Article

Linear rotation-invariant coordinates for meshes

Authors:

Daniel Cohen-OrAuthors Info & Claims

SIGGRAPH '05: ACM SIGGRAPH 2005 Papers

Pages 479 - 487

https://doi.org/10.1145/1186822.1073217

Published: 01 July 2005 Publication History

Abstract

We introduce a rigid motion invariant mesh representation based on discrete forms defined on the mesh. The reconstruction of mesh geometry from this representation requires solving two sparse linear systems that arise from the discrete forms: the first system defines the relationship between local frames on the mesh, and the second encodes the position of the vertices via the local frames. The reconstructed geometry is unique up to a rigid transformation of the mesh. We define surface editing operations by placing user-defined constraints on the local frames and the vertex positions. These constraints are incorporated in the two linear reconstruction systems, and their solution produces a deformed surface geometry that preserves the local differential properties in the least-squares sense. Linear combination of shapes expressed with our representation enables linear shape interpolation that correctly handles rotations. We demonstrate the effectiveness of the new representation with various detail-preserving editing operators and shape morphing.

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References

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Cited By

Kim KAngelina Uy MPaschalidou DJacobson AGuibas LSung M(2023)OptCtrlPoints: Finding the Optimal Control Points for Biharmonic 3D Shape DeformationComputer Graphics Forum10.1111/cgf.1496342:7Online publication date: 5-Nov-2023
https://doi.org/10.1111/cgf.14963
Regateiro JBoyer E(2022)Temporal Shape Transfer Network for 3D Human Motion2022 International Conference on 3D Vision (3DV)10.1109/3DV57658.2022.00054(424-432)Online publication date: Sep-2022
https://doi.org/10.1109/3DV57658.2022.00054
Sung MJiang ZAchlioptas PMitra NGuibas L(2020)DeformSyncNetACM Transactions on Graphics10.1145/3414685.341778339:6(1-16)Online publication date: 27-Nov-2020
https://dl.acm.org/doi/10.1145/3414685.3417783
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Index Terms

Linear rotation-invariant coordinates for meshes
1. Computing methodologies
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices
      2. Interpolation

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cover image ACM Conferences

SIGGRAPH '05: ACM SIGGRAPH 2005 Papers

July 2005

826 pages

ISBN:9781450378253

DOI:10.1145/1186822

Editor:
Markus Gross
Eidgenössische Technische Hochschule Zürich

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 July 2005

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SIGGRAPH05: Special Interest Group on Computer Graphics and Interactive Techniques Conference

July 31 - August 4, 2005

California, Los Angeles

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SIGGRAPH '05 Paper Acceptance Rate 98 of 461 submissions, 21%;

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

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Cited By

Kim KAngelina Uy MPaschalidou DJacobson AGuibas LSung M(2023)OptCtrlPoints: Finding the Optimal Control Points for Biharmonic 3D Shape DeformationComputer Graphics Forum10.1111/cgf.1496342:7Online publication date: 5-Nov-2023
https://doi.org/10.1111/cgf.14963
Regateiro JBoyer E(2022)Temporal Shape Transfer Network for 3D Human Motion2022 International Conference on 3D Vision (3DV)10.1109/3DV57658.2022.00054(424-432)Online publication date: Sep-2022
https://doi.org/10.1109/3DV57658.2022.00054
Sung MJiang ZAchlioptas PMitra NGuibas L(2020)DeformSyncNetACM Transactions on Graphics10.1145/3414685.341778339:6(1-16)Online publication date: 27-Nov-2020
https://dl.acm.org/doi/10.1145/3414685.3417783
Chandran PBradley DGross MBeeler T(2020)Semantic Deep Face Models2020 International Conference on 3D Vision (3DV)10.1109/3DV50981.2020.00044(345-354)Online publication date: Nov-2020
https://doi.org/10.1109/3DV50981.2020.00044
Uy MHuang JSung MBirdal TGuibas L(2020)Deformation-Aware 3D Model Embedding and RetrievalComputer Vision – ECCV 202010.1007/978-3-030-58571-6_24(397-413)Online publication date: 9-Nov-2020
https://doi.org/10.1007/978-3-030-58571-6_24
Xie HIgarashi TMiyata K(2018)Precomputed Panel Solver for Aerodynamics SimulationACM Transactions on Graphics10.1145/318576737:2(1-12)Online publication date: 23-Mar-2018
https://dl.acm.org/doi/10.1145/3185767
Marco JJarabo AJarosz WGutierrez D(2018)Second-Order Occlusion-Aware Volumetric Radiance CachingACM Transactions on Graphics10.1145/318522537:2(1-14)Online publication date: 2-Jul-2018
https://dl.acm.org/doi/10.1145/3185225
Rabinovich MHoffmann TSorkine-Hornung O(2018)Discrete Geodesic Nets for Modeling Developable SurfacesACM Transactions on Graphics10.1145/318049437:2(1-17)Online publication date: 28-Feb-2018
https://dl.acm.org/doi/10.1145/3180494
Brandt CScandolo LEisemann EHildebrandt K(2018)Modeling n-Symmetry Vector Fields using Higher-Order EnergiesACM Transactions on Graphics10.1145/317775037:2(1-18)Online publication date: 13-Mar-2018
https://dl.acm.org/doi/10.1145/3177750
Belcour LXie GHery CMeyer MJarosz WNowrouzezahrai D(2018)Integrating Clipped Spherical Harmonics ExpansionsACM Transactions on Graphics10.1145/301545937:2(1-12)Online publication date: 23-Mar-2018
https://dl.acm.org/doi/10.1145/3015459
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