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(1)A Dynamic Meshing Real-time Cloth Simulation System Ji-Han Jiang. Wei-Huang Huang National Lo-Tung Commercial Senior High School E-mail: g1334005@stdmail.fgu.edu.tw. National Huwei Institute of Technology E-mail: jhjiang@sunws.nhit.edu.twjhjiang. Kang [12][13][14] Approximate Implicit Integration. 3D. 3D. cloth object. deformable numerical simulation dynamic mesh adjustment. 3D. [6]. [3][4]. Kang Baraff Witkin [1] Modified Conjugated. [12][13][14] Post Dynamic Mesh. Adjustment Method. Gradient Method. Desbrun [8] Precomputed Filter. -1-.

(2) r. 2 /. Particle System Mass-Spring Model Numerical Analysis. Discrete. Numerical Solution. [18]. Newton’s Second Law of Motion Hook’s Law F = ma m. Explicit Euler Method Forward Euler Method Ordinary Differential Equations ODE [23] First-Order Approximation 1 Truncation Error. F. a F = k ( x-L ). F. k x Rest Length ma = k ( x–L ). L. x˝ = m-1 k ( x - L ) x˝ = f ( t , x ) x. t. Stiff Stiff Equations. x˝ = f ( t , x, x´ ) 2 Stretchability In-plane Stretch. Out-of-plane Bend. x(t) = r cos ( t ) m. = ( k/m )1/2 k. -2-.

(3) 45 Stiff System. Shearing Force. Coarse 6 Kang [12][13][14] Dynamic Mesh Resolution Adjusted Mesh Triangulation. O(n). 7 Curvature 8. 9 3D. Geometry Object 10 2. O(n ) [5][11]. 11. 3 Structure Spring Spring. 4. Texture Application Program Interface. Bendind Shearing Spring. 5 Warp. Weft. Texture Coordinate. -3-. 3D API.

(4) 27×27. 14 (a) 14 (b). 14 (a) 14 (d). 15 (a) 15 (b) 15 (d). 21×21 53×53 17. 2 27×27 27×27 53×53. 1 12. 2 3 16. 53×53. 13. -4-.

(5) [8] Desbrun, M., Schroder, P., and Barr, A., “Interactive Animation of Structured Deformable Objects,” Proceedings of Graphics Interface 1999, 1999, pp. 1-8. [9] Gibson, S. and Mirtich, B., “A Survey of Deformable Modeling in Computer Graphics,” Technology Report No. TR-97-19, Mitsubishi Electric Research Lab. , 1997. [10] Gottschalk, S., Lin, M., and Manocha, D., “OBB-Tree: A Hierarchical Structure for Rapid Interference Detection,” Proceedings of SIGGRAPH '96, ACM Press, 1996, pp. 171-180. [11] Huh, S., Metaxas, D., and Badler, N., “Collision Resolutions in Cloth Simulation,” Computer Animation, 2001, pp.122-127. [12] Kang, Y. M., Choi, J. H., Cho, H. G., and Park, C. J., “Fast and Stable Animation of Cloth with An Approximated Implicit Method,” Proceedings of Computer Graphics International 2000, 2000, pp. 247-256. [13] Kang, Y. M., Choi, J. H., Cho, H. G., and Lee, D. H., “An Efficient Animation of Wrinkled Cloth with Approximate Implicit Integration,” The Visual Computer Journal, Springer-Verlag, Vol. 17, 2001, pp. 147-157. [14] Kang, Y. M., Choi, J. H., Cho, H. G., Lee, D. H., and Park, C. J., “Real-Time Animation Technique for Flexible and Thin Objects,” Proceedings of WSCG 2000, 2000, pp. 322-329. [15] Lin, M. C. and Gottschalk, S., “Collision Detection between Geometric Models: A Survey,” Proceedings of IMA Conference on Mathematics of Surfaces, 1998, pp. 37-56. [16] Mirtich, B., “V-Clip: Fast and Robust Polyhedral Collision Detection,” ACM Transactions on Graphics (TOG), ACM Press, Vol. 17, 1998, pp. 177-208. [17] Peachey, D. R., “Modeling Waves and Surf,” Proceedings of SIGGRAPH '86, ACM Press, 1986, pp. 65-74. [18] Provot, X., “Deformation Constraints in A Mass-Spring Model to Describe Rigid Cloth Behavior,” Proceedings of Graphic Interface '95, 1995, pp. 147-154. [19] Szeliski, R. and Tonnesen, D., “Surface Modeling with Oriented Particle Systems,” Proceedings of SIGGRAPH '92, ACM Press, 1992, pp. 185–194. [20] Volino, P. and Magnenat-Thalmann, N., “Comparing Efficiency of Integration Methods for Cloth Animation,” Proceedings of Computer Graphics International (CGI) 2001, 2001, pp. 256-267. [21] Volino, P., Courchesne, M., and Magnenat-Thalmann, N., “Versatile and Efficient Techniques for Simulating Cloth and Other Deformable Objects,” Proceedings of SIGGRAPH '95, ACM Press, 1995, pp. 137-44. [22] Weil, J., “The Synthesis of Cloth Objects,” Proceedings of SIGGRAPH '86, ACM Press, 1986, pp. 49-54. [23] Zill, D. G., A First Course in Differential Equations with Modeling Applications, 6th ed. , Brooks/Cole, 199. [1] Baraff, D. and Witkin, A., “Large Steps in Cloth Simulation, ” Proceedings of SIGGRAPH '98, ACM Press, 1998, pp. 43-54. [2] Bergen, G., “Efficient Collision Detection of Complex Deformable Models Using AABB Trees,” Journal of Graphics Tools, Vol. No. 4, 1997, pp. 1-13. [3] Breen, D. E., House, D. H., and Wozny, M. J., “Predicting the Drape of Woven Cloth Using Interacting Particles,” Proceedings of SIGGRAPH '94, ACM Press, 1994, pp. 365-372. [4] Breen, D. E., House, D. H., and Wozny, M. J., “A Particle-Based Model for Simulating the Draping Behavior of Woven Cloth,” Textile Research Journal, TRI/Princeton, Vol. 64, 1994, pp. 663-685. [5] Bridson, R., Fedkiw, R., and Anderson, J., “Robust Treatment of Collisions, Contact and Friction for Cloth Animation,” Proceedings of SIGGRAPH '02, ACM Press, 2002, pp. 594-603. [6] Carignan, M., Yang, Y., Magnenat-Thalmann, N., and Thalmann, D., “Dressing Animated Synthetic Actors with Complex Deformable Clothes,” Proceedings of SIGGRAPH '92, ACM Press, 1992, pp. 99-104. [7] Cohen, J. D., Lin, M. C., Manocha, D., and Ponamgi, M. K., “ I-COLLIDE: An Interactive and Exact Collision Detection System for Large-Scale Environments,” Proceedings of ACM Interactive 3D Graphics Conference, 1995, pp. 189-196.. -5-.

(6) 1 21×2123×2325×2527×2729×2931×3133×3335×3537×37 21.1 24.6 21.6 22.9 32.4 38.4 48.8 55.8 63.7 39×3941×4143×4345×4547×4749×4951×5153×53 78.8 72.7 81.6 122.2 124.3 138.1 155.8 221.5. 2. 3 (. ). 27 27. 5.4. 1352. 27 27. 22.9. 1352. 27 27. 5.9. 4563. 27 27. 24.7. 3072. 53 53. 33.9. 5408. 53 53. 221.5. 5408. 0.95 2. 27×27 53×53. 0.95 2. 422 1562. 59 219. 4. 1 5. 2. 6. 3 -6-. 8. 31.

(7) 10. 8. 9. 11. 12. (a). (. ). (c). (. ). (e). (. ). (b). (. ). (d). (. ). (f). (. ). 13. -7-.

(8) (a). (b). (c). (d) 14. (a). —. (b). (c). 15. (d). —. (a). (b). (c). (d). (e). 16. -8-. (f).

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