6-DOF haptic rendering using geometric algebra

A new six-degree-of-freedom (6-DOF) haptic algorithm that uses geometric algebra for the computations is presented. It takes advantage of the power of this newly discovered branch of mathematics and allows for a force model that is based on a continuous volumetric approach. We show that the graphics model and haptic representation should not be identical, yet should both be based on the same geometric representations. Our sense of touch is not as easily fooled as our eyes and it is therefore necessary to have a more accurate model for computing the feeling of virtual objects. This paper presents an approach that uses an evenly distributed collection of points to represent the tool. There is a limit to this concentration where it yields a continuous model of the volume of the actual tool. This algorithm was implemented in a simple proof-of-concept demonstration.