Article

GPU-assisted positive mean value coordinates for mesh deformations

Authors:

Yaron Lipman,

Johannes Kopf,

Daniel Cohen-Or,

David LevinAuthors Info & Claims

SGP '07: Proceedings of the fifth Eurographics symposium on Geometry processing

Pages 117 - 123

Published: 04 July 2007 Publication History

Abstract

In this paper we introduce positive mean value coordinates (PMVC) for mesh deformation. Following the observations of Joshi et al. [JMD*07] we show the advantage of having positive coordinates. The control points of the deformation are the vertices of a "cage" enclosing the deformed mesh. To define positive mean value coordinates for a given vertex, the visible portion of the cage is integrated over a sphere.

Unlike MVC [JSW05], PMVC are computed numerically. We show how the PMVC integral can be efficiently computed with graphics hardware. While the properties of PMVC are similar to those of Harmonic coordinates [JMD*07], the setup time of the PMVC is only of a few seconds for typical meshes with 30K vertices. This speed-up renders the new coordinates practical and easy to use.

References

[1]

{Coq90} Coquillart S.: Extended free-form deformation: a sculpturing tool for 3d geometric modeling. Proceedings of SIGGRAPH '90 (1990), 187--196.

Digital Library

Google Scholar

[2]

{FKR05} Floater M. S., Kos G., Reimers M.: Mean value coordinates in 3d. Computer Aided Geometric Design 22, 7 (2005), 623--631.

Digital Library

Google Scholar

[3]

{Flo03} Floater M. S.: Mean value coordinates. Computer Aided Geometric Design 20, 1 (2003), 19--27.

Digital Library

Google Scholar

[4]

{HF06} Hormann K., Floater M. S.: Mean value coordinates for arbitrary planar polygons. ACM Transactions on Graphics 25, 4 (2006), 1424--1441.

Digital Library

Google Scholar

[5]

{JMD*07} Joshi P., Meyer M., DeRose T., Green B., Sanocki T.: Harmonic coordinates for character articulation. Transactions on Graphics 26, 3 (Proc. SIGGRAPH) (2007).

Digital Library

Google Scholar

[6]

{JSW05} Ju T., Schaefer S., Warren J.: Mean value coordinates for closed triangular meshes. vol. 24, 3 (Proc. SIGGRAPH), pp. 561--566.

Digital Library

Google Scholar

[7]

{SP86} Sederberg T. W., Parry S. R.: Free-form deformation of solid geometric models. Proceedings of SIGGRAPH '86 (1986), 151--160.

Digital Library

Google Scholar

Cited By

View all

Qin KZhou YYing CLi YDeng C(2024)C^0 Generalized Coons Patches for High-order Cage-based DeformationACM Transactions on Graphics10.1145/368797243:6(1-15)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687972
Lin ZChen R(2024)Polynomial Cauchy Coordinates for Curved CagesSIGGRAPH Asia 2024 Conference Papers10.1145/3680528.3687654(1-8)Online publication date: 3-Dec-2024
https://dl.acm.org/doi/10.1145/3680528.3687654
Dodik AStein OSitzmann VSolomon J(2023)Variational Barycentric CoordinatesACM Transactions on Graphics10.1145/361840342:6(1-16)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618403
Show More Cited By

Index Terms

GPU-assisted positive mean value coordinates for mesh deformations
1. Computing methodologies
  1. Computer graphics
    1. Image manipulation
    2. Rendering

Recommendations

Mean value coordinates for quad cages in 3D

Space coordinates offer an elegant, scalable and versatile framework to propagate (multi-)scalar functions from the boundary vertices of a 3-manifold, often called a cage, within its volume. These generalizations of the barycentric coordinate system ...
Mean value coordinates for closed triangular meshes

Constructing a function that interpolates a set of values defined at vertices of a mesh is a fundamental operation in computer graphics. Such an interpolant has many uses in applications such as shading, parameterization and deformation. For closed ...
Mean value coordinates

We derive a generalization of barycentric coordinates which allows a vertex in a planar triangulation to be expressed as a convex combination of its neighbouring vertices. The coordinates are motivated by the Mean Value Theorem for harmonic functions ...

Comments

Information & Contributors

Information

Published In

SGP '07: Proceedings of the fifth Eurographics symposium on Geometry processing

July 2007

273 pages

ISBN:9783905673463

Conference Chairs:
Alexander Belyaev
MPI Informatik
,
Michael Garland
NVIDIA Corporation

Publisher

Eurographics Association

Goslar, Germany

Publication History

Published: 04 July 2007

Check for updates

Qualifiers

Article

Conference

SGP '07

Sponsor:

EUROGRAPHICS

SGP '07: Geometry processing

July 4 - 6, 2007

Barcelona, Spain

Acceptance Rates

SGP '07 Paper Acceptance Rate 21 of 74 submissions, 28%;

Overall Acceptance Rate 64 of 240 submissions, 27%

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

56
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 24 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Qin KZhou YYing CLi YDeng C(2024)C^0 Generalized Coons Patches for High-order Cage-based DeformationACM Transactions on Graphics10.1145/368797243:6(1-15)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687972
Lin ZChen R(2024)Polynomial Cauchy Coordinates for Curved CagesSIGGRAPH Asia 2024 Conference Papers10.1145/3680528.3687654(1-8)Online publication date: 3-Dec-2024
https://dl.acm.org/doi/10.1145/3680528.3687654
Dodik AStein OSitzmann VSolomon J(2023)Variational Barycentric CoordinatesACM Transactions on Graphics10.1145/361840342:6(1-16)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618403
Michel ÉThiery J(2023)Polynomial 2D Green Coordinates for Polygonal CagesACM SIGGRAPH 2023 Conference Proceedings10.1145/3588432.3591499(1-9)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.1145/3588432.3591499
Thiery JMemari PBoubekeur T(2018)Mean value coordinates for quad cages in 3DACM Transactions on Graphics10.1145/3272127.327506337:6(1-14)Online publication date: 4-Dec-2018
https://dl.acm.org/doi/10.1145/3272127.3275063
Savoye Y(2018)Cage-based performance captureACM SIGGRAPH 2018 Courses10.1145/3214834.3214836(1-72)Online publication date: 12-Aug-2018
https://dl.acm.org/doi/10.1145/3214834.3214836
Bang SLee S(2018)Spline Interface for Intuitive Skinning Weight EditingACM Transactions on Graphics10.1145/318656537:5(1-14)Online publication date: 14-Sep-2018
https://dl.acm.org/doi/10.1145/3186565
Chen RWeber O(2017)GPU-accelerated locally injective shape deformationACM Transactions on Graphics10.1145/3130800.313084336:6(1-13)Online publication date: 20-Nov-2017
https://dl.acm.org/doi/10.1145/3130800.3130843
Hefetz EChien EWeber O(2017)Fast Planar Harmonic Deformations with Alternating Tangential ProjectionsComputer Graphics Forum10.1111/cgf.1325536:5(175-188)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1111/cgf.13255
Meng WGuo JBonaventura XSbert MZhang X(2017)Shape exploration of 3D heterogeneous models based on cagesMultimedia Tools and Applications10.1007/s11042-016-3642-576:10(12369-12390)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s11042-016-3642-5
Show More Cited By

Abstract

References

Cited By

Index Terms

Recommendations

Mean value coordinates for quad cages in 3D

Mean value coordinates for closed triangular meshes

Mean value coordinates

Comments

Information

Published In

Sponsors

Publisher

Publication History

Check for updates

Qualifiers

Conference

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Share

Share this Publication link

Share on social media

Affiliations