Comparative evaluation of spline-based and Laplace-based interpolation for joint torque field reconstruction: a simulation study

Each condition was simulated 1000 times, and reconstruction accuracy was quantified by root mean square error (RMSE) and absolute deviation from the median, with method comparisons performed using Wilcoxon signed-rank tests. For the single-peak surface, TPSS with greater smoothing consistently yielded the lowest RMSE across outlier conditions, whereas TPS was most adversely affected by outliers. For the two-peak surface, TPS outperformed other methods, and Laplace interpolation consistently produced the largest RMSE.

Under missing-data conditions, spline-based methods showed comparable or superior accuracy to Laplace interpolation, despite its theoretical suitability for handling missing data. These findings empirically demonstrate condition-dependent differences in interpolation accuracy across methods and suggest that method selection should be guided by prior knowledge or preliminary assessment of the spatial complexity of the target torque field.</p>