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.