Skip to main content
SpringerLink
Log in

Texture mapping subdivision surfaces with hard constraints

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

We propose a texture mapping technique that allows user to directly manipulate texture coordinates of subdivision surfaces through adding feature correspondences. After features, or constraints, are specified by user on the subdivision surface, the constraints are projected back to the control mesh and a polygon matching/embedding algorithm is performed to generate polygon regions that embed texture coordinates of control mesh into different regions. After this step, some Steiner points are added to the control mesh. The generated texture coordinates exactly satisfy the input constraints but with high distortions. Then a constrained smoothing algorithm is performed to minimize distortions of the subdivision surface via updating texture coordinates of the control mesh. Finally, an Iterative Closest Point (ICP)-based deformation algorithm is performed to remove subdivision errors caused by the added Steiner points.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Algorithm 1
Fig. 3
Fig. 4
Fig. 5
Algorithm 2
Fig. 6
Algorithm 3
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Alexa, M.: Differential coordinates for local mesh morphing and deformation. Vis. Comput. V 19(2), 105–114 (2003)

    MATH  Google Scholar 

  2. Botsch, M., Sorkine, O.: On linear variational surface deformation methods. IEEE Trans. Vis. Comput. Graph. 14(1), 213–230 (2008)

    Article  Google Scholar 

  3. Catmull, E., Clark, J.: Recursively generated B-spline surfaces on arbitrary topological meshes. In: Seminal Graphics, pp. 183–188. ACM, New York (1998)

    Google Scholar 

  4. Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’99, pp. 317–324. ACM, New York (1999)

    Chapter  Google Scholar 

  5. Eck, M., DeRose, T., Duchamp, T., Hoppe, H., Lounsbery, M., Stuetzle, W.: Multiresolution analysis of arbitrary meshes. In: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’95, pp. 173–182. ACM, New York (1995)

    Chapter  Google Scholar 

  6. Eckstein, I., Surazhsky, V., Gotsman, C.: Texture mapping with hard constraints. Comput. Graph. Forum 20(3), 95–104 (2001)

    Article  Google Scholar 

  7. Guenter, B., Grimm, C., Wood, D., Malvar, H., Pighin, F.: Making faces. In: ACM SIGGRAPH 2005 Courses, SIGGRAPH’05. ACM, New York (2005)

    Google Scholar 

  8. He, L., Schaefer, S., Hormann, K.: Parameterizing subdivision surfaces. ACM Trans. Graph. 120, 1 (2010)

    Article  Google Scholar 

  9. Hormann, K., Lévy, B., Sheffer, A.: Mesh parameterization: theory and practice. In: ACM SIGGRAPH 2007 Courses, SIGGRAPH’07. ACM, New York (2007)

    Google Scholar 

  10. Huang, J., Shi, X., Liu, X., Zhou, K., Wei, L.-Y., Teng, S.-H., Bao, H., Guo, B., Shum, H.-Y.: Subspace gradient domain mesh deformation. In: ACM SIGGRAPH 2006 Papers, SIGGRAPH’06, pp. 1126–1134. ACM, New York (2006)

    Chapter  Google Scholar 

  11. Kraevoy, V., Sheffer, A., Gotsman, C.: Matchmaker: constructing constrained texture maps. ACM Trans. Graph. 22(3), 326–333 (2003)

    Article  Google Scholar 

  12. Lévy, B.: Constrained texture mapping for polygonal meshes. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH’01, pp. 417–424. ACM, New York (2001)

    Chapter  Google Scholar 

  13. Léy, B., Petitjean, S., Ray, N., Maillo, J.: Least squares conformal maps for automatic texture atlas generation. In: ACM SIGGRAPH Conference Proceedings. ACM Press, New York (2002)

    Google Scholar 

  14. Lipman, Y., Sorkine, O., Levin, D., Cohen-Or, D.: Linear rotation-invariant coordinates for meshes. In: Proceedings of ACM SIGGRAPH 2005, pp. 479–487. ACM Press, New York (2005)

    Chapter  Google Scholar 

  15. Liu, L., Zhang, L., Xu, Y., Gotsman, C., Gortler, S.J.: A local/global approach to mesh parameterization. Comput. Graph. Forum 27(5), 1495–1504 (2008)

    Article  Google Scholar 

  16. Loop, C.: Smooth subdivision surfaces based on triangles. Department of mathematics, University of Utah, Utah, USA (1987)

  17. Pinkall, U., Juni, S.D., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2, 15–36 (1993)

    Article  MATH  Google Scholar 

  18. Popa, T., Julius, D., Sheffer, A.: Material aware mesh deformations. In: ACM SIGGRAPH 2005 Posters, SIGGRAPH’05. ACM, New York (2005)

    Google Scholar 

  19. Shoemake, K., Duff, T.: Matrix animation and polar decomposition. In: Proceedings of the Conference on Graphics Interface’92, pp. 258–264. Morgan Kaufmann, San Francisco (1992)

    Google Scholar 

  20. Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., Seidel, H.-P.: Laplacian surface editing. In: Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP’04, pp. 175–184. ACM, New York (2004)

    Chapter  Google Scholar 

  21. Tutte, W.T.: Convex representations of graphs. Proc. Lond. Math. Soc. 10, 304–320 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  22. Weng, Y., Li, D., Tong, Y.: Constrained texture mapping on subdivision surfaces. In: Proceedings of the Computational Visual Media Conference (2012)

    Google Scholar 

  23. Yang, Y.-L., Kim, J., Luo, F., Hu, S.-M., Gu, X.: Optimal surface parameterization using inverse curvature map. IEEE Trans. Vis. Comput. Graph. 14(5)

  24. Zeng, W., Lui, L., Luo, F., Chan, T., Yau, S., Gu, X.: Computing quasiconformal maps on Riemann surfaces using discrete curvature flow (2010). arXiv:1005.4648v2 [math.NA]

  25. Zhou, K., Huang, J., Snyder, J., Liu, X., Bao, H., Guo, B., Shum, H.-Y.: Large mesh deformation using the volumetric graph Laplacian. ACM Trans. Graph. 24(3), 496–503 (2005)

    Article  Google Scholar 

  26. Zhou, K., Huang, X., Xu, W., Guo, B., Shum, H.-Y.: Direct manipulation of subdivision surfaces on GPUs. ACM Trans. Graph. 26(3) (2007)

Download references

Acknowledgements

This work was supported by the NSF of China (No. 61003145) and the National High-Tech R&D program of China (No. 2012AA011503). An early version of the work was presented at Computational Visual Media Conference 2012 [22].

The authors would like to thank Kun Zhou for helpful discussions on constrained texture mapping.

Author information

Authors and Affiliations

  1. Zhejiang University, Hangzhou, China

    Yanlin Weng & Dongping Li

  2. Michigan State University, East Lansing, MI, USA

    Yiying Tong

Authors
  1. Yanlin Weng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dongping Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yiying Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanlin Weng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weng, Y., Li, D. & Tong, Y. Texture mapping subdivision surfaces with hard constraints. Vis Comput 29, 1231–1241 (2013). https://doi.org/10.1007/s00371-013-0794-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-013-0794-4

Keywords

Search

Navigation