Abstract
We argue that B-spline solids are effective primitives for the animation of physically-based deformable objects. After reviewing the mathematical formulation of B-spline solids, we describe how to quickly display and modulate their shapes. We apply our ideas to muscle modelling and provide techniques for initial shape definition and subsequent shape deformation. Data-fitting techniques are developed to build muscles from profile curves or from contour data taken from medical images. By applying a spring-mass model to the resulting B-spline solid, we have transformed a static model to a deformable one. The 3-D parameterization of the solid allows us to model microstructures within the solids such as fibre bundles in a muscle. B-spline solids are powerful and versatile deformable shape primitives that can be used in practical settings, such as the building-blocks of a muscle-based modeller and animation system for anatomical design.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
James F. Blinn. A generalization of algebraic surface drawing ACM Transactions on Graphics, 1 (3): 235 - 256, July 1982
Jules Bloomenthal and Brian Wyvill. Interactive techniques for implicit modeling. In Rich Riesenfeld and Carlo Sequin, editors, Computer Graphics (1990 Symposium on Interactive 3D Graphics), volume 24, pages 109–116, March 1990.
Sabine Coquillart. Extended free-form deformation: A sculpturing tool for 3D geometric modeling. In Forest Baskett, editor, Computer Graphics (SIGGRAPH ’90 Proceedings), volume 24, pages 187 - 196, August 1990.
David T. Chen and David Zeltzer. Pump it up: Computer animation of a biomechanically based model of muscle using the finite element method. In Edwin E. Catmull, editor, Computer Graphics (SIGGRAPH ’92 Proceedings), volume 26, pages 89 - 98, July 1992.
Scott L. Delp, J. Peter Loan, Melissa G. Hoy, Felix E. Zajac, Eric L. Topp, and Joseph M. Rosen. An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures. IEEE Transactions on Biomedical Engineering, 37 (8): 757 - 767, 1990.
J. E. Dennis Jr. and Robert B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Inc., 1983.
David R. Forsey and Richard H. Bartels. Hierarchical B-spline refinement. In John Dill, editor, Computer Graphics (SIGGRAPH ’98 Proceedings), volume 22, pages 205 - 212, August 1988.
Eliot Goldfinger. Human Anatomy for Artists. Oxford University Press, 1991.
Andrew Grace. Optimization Toolbox User’s Guide. The Math Works, Inc., Natick, Mass., 1994.
William M. Hsu, John E Hughes, and Henry Kaufman. Direct manipulation of free-form deformations. In Computer Graphics (SIGGRAPH ’92 Proceedings), volume 26, pages 177 - 184, 1992.
Josef Hoschek and Dieter Lasser. Fundamentals of Computer Aided Geometric Design. A K Peters, 1989.
Michael Kass, Andrew Witkin, and Demetri Terzopoulos. Snakes: Active contour models. International Journal of Computer Vision, 1 (4): 321 - 331, 1987.
Henry J. Lamousin and Warren N. Waggenspack Jr. Nurbs-based free-form deformations. IEEE Computer Graphics and Applications,pages 59–65, November 1994.
Michael D. McCool. Analytic antialiasing with prism splines. In Computer Graphics (SIGGRAPH ’95 Proceedings), volume 29, pages 429 - 436, August 1995.
U.S. National Library of Medicine. The visible human project. http://www.nlm.nih.gov/research/visible/visible_human. html, October 1996.
Hans Kohling Pedersen. Decorating implicit surfaces. In Computer Graphics (SIGGRAPH ’95 Proceedings), volume 29, pages 291 - 300, 1995.
Ari Rappoport, Alla Sheffer, and Michel Bercovier. Volume-preserving free-form solids. In Solid Modelling ’95, pages 361 - 372, 1995.
Coenraad Frederik Scheepers. Anatomy-Based Surface Generation for Articulated Models of Human Figures. PhD thesis, Ohio State University, 1996.
Sudhanshu K. Semwal and John J. Hallauer. Biomechanical modeling: im-plementing line-of-action algorithm for human muscles and bones using generalized cylinders. Computers and Graphics, 18 (1): 105 - 112, 1994.
Uri Shani. Splines as embeddings for generalized cylinders, Graphics and Image Processing, 27: 129 - 156, 1984.
Thomas W. Sederberg and Scott R. Parry. Free-form deformation of solid geometric models. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH ’96 Proceedings), volume 20, pages 151 - 160, August 1986.
Jianhua Shen and Daniel Thalmann. Interactive shape design using meta-balls and splines. In Implicit Surfaces ’95, pages 187 - 193, 1995.
James Stewart. Calculus. Brooks/Cole Publishing Company, 1987.
Andrew P. Witkin and Paul S. Heckbert. Using particles to sample and control implicit surfaces. In Andrew Glassner, editor, Computer Graphics (SIGGRAPH ’94 Proceedings), volume 28, pages 269 - 278, 1994.
Jane Wilhelms. Animals with anatomy. IEEE Computer Graphics Applications, 17 (3): 22 - 30, 1997.
Felix E. Zajac. Muscle and tendon: Properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Engineering, 17(4): 359 - 411, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag/Wien
About this paper
Cite this paper
Ng-Thow-Hing, V., Fiume, E. (1997). Interactive display and animation of B-spline solids as muscle shape primitives. In: Thalmann, D., van de Panne, M. (eds) Computer Animation and Simulation ’97. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6874-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-7091-6874-5_6
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83048-2
Online ISBN: 978-3-7091-6874-5
eBook Packages: Springer Book Archive