Is pose-based pivot calibration superior to sphere fitting?

Calibrating a pointing stylus tracked via a dynamic reference frame (DRF) is often performed by pivoting the stylus on its tip in a divot located at a fixed position in the tracking system coordinate frame. The calibration problem is solved by estimating the location of the fixed divot position. Recent work (Yaniv,, Which pivot calibration?, Proceedings of SPIE Vol. 941527, 2015) provided evidence that solving the calibration problem using the measured poses of the stylus during pivoting is superior to fitting the measured position of the DRF during pivoting to a sphere. We constructed apparatus to acquire very high quality pivoting measurements over a much wider range of pivoting angles than could be obtained by pivoting in a divot. We tested pose-based calibration and sphere fitting and found that sphere fitting was as precise as (if not better than) pose-based calibration when using high-quality pivoting data. We performed a simple simulation where the stylus tip location deviated by a small amount during pivoting and found that the precision of sphere fitting degraded much more than pose-based calibration which suggests that pose-based calibration should be favored over sphere fitting when non-perfect pivoting is not possible.