). 2. – reference: Attene M.: A lightweight approach to repairing digitized polygon meshes. The Visual Computer 26, 11 (2010), 1393-1406. 3, 8. – reference: Freitag L. A., Plassmann P.: Local optimization-based simplicial mesh untangling and improvement. International Journal for Numerical Methods in Engineering 49, 1-2 (2000), 109-125. 6. – reference: Harmon D., Panozzo D., Sorkine O., Zorin D.: Interference aware geometric modeling. ACM Trans. Graph. 30, 6 (2011). 2, 3. – reference: Labelle F., Shewchuk J. R.: Isosurface stuffing: fast tetrahedral meshes with good dihedral angles. ACM Trans. Graph. 26, 3 (2007). 2. – reference: Lipman Y.: Bounded distortion mapping spaces for triangular meshes. ACM Trans. Graph. 31, 4 (2012). 6. – reference: Li D., Sun X., Ren Z., Lin S., Tong Y., Guo B., Zhou K.: Transcut: Interactive rendering of translucent cutouts. IEEE TVCG 19, 3 (2012). 2. – reference: Luo L., Baran I., Rusinkiewicz S., Matusik W.: Chopper: partitioning models into 3D-printable parts. ACM Trans. Graph. 31, 6 (2012). 3. – reference: Shen C., O'Brien J. F., Shewchuk J. R.: Interpolating and approximating implicit surfaces from polygon soup. ACM Trans. Graph. 23, 3 (2004), 896-904. 3. – reference: Bridson R., Fedkiw R. P., Anderson J.: Robust treatment of collisions, contact, and friction for cloth animation. ACM Trans. Graph. 21, 3 (July 2002), 594-603. 3. – reference: Si H.: TetGen: A 3D Delaunay tetrahedral mesh generator, 2003. http://tetgen.berlios.de. 1, 2, 3, 6. – reference: Shewchuk J.: Unstructured Mesh Generation. Combinatorial Scientific Computing 12 (2012), 257. 2, 3. – reference: Crane K., Pinkall U., Schröder P.: Robust fairing via conformal curvature flow. ACM Trans. Graph. 32 (2013). 8. – reference: Knupp P.: Hexahedral and tetrahedral mesh untangling. Engineering with Computers 17, 3 (2001), 261-268. 6. – reference: Botsch M., Kobbelt L., Pauly M., Alliez P., Lévy B.: Polygon Mesh Processing. AK Peters, 2010. 1. – reference: Sorkine O.: Least-squares rigid motion using SVD. Tech. rep., Courant Institute of Mathematical Sciences, New York University, Feb. 2009. 6. – reference: Eppstein D., Mumford E.: Self-overlapping curves revisited. Society for Industrial and Applied Mathematics. 3. – reference: Jacobson A., Baran I., Kavan L., Popovic J., Sorkine O.: Fast automatic skinning transformations. ACM Trans. Graph. 31, 4 (2012). 5, 8. – reference: Willmore T.: Surfaces in conformal geometry. Annals of Global Analysis and Geometry 18, 3-4 (2000). 3. – reference: Jacobson A., Kavan L., Sorkine-Hornung O.: Robust inside-outside segmentation using generalized winding numbers. ACM Trans. Graph. 32, 4 (2013), to appear. 3, 7, 8. – reference: Jacobson A., Baran I., Popovic J., Sorkine O.: Bounded biharmonic weights for real-time deformation. ACM Trans. Graph. 30, 4 (2011). 7. – reference: Xu Y., Chen R., Gotsman C., Liu L.: Embedding a triangular graph within a given boundary. Comput. Aided Geom. Des. 28, 6 (2011). 6. – reference: Chao I., Pinkall U., Sanan P., Schröder P.: A simple geometric model for elastic deformations. ACM Trans. Graph. 29, 4 (July 2010), 38:1-38:6. 4, 5, 6. – year: 2011 – year: 2009 – volume: 31 issue: 6 year: 2012 article-title: Chopper: partitioning models into 3D‐printable parts publication-title: ACM Trans. Graph. – volume: 26 start-page: 1393 issue: 11 year: 2010 end-page: 1406 article-title: A lightweight approach to repairing digitized polygon meshes publication-title: The Visual Computer – volume: 31 issue: 4 year: 2012 article-title: Fast automatic skinning transformations publication-title: ACM Trans. Graph. – volume: 49 start-page: 1 year: 2000 end-page: 2 article-title: Local optimization‐based simplicial mesh untangling and improvement publication-title: International Journal for Numerical Methods in Engineering – start-page: 341 year: 2003 end-page: 348 – year: Feb. 2009 – volume: 30 issue: 4 year: 2011 article-title: Bounded biharmonic weights for real‐time deformation publication-title: ACM Trans. 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| SubjectTerms | Algorithms Computation Computer graphics Computer science Computer simulation Discretization Finite element method Pipelines Smoothing Studies Subdivisions |
| Title | Consistent Volumetric Discretizations Inside Self-Intersecting Surfaces |
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