This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Interactive Visualization of Rotational Symmetry Fields on Surfaces
July 2011 (vol. 17 no. 7)
pp. 947-955
Jonathan Palacios, Oregon State University, Corvallis
Eugene Zhang, Oregon State University, Corvallis
Rotational symmetries (RoSys) have found uses in several computer graphics applications, such as global surface parameterization, geometry remeshing, texture and geometry synthesis, and nonphotorealistic visualization of surfaces. The visualization of N-way rotational symmetry (N-RoSy) fields is a challenging problem due to the ambiguities in the N directions represented by an N-way symmetry. We provide an algorithm that allows faithful and interactive representation of N-RoSy fields in the plane and on surfaces, by adapting the well-known line integral convolution (LIC) technique from vector and second-order tensor fields. Our algorithm captures N directions associated with each point in a given field by decomposing the field into multiple different vector fields, generating LIC images of these fields, and then blending the results. To address the loss of contrast caused by the blending of images, we observe that the pixel values in LIC images closely approximate normally distributed random variables. This allows us to use concepts from probability theory to correct the loss of contrast without the need to perform any image analysis at each frame.

[1] P. Alliez, D. Cohen-Steiner, O. Devillers, B. Lévy, and M. Desbrun, "Anisotropic Polygonal Remeshing," ACM Trans. Graphics, vol. 22, no. 3, pp. 485-493, July 2003.
[2] D. Bommes, H. Zimmer, and L. Kobbelt, "Mixed-Integer Quadrangulation," ACM Trans. Graphics, vol. 28, no. 3, pp. 1-10, 2009.
[3] B. Cabral and L.C. Leedom, "Imaging Vector Fields Using Line Integral Convolution," Proc. ACM SIGGRAPH, pp. 263-270, 1993.
[4] A. Hertzmann and D. Zorin, "Illustrating Smooth Surfaces," Proc. ACM SIGGRAPH, pp. 517-526, Aug. 2000.
[5] I. Hotz, L. Feng, H. Hagen, B. Hamann, B. Jeremic, and K. Joy, "Physically Based Methods for Tensor Field Visualization," Proc. IEEE Visualization Conf., pp. 123-130, 2004.
[6] E. Hsu, "Generalized Line Integral Convolution Rendering of Diffusion Tensor Fields," Proc. Int'l Soc. for Magnetic Resonance in Medicine (ISMRM), vol. 790, 2001.
[7] F. Kälberer, M. Nieser, and K. Polthier, "Quadcover—Surface Parameterization Using Branched Coverings," Proc. Eurographics, pp. 375-384, 2007.
[8] Y.K. Lai, M. Jin, X. Xie, Y. He, J. Palacios, E. Zhang, S.M. Hu, and X. Gu, "Metric-Driven Rosy Field Design and Remeshing," IEEE Trans. Visualization and Computer Graphics, vol. 16, no. 1, pp. 95-108, Jan./Feb. 2010.
[9] R.S. Laramee, H. Hauser, H. Doleisch, B. Vrolijk, F.H. Post, and D. Weiskopf, "The State of the Art in Flow Visualization: Dense and Texture-Based Techniques," Computer Graphics Forum, vol. 23, pp. 203-221, 2004.
[10] R.S. Laramee, B. Jobard, and H. Hauser, "Image Space Based Visualization of Unsteady Flow on Surfaces," Proc. 14th IEEE Visualization (VIS) Conf., p. 18, 2003.
[11] W.C. Li, B. Vallet, N. Ray, and B. Levy, "Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 1315-1322, Sept./Oct. 2006.
[12] Z. Liu, R. Moorhead, II, and J. Groner, "An Advanced Evenly-Spaced Streamline Placement Algorithm," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 965-972, Sept./Oct. 2006.
[13] J. Palacios and E. Zhang, "Rotational Symmetry Field Design on Surfaces," Proc. ACM SIGGRAPH Papers, p. 55, 2007.
[14] N. Ray, W.C. Li, B. Lévy, A. Sheffer, and P. Alliez, "Periodic Global Parameterization," ACM Trans. Graphics, vol. 25, no. 4, pp. 1460-1485, 2006.
[15] N. Ray, B. Vallet, W.C. Li, and B. Levy, "N-Symmetry Direction Field Design," ACM Trans. Graphics, vol. 27, no. 2, pp. 1-13, May 2008.
[16] A.R. Sanderson, C.R. Johnson, and R.M. Kirby, "Display of Vector Fields Using a Reaction-Diffusion Model," Proc. IEEE Visualization Conf., pp. 115-122, 2004.
[17] A. Schiftner, M. Hobinger, J. Wallner, and H. Pottmann, "Packing Circles and Spheres on Surfaces," ACM Trans. Graphics, vol. 28, no. 5, pp. 1-8, 2010.
[18] H.W. Shen and D.L. Kao, "A New Line Integral Convolution Algorithm for Visualizing Time-Varying Flow Fields," IEEE Trans. Visualization and Computer Graphics, vol. 4, no. 2, pp. 98-108, Apr./June 1998.
[19] D. Stalling and H.C. Hege, "Fast and Resolution Independent Line Integral Convolution," Proc. ACM SIGGRAPH, pp. 249-256, 1995.
[20] J.J. van Wijk, "Spot Noise Texture Synthesis for Data Visualization," Proc. ACM SIGGRAPH, pp. 309-318, 1991.
[21] J.J. van Wijk, "Image Based Flow Visualization," ACM Trans. Graphics, vol. 21, no. 3, pp. 745-754, July 2002.
[22] J.J. van Wijk, "Image Based Flow Visualization for Curved Surfaces," Proc. IEEE Visualization, G. Turk, J. van Wijk, and R. Moorhead, eds., pp. 123-130, Oct. 2003.
[23] L.Y. Wei and M. Levoy, "Texture Synthesis over Arbitrary Manifold Surfaces," Proc. ACM SIGGRAPH, pp. 355-360, 2001.
[24] E. Zhang, J. Hays, and G. Turk, "Interactive Tensor Field Design and Visualization on Surfaces," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 1, pp. 94-107, Jan. 2007.
[25] X. Zheng and A. Pang, "Hyperlic," Proc. 14th IEEE Visualization (VIS) Conf., p. 33, 2003.

Index Terms:
Rotational symmetry, RoSy, visualization, tensor field visualization, image blending, contrast adjustment.
Citation:
Jonathan Palacios, Eugene Zhang, "Interactive Visualization of Rotational Symmetry Fields on Surfaces," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 7, pp. 947-955, July 2011, doi:10.1109/TVCG.2010.121
Usage of this product signifies your acceptance of the Terms of Use.