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Multimedia Tools and Applications

, Volume 77, Issue 24, pp 31969–31989 | Cite as

A measure-driven method for normal mapping and normal map design of 3D models

  • Kun Qian
  • Yinghua Li
  • Kehua Su
  • Jialing Zhang
Article
  • 18 Downloads

Abstract

Normal mapping is one of the most important methods for photorealistic rendering. It preserves geometric attribute values on a simplified mesh. A normal map stores normal vectors for high-quality meshes in a 2D form. A simplified model is then rendered using these normal vectors. To keep a surface’s normal property in a map it first of all requires 2D parameterization. The most common approach to this is to divide the surface into several patches, where each patch has its own parameterization. However, this approach has some weakness when it comes to designing global normal maps. This paper presents a measure-driven method that can interactively direct design of normal maps on a 2D plane. This 2D plane has minimal distortion and, more importantly, it is possible to zoom in or shrink the area of interest. The resulting, novel framework serves as a powerful tool for normal mapping and normal map design. We provide a variety of experimental results to demonstrate the efficiency, robustness and efficacy of our approach.

Keywords

Normal mapping Normal map design Measure-driven Parameterization 

Notes

Acknowledgements

This work is partially supported by National Natural Science Foundation of China(Project Number:61772379).

References

  1. 1.
    Alexandrov A (2005) Convex polyhedra (in russian), m.: Gostekhizdat 1950; english translation in springer monographs in mathematicsGoogle Scholar
  2. 2.
    Becker BG, Max NL (1993) Smooth transitions between bump rendering algorithms. In: Proceedings of the 20th annual conference on Computer graphics and interactive techniques. ACM, pp 183–190Google Scholar
  3. 3.
    Blinn JF (1978) Simulation of wrinkled surfaces. In: ACM SIGGRAPH computer graphics, vol 12. ACM, pp 286–292Google Scholar
  4. 4.
    Brenier Y (1991) Polar factorization and monotone rearrangement of vector-valued functions. Commun Pure Appl Math 44(4):375–417MathSciNetCrossRefGoogle Scholar
  5. 5.
    Catmull E (1974) A subdivision algorithm for computer display of curved surfaces. Tech. rep., Utah Univ Salt Lake City School of ComputingGoogle Scholar
  6. 6.
    Chow B, Luo F et al. (2003) Combinatorial ricci flows on surfaces. J Differ Geom 63(1):97–129MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cignoni P, Montani C, Rocchini C, Scopigno R (1998) A general method for preserving attribute values on simplified meshes. In: Visualization’98. Proceedings. IEEE, pp 59–66Google Scholar
  8. 8.
    Cohen J, Olano M, Manocha D (1998) Appearance-preserving simplification. In: Proceedings of the 25th annual conference on computer graphics and interactive techniques. ACM, pp 115–122Google Scholar
  9. 9.
    Cook RL (1984) Shade trees. ACM Siggraph Comput Graph 18(3):223–231CrossRefGoogle Scholar
  10. 10.
    De Goes F, Cohen-Steiner D, Alliez P, Desbrun M (2011) An optimal transport approach to robust reconstruction and simplification of 2d shapes. In: Computer Graphics forum, vol 30. Wiley Online Library, pp 1593–1602Google Scholar
  11. 11.
    Desbrun M, Meyer M, Alliez P (2002) Intrinsic parameterizations of surface meshes. In: Computer Graphics forum, vol 21. Wiley Online Library, pp 209–218Google Scholar
  12. 12.
    Doggett M, Hirche J (2000) Adaptive view dependent tessellation of displacement maps. In: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on graphics hardware. ACM, pp 59–66Google Scholar
  13. 13.
    Dominitz A, Tannenbaum A (2010) Texture mapping via optimal mass transport. IEEE Trans Visual Comput Graph 16(3):419–433CrossRefGoogle Scholar
  14. 14.
    Floater MS (1997) Parametrization and smooth approximation of surface triangulations. Comput Aided Geom Des 14(3):231–250MathSciNetCrossRefGoogle Scholar
  15. 15.
    Gehling MB, Hofsetz C, Musse SR (2007) Normalpaint: an interactive tool for painting normal maps. Vis Comput 23(9-11):897–904CrossRefGoogle Scholar
  16. 16.
    Gu X, Yau ST (2003) Global conformal surface parameterization. In: Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on geometry processing. Eurographics Association, pp 127–137Google Scholar
  17. 17.
    Gu XD, Yau ST (2008) Computational conformal geometry. International Press, SomervillezbMATHGoogle Scholar
  18. 18.
    Gu X, Wang Y, Yau ST et al. (2003) Geometric compression using riemann surface structure. Commun Inf Syst 3(3):171–182MathSciNetzbMATHGoogle Scholar
  19. 19.
    Gu X, Wang Y, Chan TF, Thompson PM, Yau ST (2004) Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans Med Imaging 23(8):949–958CrossRefGoogle Scholar
  20. 20.
    Gu X, Luo F, Sun J, Yau ST (2016) Variational principles for minkowski type problems, discrete optimal transport, and discrete monge–ampère equations. Asian J Math, 20(2)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Gumhold S, Hüttner T (1999) Multiresolution rendering with displacement mapping. In: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on graphics hardware. ACM, pp 55–66Google Scholar
  22. 22.
    Guskov I, Vidimče K, Sweldens W, Schröder P (2000) Normal meshes. In: Proceedings of the 27th annual conference on computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co, pp 95–102Google Scholar
  23. 23.
    Haker S, Zhu L, Tannenbaum A, Angenent S (2004) Optimal mass transport for registration and warping. Int J Comput Vis 60(3):225–240CrossRefGoogle Scholar
  24. 24.
    Pharr M, Hanrahan P (1996) Geometry caching for ray-tracing displacement maps. In: Rendering Techniques 96: Proceedings of the Eurographics workshop in Porto. Portugal, June 17–19, 1996. Springer, p 31Google Scholar
  25. 25.
    Heidrich W, Daubert K, Kautz J, Seidel HP (2000) Illuminating micro geometry based on precomputed visibility. In: Proceedings of the 27th annual conference on computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co, pp 455–464Google Scholar
  26. 26.
    Heidrich W, Seidel H (1998) Ray-tracing procedural displacement shaders. Language 20(10):24Google Scholar
  27. 27.
    Hirche J, Ehlert A, Guthe S, Doggett M (2004) Hardware accelerated per-pixel displacement mapping. In: Proceedings of graphics interface 2004. Canadian Human-Computer Communications Society, pp 153–158Google Scholar
  28. 28.
    Hormann K, Lévy B, Sheffer A (2007) Mesh parameterization: theory and practiceGoogle Scholar
  29. 29.
    Jin M, Kim J, Luo F, Gu X (2008) Discrete surface ricci flow. IEEE Trans Vis Comput Graph 14(5):1030–1043CrossRefGoogle Scholar
  30. 30.
    Joshi AA, Shattuck DW, Thompson PM, Leahy RM (2007) Surface-constrained volumetric brain registration using harmonic mappings. IEEE Trans Medical Imag 26 (12):1657–1669CrossRefGoogle Scholar
  31. 31.
    Kautz J, Seidel HP (2001) Hardware accelerated displacement mapping for image based rendering. In: Graphics Interface, vol 2001, pp 61–70Google Scholar
  32. 32.
    Kautz J, Heidrich W, Seidel HP (2001) Real-time bump map synthesis. In: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on graphics hardware. ACM, pp 109–114Google Scholar
  33. 33.
    Krishnamurthy V, Levoy M (1996) Fitting smooth surfaces to dense polygon meshes. In: Proceedings of the 23rd annual conference on computer graphics and interactive techniques. ACM, pp 313–324Google Scholar
  34. 34.
    Lévy B, Mallet JL (1998) Non-distorted texture mapping for sheared triangulated meshes. In: Proceedings of the 25th annual conference on computer graphics and interactive techniques. ACM, pp 343–352Google Scholar
  35. 35.
    Lévy B, Petitjean S, Ray N, Maillot J (2002) Least squares conformal maps for automatic texture atlas generatio. In: Acm Transactions on graphics (tog), vol 21. ACM, pp 362–371Google Scholar
  36. 36.
    Lipman Y, Daubechies I (2009) Surface comparison with mass transportation. arXiv:0912.3488
  37. 37.
    Litke N, Droske M, Rumpf M, Schröder P (2005) An image processing approach to surface matching. In: Symposium on Geometry processing, vol 255. Citeseer, pp 207–216Google Scholar
  38. 38.
    Max NL (1988) Horizon mapping: shadows for bump-mapped surfaces. Vis Comput 4(2):109–117CrossRefGoogle Scholar
  39. 39.
    Mérigot Q (2011) A multiscale approach to optimal transport. In:Computer Graphics forum, vol 30. Wiley Online Library, pp 1583–1592Google Scholar
  40. 40.
    Meyer A, Neyret F (1998) Interactive volumetric textures. Render Techniq 98:157–168CrossRefGoogle Scholar
  41. 41.
    Nießner M, Loop C (2013) Analytic displacement mapping using hardware tessellation. ACM Trans Graph (TOG) 32(3):26CrossRefGoogle Scholar
  42. 42.
    Sander PV, Snyder J, Gortler SJ, Hoppe H (2001) Texture mapping progressive meshes. In: Proceedings of the 28th annual conference on computer graphics and interactive techniques. ACM, pp 409–416Google Scholar
  43. 43.
    Shi R, Zeng W, Su Z, Damasio H, Lu Z, Wang Y, Yau ST, Gu X (2013) Hyperbolic harmonic mapping for constrained brain surface registration. In: Proceedings of the IEEE Conference on computer vision and pattern recognition, pp 2531–2538Google Scholar
  44. 44.
    Su Z, Sun J, Gu X, Luo F, Yau ST (2014) Optimal mass transport for geometric modeling based on variational principles in convex geometry. Eng Comput 30(4):475–486CrossRefGoogle Scholar
  45. 45.
    Su K, Cui L, Qian K, Lei N, Zhang J, Zhang M, Gu XD (2016) Area-preserving mesh parameterization for poly-annulus surfaces based on optimal mass transportation. Comput Aided Geom De 46:76–91MathSciNetCrossRefGoogle Scholar
  46. 46.
    Su K, Chen W, Lei N, Cui L, Jiang J, Gu XD (2016) Measure controllable volumetric mesh parameterization. Comput Aided Des 78:188–198CrossRefGoogle Scholar
  47. 47.
    Su K, Chen W, Lei N, Zhang J, Qian K, Gu X (2017) Volume preserving mesh parameterization based on optimal mass transportation. Comput Aided Des 82:42–56MathSciNetCrossRefGoogle Scholar
  48. 48.
    Szirmay-Kalos L, Umenhoffer T (2008) Displacement mapping on the gpustate of the art. In: Computer Graphics forum, vol 27. Wiley Online Library, pp 1567–1592Google Scholar
  49. 49.
    Ur Rehman T, Haber E, Pryor G, Melonakos J, Tannenbaum A (2009) 3d nonrigid registration via optimal mass transport on the gpu. Med Image Anal 13 (6):931–940CrossRefGoogle Scholar
  50. 50.
    Wang L, Wang X, Tong X, Lin S, Hu S, Guo B, Shum HY (2003) View-dependent displacement mapping. In: ACM Transactions on graphics (TOG), vol 22. ACM, pp 334–339Google Scholar
  51. 51.
    Wang Y, Gupta M, Zhang S, Wang S, Gu X, Samaras D, Huang P (2008) High resolution tracking of non-rigid motion of densely sampled 3d data using harmonic maps. Int J Comput Vis 76(3):283–300CrossRefGoogle Scholar
  52. 52.
    Zhang D, Hebert M (1999) Harmonic maps and their applications in surface matching. In: IEEE Computer Society conference on computer vision and pattern recognition, 1999. vol 2. IEEE, pp 524–530Google Scholar
  53. 53.
    Zhao X, Su Z, Gu XD, Kaufman A, Sun J, Gao J, Luo F (2013) Area-preservation mapping using optimal mass transport. IEEE Trans Visual Comput Graph 19(12):2838–2847CrossRefGoogle Scholar
  54. 54.
    Zhu L, Haker S, Tannenbaum A (2003) Area-preserving mappings for the visualization of medical structures. In: International Conference on medical image computing and computer-assisted intervention. Springer, pp 277–284Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Kun Qian
    • 1
    • 2
    • 4
  • Yinghua Li
    • 2
  • Kehua Su
    • 3
  • Jialing Zhang
    • 1
    • 2
  1. 1.School of Civil Engineering and ArchitectureKunming University of Science and TechnologyKunmingChina
  2. 2.Faculty of ScienceKunming University of Science and TechnologyKunmingChina
  3. 3.School of Computer ScienceWuhan UniversityWuhanChina
  4. 4.Center of Engineering MathematicsKunming University of Science and TechnologyKunmingChina

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