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.
Similar content being viewed by others
References
Alexandrov A (2005) Convex polyhedra (in russian), m.: Gostekhizdat 1950; english translation in springer monographs in mathematics
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 183–190
Blinn JF (1978) Simulation of wrinkled surfaces. In: ACM SIGGRAPH computer graphics, vol 12. ACM, pp 286–292
Brenier Y (1991) Polar factorization and monotone rearrangement of vector-valued functions. Commun Pure Appl Math 44(4):375–417
Catmull E (1974) A subdivision algorithm for computer display of curved surfaces. Tech. rep., Utah Univ Salt Lake City School of Computing
Chow B, Luo F et al. (2003) Combinatorial ricci flows on surfaces. J Differ Geom 63(1):97–129
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 59–66
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 115–122
Cook RL (1984) Shade trees. ACM Siggraph Comput Graph 18(3):223–231
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 1593–1602
Desbrun M, Meyer M, Alliez P (2002) Intrinsic parameterizations of surface meshes. In: Computer Graphics forum, vol 21. Wiley Online Library, pp 209–218
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 59–66
Dominitz A, Tannenbaum A (2010) Texture mapping via optimal mass transport. IEEE Trans Visual Comput Graph 16(3):419–433
Floater MS (1997) Parametrization and smooth approximation of surface triangulations. Comput Aided Geom Des 14(3):231–250
Gehling MB, Hofsetz C, Musse SR (2007) Normalpaint: an interactive tool for painting normal maps. Vis Comput 23(9-11):897–904
Gu X, Yau ST (2003) Global conformal surface parameterization. In: Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on geometry processing. Eurographics Association, pp 127–137
Gu XD, Yau ST (2008) Computational conformal geometry. International Press, Somerville
Gu X, Wang Y, Yau ST et al. (2003) Geometric compression using riemann surface structure. Commun Inf Syst 3(3):171–182
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):949–958
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)
Gumhold S, Hüttner T (1999) Multiresolution rendering with displacement mapping. In: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on graphics hardware. ACM, pp 55–66
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 95–102
Haker S, Zhu L, Tannenbaum A, Angenent S (2004) Optimal mass transport for registration and warping. Int J Comput Vis 60(3):225–240
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 31
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 455–464
Heidrich W, Seidel H (1998) Ray-tracing procedural displacement shaders. Language 20(10):24
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 153–158
Hormann K, Lévy B, Sheffer A (2007) Mesh parameterization: theory and practice
Jin M, Kim J, Luo F, Gu X (2008) Discrete surface ricci flow. IEEE Trans Vis Comput Graph 14(5):1030–1043
Joshi AA, Shattuck DW, Thompson PM, Leahy RM (2007) Surface-constrained volumetric brain registration using harmonic mappings. IEEE Trans Medical Imag 26 (12):1657–1669
Kautz J, Seidel HP (2001) Hardware accelerated displacement mapping for image based rendering. In: Graphics Interface, vol 2001, pp 61–70
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 109–114
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 313–324
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 343–352
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 362–371
Lipman Y, Daubechies I (2009) Surface comparison with mass transportation. arXiv:0912.3488
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 207–216
Max NL (1988) Horizon mapping: shadows for bump-mapped surfaces. Vis Comput 4(2):109–117
Mérigot Q (2011) A multiscale approach to optimal transport. In:Computer Graphics forum, vol 30. Wiley Online Library, pp 1583–1592
Meyer A, Neyret F (1998) Interactive volumetric textures. Render Techniq 98:157–168
Nießner M, Loop C (2013) Analytic displacement mapping using hardware tessellation. ACM Trans Graph (TOG) 32(3):26
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 409–416
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 2531–2538
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):475–486
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 46:76–91
Su K, Chen W, Lei N, Cui L, Jiang J, Gu XD (2016) Measure controllable volumetric mesh parameterization. Comput Aided Des 78:188–198
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 82:42–56
Szirmay-Kalos L, Umenhoffer T (2008) Displacement mapping on the gpustate of the art. In: Computer Graphics forum, vol 27. Wiley Online Library, pp 1567–1592
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):931–940
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 334–339
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):283–300
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 524–530
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):2838–2847
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 277–284
Acknowledgements
This work is partially supported by National Natural Science Foundation of China(Project Number:61772379).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Qian, K., Li, Y., Su, K. et al. A measure-driven method for normal mapping and normal map design of 3D models. Multimed Tools Appl 77, 31969–31989 (2018). https://doi.org/10.1007/s11042-018-6207-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11042-018-6207-y