research-article

Frame field generation through metric customization

Authors:

Xianzhong Fang,

Mathieu DesbrunAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 34, Issue 4

Article No.: 40, Pages 1 - 11

https://doi.org/10.1145/2766927

Published: 27 July 2015 Publication History

Abstract

This paper presents a new technique for frame field generation. As generic frame fields (with arbitrary anisotropy, orientation, and sizing) can be regarded as cross fields in a specific Riemannian metric, we tackle frame field design by first computing a discrete metric on the input surface that is compatible with a sparse or dense set of input constraints. The final frame field is then found by computing an optimal cross field in this customized metric. We propose frame field design constraints on alignment, size, and skewness at arbitrary locations on the mesh as well as along feature curves, offering much improved flexibility over previous approaches. We demonstrate the advantages of our frame field generation through the automatic quadrangulation of man-made and organic shapes with controllable anisotropy, robust handling of narrow surface strips, and precise feature alignment. We also extend our technique to the design of n-vector fields.

Supplementary Material

MP4 File (a40.mp4)

Download
16.17 MB

References

[1]

Alliez, P., Cohen-Steiner, D., Devillers, O., Lévy, B., and Desbrun, M. 2003. Anisotropic polygonal remeshing. ACM Trans. Graph. 22, 3 (July), 485--493.

Digital Library

[2]

Ben-Chen, M., Gotsman, C., and Bunin, G. 2008. Conformal flattening by curvature prescription and metric scaling. Comput. Graph. Forum 27, 2, 449--458.

[3]

Bommes, D., Zimmer, H., and Kobbelt, L. 2009. Mixed-integer quadrangulation. ACM Trans. Graph. 28, 3 (July), 77:1--77:10.

Digital Library

[4]

Crane, K., Desbrun, M., and Schrder, P. 2010. Trivial connections on discrete surfaces. Comput. Graph. Forum 29, 5, 1525--1533.

[5]

de Goes, F., Liu, B., Budninskiy, M., Tong, Y., and Desbrun, M. 2014. Discrete 2-tensor fields on triangulations. Comput. Graph. Forum 33, 5, 13--24.

Digital Library

[6]

Diamanti, O., Vaxman, A., Panozzo, D., and Sorkine-Hornung, O. 2014. Designing n-polyvector fields with complex polynomials. Comput. Graph. Forum 33, 5.

Digital Library

[7]

Ebke, H.-C., Bommes, D., Campen, M., and Kobbelt, L. 2013. Qex: Robust quad mesh extraction. ACM Trans. Graph. 32, 6 (Nov.), 168:1--168:10.

Digital Library

[8]

Hertzmann, A., and Zorin, D. 2000. Illustrating smooth surfaces. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, 517--526.

Digital Library

[9]

Jin, M., Wang, Y., Yau, S.-T., and Gu, X. 2004. Optimal global conformal surface parameterization. In IEEE Visualization, 267--274.

Digital Library

[10]

Jin, M., Kim, J., and Gu, X. D. 2007. Discrete surface ricci flow: Theory and applications. In Proceedings of the 12th IMA International Conference on Mathematics of Surfaces XII, Springer-Verlag, 209--232.

Digital Library

[11]

Knöppel, F., Crane, K., Pinkall, U., and Schröder, P. 2013. Globally optimal direction fields. ACM Trans. Graph. 32, 4 (July), 59:1--59:10.

Digital Library

[12]

Lai, Y.-K., Jin, M., Xie, X., He, Y., Palacios, J., Zhang, E., Hu, S.-M., and Gu, X. 2010. Metric-driven RoSy field design and remeshing. IEEE Trans. Vis. Comput. Graph. 16, 1 (Jan.), 95--108.

Digital Library

[13]

Ling, R., Huang, J., Jüttler, B., Sun, F., Bao, H., and Wang, W. 2014. Spectral quadrangulation with feature curve alignment and element size control. ACM Trans. Graph. 34, 1 (Dec.), 11:1--11:11.

Digital Library

[14]

Liu, Y., Xu, W., Wang, J., Zhu, L., Guo, B., Chen, F., and Wang, G. 2011. General planar quadrilateral mesh design using conjugate direction field. ACM Trans. Graph. 30, 6 (Dec.), 140:1--140:10.

Digital Library

[15]

Liu, B., Tong, Y., de Goes, F., and Desbrun, M. 2015. Discrete connection and covariant derivative for vector field analysis and design. ACM Trans. Graph. (to appear).

[16]

Moler, C., and Loan, C. V. 2003. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review 45, 1, 3--49.

Digital Library

[17]

Myles, A., and Zorin, D. 2012. Global parametrization by incremental flattening. ACM Trans. Graph. 31, 4 (July), 109:1--09:11.

Digital Library

[18]

Myles, A., and Zorin, D. 2013. Controlled-distortion constrained global parametrization. ACM Trans. Graph. 32, 4 (July), 105:1--105:14.

Digital Library

[19]

Oprea, J. 2007. Differential Geometry and Its Applications. Mathematical Association of America.

[20]

Palacios, J., and Zhang, E. 2007. Rotational symmetry field design on surfaces. ACM Trans. Graph. 26, 3 (July).

Digital Library

[21]

Panozzo, D., Puppo, E., Tarini, M., and Sorkine-Hornung, O. 2014. Frame fields: Anisotropic and non-orthogonal cross fields. ACM Trans. Graph. 33, 4 (July), 134:1--134:11.

Digital Library

[22]

Ray, N., Vallet, B., Li, W. C., and Lévy, B. 2008. N-symmetry direction field design. ACM Trans. Graph. 27, 2 (May), 10:1--10:13.

Digital Library

[23]

Ray, N., Vallet, B., Alonso, L., and Levy, B. 2009. Geometry-aware direction field processing. ACM Trans. Graph. 29, 1 (Dec.), 1:1--1:11.

Digital Library

[24]

Schelter, W., 2015. Maxima -- a computer algebra system (version 5.35). http://maxima.sourceforge.net.

[25]

Springborn, B., Schröder, P., and Pinkall, U. 2008. Conformal equivalence of triangle meshes. ACM Trans. Graph. 27, 3 (Aug.), 77:1--77:11.

Digital Library

Cited By

Banerjee CNguyen KFookes CGeorge K(2024)Physics-Informed Computer Vision: A Review and PerspectivesACM Computing Surveys10.1145/368903757:1(1-38)Online publication date: 20-Aug-2024
https://dl.acm.org/doi/10.1145/3689037
Zhou JChen DDeng MDeng YSun YWang SXiong SZhu B(2024)Eulerian-Lagrangian Fluid Simulation on Particle Flow MapsACM Transactions on Graphics10.1145/365818043:4(1-20)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658180
Tao NRuan LDeng YZhu BWang BChen B(2024)A Vortex Particle-on-Mesh Method for Soap Film SimulationACM Transactions on Graphics10.1145/365816543:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658165
Show More Cited By

Index Terms

Frame field generation through metric customization
1. Computing methodologies
  1. Computer graphics
    1. Image manipulation
    2. Rendering

Recommendations

Boundary aligned smooth 3D cross-frame field

In this paper, we present a method for constructing a 3D cross-frame field, a 3D extension of the 2D cross-frame field as applied to surfaces in applications such as quadrangulation and texture synthesis. In contrast to the surface cross-frame field (...
Metric-Driven 3D Frame Field Generation
Controlling the size and shear of elements is crucial in pure hex or hex-dominant meshing. To this end, non-orthonormal frame fields that are almost everywhere integrable (except for the singularities) can play a key role. However, it is often challenging ...
Smoothness driven frame field generation for hexahedral meshing

For many years, providing an algorithm to generate hexahedral meshes that fulfill minimal geometric criteria (boundary-alignment, minimum of singularity vertices) and that is not limited to a category of geometries has been an open issue. In the past ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 34, Issue 4

August 2015

1307 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2809654

Issue’s Table of Contents

Copyright © 2015 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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 27 July 2015

Published in TOG Volume 34, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

67
Total Citations
View Citations
690
Total Downloads

Downloads (Last 12 months)37
Downloads (Last 6 weeks)3

Reflects downloads up to 04 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Banerjee CNguyen KFookes CGeorge K(2024)Physics-Informed Computer Vision: A Review and PerspectivesACM Computing Surveys10.1145/368903757:1(1-38)Online publication date: 20-Aug-2024
https://dl.acm.org/doi/10.1145/3689037
Zhou JChen DDeng MDeng YSun YWang SXiong SZhu B(2024)Eulerian-Lagrangian Fluid Simulation on Particle Flow MapsACM Transactions on Graphics10.1145/365818043:4(1-20)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658180
Tao NRuan LDeng YZhu BWang BChen B(2024)A Vortex Particle-on-Mesh Method for Soap Film SimulationACM Transactions on Graphics10.1145/365816543:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658165
Segall ARen JVaxman ASorkine-Hornung O(2024)Fabric Tessellation: Realizing Freeform Surfaces by SmockingACM Transactions on Graphics10.1145/365815143:4(1-20)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658151
Li XLi MHan XWang HYang YJiang C(2024)A Dynamic Duo of Finite Elements and Material PointsACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657449(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657449
Jain PQu ZChen PStein O(2024)Neural Monte Carlo Fluid SimulationACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657438(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657438
Simons LAmenta N(2024)Anisotropy and Cross FieldsComputer Graphics Forum10.1111/cgf.15132Online publication date: 5-Aug-2024
https://doi.org/10.1111/cgf.15132
Rodriguez CHuang T(2024)A variationally consistent reproducing kernel enhanced material point method and its applications to incompressible materialsComputational Mechanics10.1007/s00466-023-02381-073:3(599-618)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1007/s00466-023-02381-0
Lei NZhang PZheng XZhu YLuo Z(2023)Feature Preserving Parameterization for Quadrilateral Mesh Generation Based on Ricci Flow and Cross FieldComputer Modeling in Engineering & Sciences10.32604/cmes.2023.027296137:1(843-857)Online publication date: 2023
https://doi.org/10.32604/cmes.2023.027296
Deng YYu HZhang DWu JZhu B(2023)Fluid Simulation on Neural Flow MapsACM Transactions on Graphics10.1145/361839242:6(1-21)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618392
Show More Cited By

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents