Developing a Model for Curve-Fitting a Tree Stem’s Cross-Sectional Shape and Sapwood–Heartwood Transition in a Polar Diagram System Using Nonlinear Regression

A function from the domain (x-set) to codomain (y-set) connects each x element precisely one y element. Since x-point originating corresponds two y-points on graph of a closed curve (i.e., circle, ellipse, superellipse, or ovoid) in rectangular (Cartesian) diagram, it does not fulfil function’s requirements. This non-function phenomenon obstructs nonlinear regression application for fitting observed data resembling curve; thus, requires transforming coordinate system into polar system. study discusses fit circumference tree stem’s cross-section and its sapwood–heartwood transition by coordinates (x, y) points’ positions (r, θ). Following model, circular fits log’s cross-sectional shape transition. Ellipse models result better goodness than ones, while rotated ellipse is best-fit one. Deviation indicates environmental effects vascular cambium differentiation. Foresters have good choices: (1) continuing using model as simplest (2) changing because gives best estimate shape; therefore, more reliable determine basal area, volume, trunk biomass. Computer modelling transforms model’s formulas Python scripts provided Wolfram engine libraries.