The skeleton layer, represented by a set of joints and bones, controls the animation of the human body model using inverse kinematics. Muscles are represented by action lines, which are de¯ned by a set of control points. The action line expresses the force produced by a muscle on the bones and on the skin mesh. The skin layer is modeled in a 3D modeler and deformed during animation by binding the skin layer to both the skeleton layer and the muscle layer. The skin is deformed by a two-step algorithm according to the current state of the skeleton and muscle layers. In the ¯rst step, the skin is deformed by a variant of the skinning algorithm, which deforms the skin based on the motion of the skeleton. In the second step, the skin is deformed by the underlying muscular layer. Visual results produced by the implementation is also presented. Performance experiments show that it is possible to obtain real-time frame rates for a moderately complex human model containing approximately
33,000 triangles on the skin layer.

[2] Barr, A., \Dynamic constraints", State of the Art in Image Synthesis Course Notes, ACM SIGGRAPH'86, 1986.
[3] Badler, N. and Smoliar, S., \Digital representations of human movement", ACM Computing Surveys, Vol. 11, No. 1, pp. 19-38, March 1979.
[4] Badler, N., \Graphical behavior and animated agents", Advanced Techniques in Human Modeling, Animation and Rendering, ACM SIG-
GRAPH'92 Course Notes #17, July 1992.
[5] Blinn, J., \A generalization of algebraic surface drawing", Transactions on Graphics, Vol. 1, pp. 235-256, 1982.
[6] Bloomenthal, J. and Shoemake, K., \Convolution surfaces", ACM Computer Graphics (Proceedings of SIGGRAPH'91), pp. 251-256, 1991.
[7] Bloomenthal, J., \Hand crafted", Modeling, Visualization and Animating Implicit Surfaces, ACM SIGGRAPH Course Notes #25, 1993.
[8] Cani-Gascuel, M.P.,\Layered deformable models with implicit surfaces", Graphics Interface'98, Vancouver, Canada, 1998.
67
[9] Chadwick, J., Haumann, D. and Parent, R., \Layered construction for deformable animated characters", ACM Computer Graphics (Proceedings of SIGGRAPH'89), pp. 243-252, July 1989.
[10] Deepak, T., Goswami, A., Badler, N., \Real-time inverse kinematics techniques for anthropomorphic limbs", Graphical Models, Vol. 62, No. 5, pp. 353-388, September 2000.
[11] Delp, S.L. and Loan, J.P., \A computational framework for simulating and analyzing human and animal movement", IEEE Computing in Science & Engineering, Vol. 2, No. 5, pp. 46-55, Sept-Oct 2000.
[12] DeLoura, M.A., Game Programming Gems, Charles River Media Inc., Rockland, Massachusetts, 2000.
[13] DeRose, T., Kass, M., and Truong, T., \Subdivision surfaces in character animation", ACM Computer Graphics (Proceedings of SIGGRAPH'98),pp. 85-94, 1998.
[14] Fung, Y.C., Biomechanics: Mechanical Properties of Living Tissues,Springer-Verlag, New York, 1981.
[15] Gascuel, M.P., Verroust, A., and Puech, C., \A modeling system for com- plex deformable bodies suited to animation and collision processing", The Journal of Visualization and Computer Animation, Vol. 2, No. 3, pp. 82-91,
1991.
[16] Gascuel, M.P., \An implicit formulation for precise contact modeling be-tween °exible solids", ACM Computer Graphics (Proceedings of SIG-GRAPH'93), pp. 313-320, 1993.
[17] Haumann, D.R. and Parent, R.E., \The behavioral testbed: Obtaining com-plex behavior from simple rules", The Visual Computer, Special Issue on Mechanics, Control and Animation, Vol. 4, No. 6, December 1988. 68
[18] Herbison-Evans, D., \Nudes 2: A numeric utulity displaying ellipsoid solids", SIGGRAPH'78 Conference Proceedings, pp. 354-356, August 1978.
[19] Hirota, G., Fisher, S., State, A., Lee, C., and Fuchs, H., \An implicit ¯- nite element method for elastic solids in contact", Proceedings of Computer Animation'01, Seoul, Korea, 2001.
[20] Kavan, L. and Zara, J., \Real time skin deformation with bones blending", WSCG'2003 Short Papers, University of West Bohemia, Pilsen, Chech Re- public, pp. 69-74, 2003.
[21] Komatsu, K., \Human skin model capable of natural shape variation", The Visual Computer, Vol. 3, No. 5, pp. 265-271, 1988.
[22] Korein, J. and Badler, N., \Techniques for generating the goal directed motions of articulated ¯gures", IEEE Computer Graphics and Applications, Vol. 2, No. 9, pp. 71-74, 1982.
[23] Korein, J., A Geometric Investigation of Reach, The MIT Press, Cambridge, 1985.
[24] Lander, K., \Skin them bones", Game Developer, pp. 11-16, May 1998.
[25] Lanir, Y., \Skin mechanics". In Handbook of Bioengineering, Edited by R. Skalak, McGraw Hill, 1987.
[26] Lasseter, J., \Principles of traditional animation applied to 3D computeranimation", ACM Computer Graphics (Proceedings of SIGGRAPH'87), pp. 35-44, 1987.
[27] Leclercq, A., Akkouche, S., and Galin, E., \Mixing triangle meshes and implicit surfaces in character animation", Proceedings of Animation and Simulation'01, pp. 37-47, Manchester, England, 2001.
69
[28] Maurel, W., Wu, Y., Thalmann, M., and Thalmann, D., Biomechani-cal Models for Soft Tissue Simulation, Springer-Verlag, Berlin/Heidelberg, 1998.
[29] Maurel, W. and Thalmann, D. \Human upper limb modeling including scapulo-thoracic constraint and joint sinus cones", Computers & Graphics, Vol. 24, No. 2, pp. 203 - 218, 2000.
[30] Memi»so¸glu, A., \Human motion control using inverse kinematics", MS. The- sis, Department of Computer Engineering, Bilkent University, August 2003. [31] Min, K., Baek, S., Lee, G.A., Choi, H., and Park, C., \Anatomically-based modeling and animation of human upper limbs", Proceedings of Interna- tional Conference on Human Modeling and Animation, Seoul, Korea, June 2000.
[32] \MetaCreations Software", Poser 4, http://www.metacreations.com/products/poser.
[33] Moccozet, L., \Hand modeling and animation for virtual humans", PhD Thesis, No 442, University of Geneva, 1996.
[34] Nedel, L. and Thalmann, D., \Real time muscle deformations using mass-spring systems", Proceedings of Computer Graphics International (CGI'98), pp. 156-165, 1998.
[35] Ng-Thow-Hing, V., \Anatomically-based models for physical and geometric reconstruction of humans and other animals", Ph.D. Thesis, Department of Computer Science, University of Toronto, 2000.
[36] The National Library of Medicine, \The visible human project", available at http://www.nlm.nih.gov/research/visible/visible human.html. 70
[37] Porcher-Nedel, L. \Anatomic modeling of human bodies using physically-based muscle simulation", Ph.D. Thesis, No 1831, Swiss Federal Institute of Technology, 1998.
[38] Richer, P., \Trait danatomie artistique", Bibliothque de limage, 1996.
[39] Scheepers, F., \Anatomy based surface generation for articulated models of human ¯gures", PhD thesis, Department of Computer and Information Science, The Ohio State University, 1996.
[40] Scheepers, F., Parent, R., May, F., and Carlson, W., \Procedural approach to modeling and animating the skeletal support of the upper limb", Techni-cal Report, OSU-ACCAD-1/96/TR1, The Ohio State University, 1996.
[41] Scheepers, F., Parent, R., Carlson, W. and May, S., \Anatomy based mod- eling of the human musculature", ACM Computer Graphics (Proceedings of SIGGRAPH'97), pp. 163-172, 1997.
[42] Sederberg, T. and Parry, S., \Free-from deformation of solid geometric mod- els", ACM Computer Graphics (Proceedings of SIGGRAPH'86), pp. 151-160, 1986.
[43] Singh, K., Ohya, J., Kishino, F. and Parent, R., \Human ¯gure synthesis and animation for virtual space teleconferencing", Virtual Reality Annual International Symposium'95, pp. 118-126, North Carolina, March 1995.
[44] Singh, K., \Human ¯gure synthesis and animation for VR applications", PhD thesis, The Ohio State University, 1995.
[45] Singh, K., Kokkevis, E., \Skinning characters using surface-oriented free form deformations", Proceedings of Graphics Interface 2000, pp. 35-42, 2000.
[46] Sloan, P.P., Rose, C.F., and Cohen, M., \Shape by example", Proceedings of the Symposium on Interactive 3D Graphics, pp. 135-143, March 2001. 71
[47] \Speci¯cation for a Standard Humanoid", Version 1.1, http://h-anim.org/Specifications/H-Anim1.1.
[48] Steketee, J. and Badler, N., \Parametric keyframe interpolation incorporating kinetic adjustment and phrasing control", ACM Computer Graphics (Proceedings of SIGGRAPH'85), pp. 255-262, July 1985.
[49] Sun, W., Hilton, A., Smith, R., and Illingworth, J., \Layered animation of captured data", Proceedings of the 10th Eurographics Workshop on Anima-tion and Simulation, Milano, Italy, 1999.
[50] Talbot, D., \Accurate characterization of skin deformations using range data", Master's thesis, University of Toronto, 1998.
[51] Terzopoulus, D., Platt, J.C., Barr H., and Fleischer, K., \Elastically deformable models", ACM Computer Graphics (Proceedings of SIG-GRAPH'87), July 1987.
[52] Thalmann, M.N. and Thalmann, D., Computer Animation: Theory and Practice, Springer-Verlag, Berlin, 1985.
[53] Thalmann, M.N. and Thalmann, D., \The direction of synthetic actors in the ¯lm Rendez-vous µa Montreµal", IEEE Computer Graphics and Applica-tions, Vol. 7, No. 12, pp. 9-19, 1987.
[54] Thalmann, M.N. and Thalmann, D., Synthetic Actors in 3D Computer- Generated Films, Springer-Verlag, New York, 1990.
[55] Thalmann, D., Shen, J., and Chauvineau, E., \Fast human body deforma- tions for animation and VR applications", Proceedings of Computer Graph-ics International'96, pp. 166-174. IEEE Computer Society Press, June 1996.
[56] Turner, R. and Thalmann, D., \The elastic surface layer model for ani-mated character construction", Proceedings of the Computer Graphics In- ternational'93, Lausanne, Switzerland, Springer-Verlag, pp. 399-412.
72
[57] Turner, R., \Leman: A system for construsting and animating layered elas- tic characters", Computer Graphics-Developments in Virtual Environments, pp. 185-203, Academic Press, San Diego, CA, June 1995.
[58] Wilhelms, J., \Modeling animals with bones, muscles and skin", Technical Report UCSC-CRL-95-01, University of California, Santa Cruz, January 1995.
[59] Wilhelms, J., \Animals with anatomy", IEEE Computer Graphics And Ap- plications, Vol. 17, No. 3, pp. 22-30, May 1997.
[60] Wilhelms, J. and Van Gelder, A., \Anatomically based modeling", ACM Computer Graphics (Proceedings of SIGGRAPH'97), pp. 173-180, 1997.