Interactive Haptic Rendering of Deformable Surfaces Based on the Medial Axis Transform

We present a new method for interactive deformation and haptic rendering of viscoelastic surfaces. Objects are defined by a discretized Medial Axis Transform (MAT), which consists of an ordered set of circles (in 2D) or spheres (in 3D) whose centers are connected by a skeleton. The skeleton and physical properties of the object, including the radii of the spheres centered on the skeleton and material properties, are encapsulated in a single high dimensional parametric surface. To compute the force upon deformation, we use a mass-spring-damper model that takes into account both normal and shear surface forces. Our implementation attains real time 3D haptic and graphic rendering rates, making it appropriate to model deformation in complex haptic virtual environments. The algorithm is appealing because it takes advantage of single-point haptic interaction to render efficiently while maintaining a very low memory footprint.

[1]  B. Barsky,et al.  An Introduction to Splines for Use in Computer Graphics and Geometric Modeling , 1987 .

[2]  Dinesh K. Pai,et al.  ArtDefo: accurate real time deformable objects , 1999, SIGGRAPH.

[3]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[4]  Hong Qin,et al.  Dynamic NURBS with geometric constraints for interactive sculpting , 1994, TOGS.

[5]  Daniel Bielser,et al.  Open surgery simulation. , 2002, Studies in health technology and informatics.

[6]  Ricardo S. Avila,et al.  A haptic interaction method for volume visualization , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[7]  P. Hunter,et al.  FEM/BEM NOTES , 2001 .

[8]  Elaine Cohen,et al.  Direct haptic rendering of sculptured models , 1997, SI3D.

[9]  Christian Laugier,et al.  Towards a Realistic Medical Simulator using Virtual Environments and Haptic Interaction , 2001, ISRR.

[10]  Sabine Coquillart,et al.  Extended free-form deformation: a sculpturing tool for 3D geometric modeling , 1990, SIGGRAPH.

[11]  L. Piegl.  Modifying the shape of rational B-splines. part2: surfaces , 1989 .

[12]  Tamal K. Dey,et al.  Approximate medial axis as a voronoi subcomplex , 2002, SMA '02.

[13]  Anselmo Lastra,et al.  Interactive display of large-scale NURBS models , 1995, I3D '95.

[14]  Rynson W. H. Lau,et al.  Interactive Rendering of Deforming NURBS Surfaces , 1997 .

[15]  David E. Johnson,et al.  Improved method for haptic tracing of a sculptured surface , 1998 .

[16]  Herve Delingette,et al.  Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation , 1999, IEEE Trans. Vis. Comput. Graph..

[17]  Stephen M. Pizer,et al.  M-Reps: A New Object Representation for Graphics , 1999 .

[18]  Brian Mirtich,et al.  A Survey of Deformable Modeling in Computer Graphics , 1997 .

[19]  Ronald N. Perry,et al.  Mitsubishi Electric Research Laboratory , 2001 .

[20]  Deborah Silver,et al.  Parameter-controlled skeletonization: a framework for volume graphics , 2001 .

[21]  Allison M. Okamura,et al.  Feature-guided exploration with a robotic finger , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).