Previous work in haptics surface tracing for virtual prototyping and surface design applications has used a point model for virtual finger-surface interaction. We extend this tracing method for surface-to-surface interactions. A straightforward extension of the point-surface formulation to surface-surface can yield extraneous, undesirable solutions, although we rework the formulation to yield more satisfactory solutions. Additionally, we derive an alternative novel velocity formulation for use in a surface-surface tracing paradigm that exhibits additional stability beyond the Newton methods. Both methods require evaluating the surface point and first and second surface partial derivatives for both surfaces, an efficient kilohertz rate computation. These methods are integrated into a three step tracking process that uses a global minimum distance method, the local Newton formulation, and the new velocity formulation.

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