Skip to main content

Field-Aware Parameterization for 3D Painting

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11542))

Abstract

We present a two-phase method that generates a near-isometric parameterization using a local chart of the surface while still being aware of the geodesic metric. During the first phase, we utilize a novel method that approximates polar coordinates to obtain a preliminary parameterization as well as the gradient of the geodesic field. For the second phase, we present a new optimization that generates a near isometric parameterization while considering the gradient field, allowing us to generate high quality parameterizations while keeping the geodesic information. This local parameterization is applied in a view-dependent 3D painting system, providing a local adaptive map computed at interactive rates.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Burley, B., Lacewell, D.: Ptex: per-face texture mapping for production rendering. Comput. Graph. Forum 27(4), 1155–1164 (2008)

    Article  Google Scholar 

  2. Crane, K., Weischedel, C., Wardetzky, M.: Geodesics in heat: a new approach to computing distance based on heat flow. ACM Trans. Graph. (TOG) 32(5), 152 (2013)

    Article  Google Scholar 

  3. Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Dodgson, N.A., Floater, M.S., Sabin, M.A. (eds.) Advances in Multiresolution for Geometric Modelling, pp. 157–186. Springer, Heidelberg (2005). https://doi.org/10.1007/3-540-26808-1_9

    Chapter  Google Scholar 

  4. Fu, X.M., Liu, Y.: Computing inversion-free mappings by simplex assembly. ACM Trans. Graph. (TOG) 35(6), 216 (2016)

    Article  Google Scholar 

  5. Fu, X.M., Liu, Y., Guo, B.: Computing locally injective mappings by advanced MIPS. ACM Trans. Graph. (TOG) 34(4), 71 (2015)

    MATH  Google Scholar 

  6. Igarashi, T., Cosgrove, D.: Adaptive unwrapping for interactive texture painting. In: Proceedings of the 2001 symposium on Interactive 3D graphics, pp. 209–216 (2001)

    Google Scholar 

  7. Joseph, S., Mount, D., Papadimitriou, C.: The discrete geodesic problem. SIAM J. Comput. 16(4), 647–668 (1987)

    Article  MathSciNet  Google Scholar 

  8. Kami, Z., Gotsman, C., Gortler, S.J.: Free-boundary linear parameterization of 3D meshes in the presence of constraints. In: 2005 International Conference on Shape Modeling and Applications, pp. 266–275. IEEE (2005)

    Google Scholar 

  9. Kovalsky, S.Z., Galun, M., Lipman, Y.: Accelerated quadratic proxy for geometric optimization. ACM Trans. Graph. (TOG) 35(4), 134 (2016)

    Article  Google Scholar 

  10. Liu, L., Zhang, L., Xu, Y., Gotsman, C., Gortler, S.J.: A local/global approach to mesh parameterization. In: Computer Graphics Forum, vol. 27, pp. 1495–1504. Wiley, Hoboken (2008)

    Article  Google Scholar 

  11. Melvær, E.L., Reimers, M.: Geodesic polar coordinates on polygonal meshes. In: Computer Graphics Forum, vol. 31, pp. 2423–2435. Wiley, Hoboken (2012)

    Google Scholar 

  12. Rabinovich, M., Poranne, R., Panozzo, D., Sorkine-Hornung, O.: Scalable locally injective mappings. ACM Trans. Graph. (TOG) 36(2), 16 (2017)

    Article  Google Scholar 

  13. Schmidt, R., Grimm, C., Wyvill, B.: Interactive decal compositing with discrete exponential maps. ACM Trans. Graph. (TOG) 25, 605–613 (2006)

    Article  Google Scholar 

  14. Schmidt, R.: Stroke parameterization. In: Computer Graphics Forum, vol. 32, pp. 255–263. Wiley, Hoboken (2013)

    Article  Google Scholar 

  15. Sharp, N., Soliman, Y., Crane, K.: The vector heat method. arXiv preprint arXiv:1805.09170 (2018)

  16. Smith, J., Schaefer, S.: Bijective parameterization with free boundaries. ACM Trans. Graph. (TOG) 34(4), 70 (2015)

    Article  Google Scholar 

  17. Sun, Q., et al.: Texture brush: an interactive surface texturing interface. In: Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, pp. 153–160. ACM (2013)

    Google Scholar 

  18. Surazhsky, V., Surazhsky, T., Kirsanov, D., Gortler, S.J., Hoppe, H.: Fast exact and approximate geodesics on meshes. ACM Trans. Graph. (TOG) 24, 553–560 (2005)

    Article  Google Scholar 

  19. Xu, S.: Numerical and geometric optimizations for surface and tolerance modeling. Ph.D. thesis, Texas A&M University, December 2015

    Google Scholar 

  20. Yuksel, C., Keyser, J., House, D.H.: Mesh colors. ACM Trans. Graph. 29(2), 1–11 (2010)

    Article  Google Scholar 

  21. Zhang, X., Kim, Y.J., Ye, X.: Versatile 3D texture painting using imaging geometry. In: Korea-China Joint Conference on Geometric and Visual Computing (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John Keyser .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Xu, S., Li, H., Keyser, J. (2019). Field-Aware Parameterization for 3D Painting. In: Gavrilova, M., Chang, J., Thalmann, N., Hitzer, E., Ishikawa, H. (eds) Advances in Computer Graphics. CGI 2019. Lecture Notes in Computer Science(), vol 11542. Springer, Cham. https://doi.org/10.1007/978-3-030-22514-8_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-22514-8_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22513-1

  • Online ISBN: 978-3-030-22514-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics