We propose to employ the MAT as the underlying physical representation for viscoelastic surfaces. Since the MAT is defined as a skeletal axis and a set of locally maximal circles centered about the axis, it is an excellent model for use in single point haptic interaction where the use of implicit equations is common for efficient force rendering computation.
As input to our algorithm, a set of MAT points are used to fully describe the necessary information of the object: position, radius, surface parameters (stiffness, etc). Through these data point we interpolate a high-dimensional parametric curve (the dimension of the curve is equal to the number of parameters, for 2d position and radius it would be 3 dimensional, for 3d position, radius, and mass it would be 5-dimension). This curve is the skeletal curve (2d) or surface (3d) against which all haptic interaction and deformation takes place. To aid in graphic rendering of these surfaces, we then extropolate an enveloping contour curve. The figure on the right displays these curves for a simple 2d MAT object. The green circle represent the input MAT points and the green curve is the medial axis. The dotted orange curve represents the extrapolated contour of the body.
For more details about the modeling technique and the interactive rendering and deformation algorithms please see the paper.