動態錯覺指的是經由特定顏色與圖案組成的靜態影像所產生錯覺運動的現象。在這個研究中，我們首次提出了一個能夠在3D 模型表面上產生動態錯覺的方法，不僅應用在形狀描繪，也可用較為藝術的方式來視覺化向量場以及張量場。我們的方法將[Chi et al. 2008]在平面上產生動態錯覺的方式擴增至3D模型表面。此外，我們也提出了新的非對稱循環圖案（Repeated Asymmetric Patterns, RAPs）用來視覺化雙向以及四個方向的流向，因此我們也能夠在平面或是3D 模型表面上視覺化張量場以及4 褶轉稱場（four-fold rotational symmetry field, 4-Rosy）。我們藉形狀描繪的應用以及在3D 模型表面上向量場與張量場視覺化的應用來佐證我們方法的效果。

Illusory motion refers to the phenomenon in which static images composed of certain colors and patterns lead to the illusion of motions. This paper presents a first approach to generating illusory as well as artistic visualization of vector and tensor fields on surfaces. Our method extends previous work on generating illusory motion in the plane, which we adapt to 3D surfaces. In addition, we propose novel Repeated Asymmetric Patterns (RAPs) to visualize bidirectional and quadridirectional flows, thus enabling the visualization of tensor fields and four‐fold rotational symmetry (4‐Rosy) fields in the plane and on surfaces. We demonstrate the effectiveness of our method with applications in shape illustration as well as vector and tensor field visualization on surfaces.

［1］ BHAT, P., INGRAM, S., AND TURK, G. 2004. Geometric texture synthesis by example. In SGP ’04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, ACM, New York, NY, USA, 41–44.
［2］ CABRAL, B., AND LEEDOM, L. C. 1993. Imaging vector fields using line integral convolution. In Proceedings of ACM SIGGRAPH 1993, ACM Press / ACM SIGGRAPH, New York, NY, USA, 263–270.
［3］ CHI, M.‐T., LEE, T.‐Y., QU, Y., AND WONG, T.‐T. 2008. Selfanimating images: illusory motion using repeated asymmetric patterns. In SIGGRAPH ’08: ACM SIGGRAPH 2008 papers, ACM, New York, NY, USA, 1–8.
［4］ DAVID, H. A. 1963. The Method of Paired Comparisons. Charles Griffin Company.
［5］ DECARLO, D., FINKELSTEIN, A., RUSINKIEWICZ, S., AND
SANTELLA, A. 2003. Suggestive contours for conveying shape.
ACM Trans. Graph. 22, 3, 848–855.
［6］ DELMARCELLE, T., AND HESSELINK, L. 1994. The topology of symmetric, second‐order tensor fields. In VIS ’94: Proceedings of the conference on Visualization ’94, IEEE Computer Society Press, Los Alamitos, CA, USA, 140–147.
［7］ Dong, S., Kircher, S., Garland, M. 2005. Harmonic functions for quadrilateral remeshing of arbitrary manifolds. July 2005. Computer Aided Geometric Design. 22, 5, 392‐423.
［8］ FOLEY, J., VAN DAM, A., FEINER, S., AND HUGHES, J. 1996. Computer Graphics: Principles and Practice. Addison‐Wesley.
［9］ GARLAND, M., AND HECKBERT, P. S. 1997. Surface simplification using quadric error metrics. In SIGGRAPH ’97: Proceedings of the 24th annual conference on Computer graphics and interactive techniques, ACM
Press/Addison‐Wesley Publishing Co., New York, NY, USA, 209–216.
［10］ GIRSHICK, A., INTERRANTE, V., HAKER, S., AND LEMOINE, T. 2000. Line direction matters: an argument for the use of principal directions in 3d line drawings. In NPAR ’00: Proceedings of the 1st international symposium on Non‐photorealistic animation and rendering,
ACM, New York, NY, USA, 43–52.
［11］ GOOCH, A., GOOCH, B., SHIRLEY, P., AND COHEN, E. 1998. A non‐photorealistic lighting model for automatic technical illustration. In SIGGRAPH ’98: Proceedings of the 25th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 447–452.
［12］ GOSSETT, N., AND CHEN, B. 2004. Self‐animating line textures.
Tech. rep. http://www.dtc.umn.edu/~gossett/publications/.
［13］ HERTZMANN, A., AND ZORIN, D. 2000. Illustrating smooth surfaces. In SIGGRAPH ’00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, ACM Press/Addison‐Wesley Publishing Co., New York, NY, USA, 517–526.
［14］ JUDD, T., DURAND, F., AND ADELSON, E. H. 2007. Apparent ridges for line drawing. ACM Trans. Graph. 26, 3, 19.
［15］ KALNINS, R. D., MARKOSIAN, L., MEIER, B. J., KOWALSKI, M. A., LEE, J. C., DAVIDSON, P. L., WEBB, M., HUGHES, J. F., AND FINKELSTEIN, A. 2002. WYSIWYG NPR: Drawing strokes directly on 3D models. ACM Transactions on Graphics (Proc. SIGGRAPH) 21, 3 (July), 755–762.
［16］ KITAOKA, A., AND ASHIDA, H. 2003. Phenomenal characteristics of the peripheral drift illusion. VISION (Journal of the Vision Society of Japan) 15, 261–262.
［17］ KITAOKA, A., 2003. Rotating snakes. http://www.psy.
ritsumei.ac.jp/~akitaoka/rotsnakee.html.
［18］ KITAOKA, A. 2006. Anomalous motion illusion and stereopsis. Journal of Three Dimensional Images (Japan) 20, 9–14.
［19］ KOLOMENKIN, M., SHIMSHONI, I., AND TAL, A. 2008.
Demarcating curves for shape illustration. In SIGGRAPH Asia ’08: ACM SIGGRAPH Asia 2008 papers, ACM, New York, NY, USA, 1–9.
［20］ LEFEBVRE, S., AND HOPPE, H. 2006. Appearance‐space texture synthesis. In SIGGRAPH ’06: ACM SIGGRAPH 2006 Papers, ACM, New York, NY, USA, 541–548.
［21］ LUFT, T., COLDITZ, C., AND DEUSSEN, O. 2006. Image
enhancement by unsharp masking the depth buffer. ACM
Transactions on Graphics 25, 3 (jul), 1206–1213.
［22］ LUM, E., STOMPEL, A., AND MA, K.‐L. 2003. Kinetic visualization. IEEE Transactions on Visualization and Graphics 9, 2 (April ‐ June), 115–126.
［23］ NORTHRUP, J. D., AND MARKOSIAN, L. 2000. Artistic silhouettes: a hybrid approach. In NPAR ’00: Proceedings of the 1st international symposium on Non‐photorealistic animation and rendering, ACM, New York, NY, USA, 31–37.
［24］ PALACIOS, J., AND ZHANG, E. 2007. Rotational symmetry field design on surfaces. ACM Trans. Graph. 26, 3, 55:1–55:10.
［25］ POTMESIL, M., AND CHAKRAVARTY, I. 1983. Modeling motion blur in computer‐generated images. SIGGRAPH Comput. Graph. 17, 3, 389–399.
［26］ PRAUN, E., FINKELSTEIN, A., AND HOPPE, H. 2000. Lapped textures. In SIGGRAPH ’00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, ACM Press/Addison‐Wesley Publishing Co., New York, NY, USA, 465–470.
［27］ RAY, N., LI, W. C., L´E 612 VY, B., SHEFFER, A., AND ALLIEZ, P. 2006. Periodic global parameterization. ACM Trans. Graph. 25, 4, 1460–1485.
［28］ RUBIN, E. 2001. Figure and ground. In Visual Perception: Essential Readings, S. Yantis, Ed. Psychology Press, 223–233.
［29］ TURK, G., AND BANKS, D. 1996. Image‐guided streamline placement. In SIGGRAPH ’96: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 453–460.
［30］ TURK, G. 2001. Texture synthesis on surfaces. In SIGGRAPH ’01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 347–354.
［31］ VAN WIJK, J. J. 2002. Image based flow visualization. In SIGGRAPH ’02: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 745–754.
［32］ VAN WIJK, J. J. 2003. Image based flow visualization for curved surfaces. In VIS ’03: Proceedings of the 14th IEEE Visualization 2003 (VIS’03), IEEE Computer Society, Washington, DC, USA, 17.
［33］ WEI, L.‐Y., AND LEVOY, M. 2001. Texture synthesis over arbitrary manifold surfaces. In SIGGRAPH ’01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 355–360.
［34］ WEI, L.‐Y. 2006. Visualizing flow fields by perceptual motion. Tech. Rep. MSR‐TR‐2006‐82, Microsoft Research, June.
［35］ XU, K., Cohen‐Or, D., JU, T., LIU., L., ZHANG, H., Zhou, S., XIONG, Y. 2009. Feature‐aligned shape texturing. ACM Trans. Graph. 28, 5,
［36］ YOSHIZAWA, S., BELYAEV, A., AND SEIDEL, H.‐P. 2005. Fast and robust detection of crest lines on meshes. In SPM ’05: Proceedings of the 2005 ACM symposium on Solid and physical modeling, ACM, New York, NY, USA, 227–232.
［37］ ZHANG, E., HAYS, J., AND TURK, G. 2007. Interactive tensor field design and visualization on surfaces. IEEE Transactions on Visualization and Computer Graphics 13, 1, 94–107.
［38］ ZHOU, K., HUANG, X., WANG, X., TONG, Y., DESBRUN, M., GUO, B., AND SHUM, H.‐Y. 2006. Mesh quilting for geometric texture synthesis. ACM Trans. Graph. 25, 3, 690–697.