Comparison of selected splines for stem form modeling: A case study in Norway spruce

Abstract

Natural cubic spline has been frequently used to represent stem forms, with other spline types rarely involved. Splines are a large class of functions and there are many other spline types which might serve that purpose. In this paper several different spline types, both interpolation and approximation, were investigated and splines more suitable for stem form representation than natural cubic spline are proposed. Their abilities to model the stem curve using different numbers of input points were compared using data of 85 carefully measured Norway spruce (Picea abies [L.] Karst.) stems. When modeling the whole stem profile all interpolation curves with second degree continuity suffer from oscillations. Approximation splines give satisfactory overall estimations, but they overestimate the lower stem and overestimate the upper stem. The best results were obtained with interpolation curves with first degree continuity. Stem curves were best described by the Catmull-Rom spline. Previously frequently used natural cubic spline performed worse than number of other splines.

Keywords

• stem curve, taper model, interpolation, approximation, norway spruce, diameter position