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Field-Aware Parameterization for 3D Painting

  • Songgang Xu
  • Hang Li
  • John KeyserEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Parameterization Painting system Geodesic 

References

  1. 1.
    Burley, B., Lacewell, D.: Ptex: per-face texture mapping for production rendering. Comput. Graph. Forum 27(4), 1155–1164 (2008)CrossRefGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 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_9CrossRefGoogle Scholar
  4. 4.
    Fu, X.M., Liu, Y.: Computing inversion-free mappings by simplex assembly. ACM Trans. Graph. (TOG) 35(6), 216 (2016)CrossRefGoogle Scholar
  5. 5.
    Fu, X.M., Liu, Y., Guo, B.: Computing locally injective mappings by advanced MIPS. ACM Trans. Graph. (TOG) 34(4), 71 (2015)zbMATHGoogle Scholar
  6. 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. 7.
    Joseph, S., Mount, D., Papadimitriou, C.: The discrete geodesic problem. SIAM J. Comput. 16(4), 647–668 (1987)MathSciNetCrossRefGoogle Scholar
  8. 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. 9.
    Kovalsky, S.Z., Galun, M., Lipman, Y.: Accelerated quadratic proxy for geometric optimization. ACM Trans. Graph. (TOG) 35(4), 134 (2016)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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. 12.
    Rabinovich, M., Poranne, R., Panozzo, D., Sorkine-Hornung, O.: Scalable locally injective mappings. ACM Trans. Graph. (TOG) 36(2), 16 (2017)CrossRefGoogle Scholar
  13. 13.
    Schmidt, R., Grimm, C., Wyvill, B.: Interactive decal compositing with discrete exponential maps. ACM Trans. Graph. (TOG) 25, 605–613 (2006)CrossRefGoogle Scholar
  14. 14.
    Schmidt, R.: Stroke parameterization. In: Computer Graphics Forum, vol. 32, pp. 255–263. Wiley, Hoboken (2013)CrossRefGoogle Scholar
  15. 15.
    Sharp, N., Soliman, Y., Crane, K.: The vector heat method. arXiv preprint arXiv:1805.09170 (2018)
  16. 16.
    Smith, J., Schaefer, S.: Bijective parameterization with free boundaries. ACM Trans. Graph. (TOG) 34(4), 70 (2015)CrossRefGoogle Scholar
  17. 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. 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)CrossRefGoogle Scholar
  19. 19.
    Xu, S.: Numerical and geometric optimizations for surface and tolerance modeling. Ph.D. thesis, Texas A&M University, December 2015Google Scholar
  20. 20.
    Yuksel, C., Keyser, J., House, D.H.: Mesh colors. ACM Trans. Graph. 29(2), 1–11 (2010)CrossRefGoogle Scholar
  21. 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

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Intel CorporationFolsomUSA
  2. 2.Texas A&M UniversityCollege StationUSA

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