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 the codomain (y-set) connects each x element to precisely one y element. Since each x-point originating from the domain corresponds to two y-points on the graph of a closed curve (i.e., circle, ellipse, superellipse, or ovoid) in a rectangular (Cartesian) diagra...

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Vydané v:Forests Ročník 14; číslo 6; s. 1102
Hlavní autori: Denih, Asep, Putra, Gustian Rama, Kurniawan, Zaqi, Bahtiar, Effendi Tri
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Basel MDPI AG 01.06.2023
Predmet:
Biomass
cambium
Carbon sequestration
Cartesian coordinates
computers
Curve fitting
Data points
Digitization
Domains
Environmental effects
Goodness of fit
Physiological aspects
Polar coordinate models
Polar coordinates
Polar diagrams
Programming languages
Regression
Regression analysis
Shape effects
Stems
Stems (Botany)
tree trunk
Trees
Indonesia
ISSN:1999-4907, 1999-4907
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Abstract A function from the domain (x-set) to the codomain (y-set) connects each x element to precisely one y element. Since each x-point originating from the domain corresponds to two y-points on the graph of a closed curve (i.e., circle, ellipse, superellipse, or ovoid) in a rectangular (Cartesian) diagram, it does not fulfil the function’s requirements. This non-function phenomenon obstructs the nonlinear regression application for fitting observed data resembling a closed curve; thus, it requires transforming the rectangular coordinate system into a polar coordinate system. This study discusses nonlinear regression to fit the circumference of a tree stem’s cross-section and its sapwood–heartwood transition by transforming rectangular coordinates (x, y) of the observed data points’ positions into polar coordinates (r, θ). Following a polar coordinate model, circular curve fitting fits a log’s cross-sectional shape and sapwood–heartwood transition. Ellipse models result in better goodness of fit than circular ones, while the rotated ellipse is the best-fit one. Deviation from the circular shape indicates environmental effects on vascular cambium differentiation. Foresters have good choices: (1) continuing using the circular model as the simplest one or (2) changing to the rotated ellipse model because it gives the best fit to estimate a tree stem’s cross-sectional shape; therefore, it is more reliable to determine basal area, tree volume, and tree trunk biomass. Computer modelling transforms the best-fit model’s formulas of the rotated ellipse using Python scripts provided by Wolfram engine libraries.
AbstractList A function from the domain (x-set) to the codomain (y-set) connects each x element to precisely one y element. Since each x-point originating from the domain corresponds to two y-points on the graph of a closed curve (i.e., circle, ellipse, superellipse, or ovoid) in a rectangular (Cartesian) diagram, it does not fulfil the function’s requirements. This non-function phenomenon obstructs the nonlinear regression application for fitting observed data resembling a closed curve; thus, it requires transforming the rectangular coordinate system into a polar coordinate system. This study discusses nonlinear regression to fit the circumference of a tree stem’s cross-section and its sapwood–heartwood transition by transforming rectangular coordinates (x, y) of the observed data points’ positions into polar coordinates (r, θ). Following a polar coordinate model, circular curve fitting fits a log’s cross-sectional shape and sapwood–heartwood transition. Ellipse models result in better goodness of fit than circular ones, while the rotated ellipse is the best-fit one. Deviation from the circular shape indicates environmental effects on vascular cambium differentiation. Foresters have good choices: (1) continuing using the circular model as the simplest one or (2) changing to the rotated ellipse model because it gives the best fit to estimate a tree stem’s cross-sectional shape; therefore, it is more reliable to determine basal area, tree volume, and tree trunk biomass. Computer modelling transforms the best-fit model’s formulas of the rotated ellipse using Python scripts provided by Wolfram engine libraries.
Audience Academic
Author Putra, Gustian Rama
Denih, Asep
Bahtiar, Effendi Tri
Kurniawan, Zaqi
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  fullname: Bahtiar, Effendi Tri
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SubjectTerms Biomass
cambium
Carbon sequestration
Cartesian coordinates
computers
Curve fitting
Data points
Digitization
Domains
Environmental effects
Goodness of fit
Physiological aspects
Polar coordinate models
Polar coordinates
Polar diagrams
Programming languages
Regression
Regression analysis
Shape effects
Stems
Stems (Botany)
tree trunk
Trees
Title 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
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