TREE FORM: DEFINITION, INTERPOLATION, EXTRAPOLATION

Abstract

Definition of tree form requires numerous measurements of height and stem radius or diameter distributed over the entire tree stem. Further definition may involve a graphic plot of stem profile, an analytic expression of radius as a polynomial or rational polynomial function of distance from apex, or the direct numeric evaluation of the major integrals of tree form (length, surface, volume). Linear, quadratic, or harmonic interpolation over short intervals can assume a monotonic one-parameter function without introducing serious error. Extrapolation should employ a two-parameter function passing through the origin and based on three measured pairs of coordinates. Appropriate surface and volume integrals are given for the convex right hyperbola (XY−QX+PY=O) and the concave parabola (Y 2 +QX−PY=O).