Addendum to “Dimensional Reduction for 6D Vibrotactile Display”

In our recent article, we found a general quadratic weighting function to predict how a six-dimensional (6D) vibrotactile stimulus rendered at the haptic interaction point (HIP) of a kinesthetic haptic interface, with the stylus held in a precision pen-hold grasp, is mapped to an equivalent one-dimensional (1D) stimulus that is normalized by the detection threshold. However, in that work we did not constrain the weighting function to be positive semidefinite, and as a result, the model will not generalize well to all future 6D inputs. In this addendum, we reconsider the original data set, incorporating the positive-semidefinite constraint. We find that as few as four independent parameters are required to describe the coupling, and the model has one fewer coupling term than originally proposed. We also describe the process of fitting a positive-semidefinite function to a new stylus at some specific excitation frequency.