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Shadow-Driven 4D Haptic Visualization
November/December 2007 (vol. 13 no. 6)
pp. 1688-1695
Just as we can work with two-dimensional floor plans to communicate 3D architectural design, we can exploit reduced-dimension shadows to manipulate the higher-dimensional objects generating the shadows. In particular, by taking advantage of physically reactive 3D shadow-space controllers, we can transform the task of interacting with 4D objects to a new level of physical reality. We begin with a teaching tool that uses 2D knot diagrams to manipulate the geometry of 3D mathematical knots via their projections; our unique 2D haptic interface allows the user to become familiar with sketching, editing, exploration, and manipulation of 3D knots rendered as projected imageson a 2D shadow space. By combining graphics and collision-sensing haptics, we can enhance the 2D shadow-driven editing protocol to successfully leverage 2D pen-and-paper or blackboard skills. Building on the reduced-dimension 2D editing tool for manipulating 3D shapes, we develop the natural analogy to produce a reduced-dimension 3D tool for manipulating 4D shapes. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the experience accessible to human beings. As far as we are aware, this paper reports the first interactive system with force-feedback that provides "4D haptic visualization" permitting the user to model and interact with 4D cloth-like objects.

[1] E. A. Abbott, Flatland. Dover Publications, Inc., 1952.
[2] T. F. Banchoff, Visualizing two-dimensional phenomena in fourdimensional space: A computer graphics approach. In E. Wegman and D. Priest, editors, Statistical Image Processing and Computer Graphics, pages 187–202. Marcel Dekker, Inc., New York, 1986.
[3] T. F. Banchoff, Beyond the third dimension: Geometry, computer graphics, and higher dimensions. Scientific American Library, 1990.
[4] D. Banks, Interactive display and manipulation of two-dimensional surfaces in four dimensional space. In Symposium on Interactive 3D Graphics, pages 197–207. ACM, 1992.
[5] W. V. Baxter, V. Scheib, and M. C. Lin, dAb: Interactive haptic painting with 3D virtual brushes. In E. Fiume, editor, SIGGRAPH 2001, Computer Graphics Proceedings, pages 461–468. ACM SIGGRAPH, ACM, 2001.
[6] J. Brown, J. C. Latombe, and K. Montgomery, Real-time knot-tying simulation. The Visual Computer, 20 (2–3): 165–179, 2004.
[7] S. A. Carey, R. P. Burton, and D. M. Campbell, Shades of a higher dimension. Computer Graphics World, pages 93–94, October 1987.
[8] J. Cohen, L. Markosian,R. Zeleznik, J. Hughes, and R. Barzel, An interface for sketching 3d curves. In SI3D '99: Proceedings of the 1999 symposium on Interactive 3D graphics, pages 17–21, New York, NY, USA, 1999. ACM Press.
[9] C.W. Reynolds, Steering behaviors for autonomous characters. In The proceedings of the 1999 Game Developers Conference, pages 763–782, 1999.
[10] M. Desbrun, M. Meyer, and A. H. Barr, Interactive animation of clothlike objects for virtual reality. In Cloth modeling and animation, pages 219–239, Natick, MA, USA, 2000. A. K. Peters, Ltd.
[11] A. K. Dewdney, The Planiverse: Computer Contact with a Two-Dimensional World. Poseidon Press, 1984.
[12] R. Egli, C. Petit, and N. F. Stewart, Moving coordinate frames for representation and visualization in four dimensions. Computers and Graphics, 20 (6): 905–919, November-December 1996.
[13] B. Forsyth, Intelligent support of interactive manual control: Design, implementation and evaluation of look-ahead haptic guidance. Master's thesis, The University of British Columbia, 2004.
[14] S. Gottschalk, M. C. Lin, and D. Manocha, OBBTree: A hierarchical structure for rapid interference detection. Computer Graphics, 30 (Annual Conference Series): 171–180, 1996.
[15] P. Haeberli, Dynadraw. Grafica OBSCURA, July 1989.
[16] A. J. Hanson and P. A. Heng, Illuminating the fourth dimension. Computer Graphics and Applications, 12 (4): 54–62, July 1992.
[17] A. J. Hanson and H. Zhang, Multimodal exploration of the fourth dimension. In Proceedings of IEEE Visualization, pages 263–270, 2005.
[18] S. Hollasch., Four-space visualization of 4D objects. Master's thesis, Arizona State University, 1991.
[19] M. Huang, R. P. Grzeszczuk, and L. H. Kauffman, Untangling knots by stochastic energy optimization. In VIS '96: Proceedings of the 7th conference on Visualization '96, pages 279–ff., Los Alamitos, CA, USA, 1996. IEEE Computer Society Press.
[20] J. Lander, Devil in blue faceted dress: Real-time cloth animation. Game Developer, 1999.
[21] J. M. Kennedy, Optics and haptics: The picture. In The conference on Multimodality of Human Communication: Theory, Problems and Applications. University of Toronto, 2002.
[22] T. Larsson and T. Akenine-Möller, Collision detection for continuously deforming bodies. In Eurographics 2001, pages 325–333, Manchester, September 2001. Eurographics Association.
[23] L. Kim, G. Sukhatme, and M. Desbrun, A haptic-rendering technique based on hybrid surface representation. IEEE Comput. Graph. Appl., 24 (2): 66–75, 2004.
[24] M. A. Noll, A computer technique for displaying n-dimensional hyperobjects. Communications of the ACM, 10 (8): 469–473, August 1967.
[25] A. M. Okamura, Haptic Exploration of Unknown Objects. PhD thesis, Stanford University, Department of Mechanical Engineering, California, USA, June 2000.
[26] A. M. Okamura and M. R. Cutkosky, Feature detection for haptic exploration with robotic fingers. The International Journal of Robotics Research, 20 (12): 925–938, Dec. 2001.
[27] J. G. Park and G. Niemeyer, Haptic rendering with predictive representation of local geometry. In HAPTICS, pages 331–338, 2004.
[28] X. Provot, Collision and self-collision andling in cloth model dedicated to design garments. In Proc. Computer Animation and Simulation'97, pages 177–189, 1997.
[29] C. Raymaekers, L. Vanacken, E. Cuppens, and K. Coninx, A comparison of different techniques for haptic cloth rendering. In HAPTEX '05: Proceedings of the VR Workshop on Haptic and Tactile Perception of Deformable Objects, pages 56–63. Magnenat-Thalmann N.[edit.], e.a., s.l., 2005.
[30] D. Roseman, Twisting and turning in four dimensions, 1993. Video animation, Department of Mathematics, University of Iowa, and the Geometry Center.
[31] R. G. Scharein, Interactive Topological Drawing. PhD thesis, Department of Computer Science, The University of British Columbia, 1998.
[32] SensAble, Inc. 3D Touch SDK OpenHaptics Toolkit Programmer's Guide, 2004.
[33] S. Snibbe, S. Anderson, and B. Verplank, Springs and constraints for 3d drawing. In Proceedings of the Third Phantom Users Group Workshop, Dedham, MA, 1998.
[34] K. V. Steiner and R. P. Burton, Hidden volumes: The 4th dimension. Computer Graphics World, pages 71–74, February 1987.
[35] W. Yu, R. Ramloll, and S. Brewster, Haptic graphs for blind computer users. In First International Workshop on Haptic Human-Computer Interaction, pages 102–107. British HCI Group, Springer, 2000.
[36] M. A. Zahariev and C. L. MacKenzie, Auditory, graphical and haptic contact cues for a reach, grasp, and place task in an augmented environment. In Proc. of 5th Intl. Conf on Multimodal Interfaces (ICMI), pages 273–276, New York, 2003. ACM, ACM Press.
[37] H. Zhang and A. J. Hanson, Physically interacting with four dimensions. In G. Bebis, R. Boyle, B. Parvin, D. Koracin, P. Remagnino, A. V. Nefian, M. Gopi, V. Pascucci, J. Zara, J. Molineros, H. Theisel, and T. Malzbender, editors, ISVC (1), volume 4291 of Lecture Notes in Computer Science, pages 232–242. Springer, 2006.
[38] C. B. Zilles and J. K. Salisbury, A constraint-based god-object method for haptic display. In IROS '95: Proceedings of the International Conference on Intelligent Robots and Systems-Volume 3, page 3146, Washington, DC, USA, 1995. IEEE Computer Society.

Index Terms:
knot theory, haptics, visualization
Citation:
Hui Zhang, Andrew Hanson, "Shadow-Driven 4D Haptic Visualization," IEEE Transactions on Visualization and Computer Graphics, vol. 13, no. 6, pp. 1688-1695, Nov.-Dec. 2007, doi:10.1109/TVCG.2007.70593
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