Spherical Harmonics: A New Method for Estimating Maximum Reach Distance

Abstract

Traditional methodology for estimating maximum reach distances has relied primarily on regression analysis or visual data smoothing. This paper evaluates alternative maximum reach estimation techniques including splines, periodic splines, and spherical harmonics. The results indicate that spherical harmonics are most suited for reach estimation due to the spherical nature of the data. A spherical harmonic maximum reach model is developed based on R² and standard error values and residual plots. Three dimensional computer plots of the residuals provide a clear picture of potential model biases. Model parameters are obtained for 5th, 50th, and 95th percentiles for individuals and populations in the constrained-back seating posture.