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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| 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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| Authors: | Asep Denih, Gustian Rama Putra, Zaqi Kurniawan, Effendi Tri Bahtiar |
| Source: | Forests, Vol 14, Iss 6, p 1102 (2023) |
| Publisher Information: | MDPI AG |
| Publication Year: | 2023 |
| Collection: | Directory of Open Access Journals: DOAJ Articles |
| Subject Terms: | algorithm, curve fit, nonlinear regression, polar diagram, Python scripts, sapwood–heartwood, Plant ecology, QK900-989 |
| Description: | 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. |
| Document Type: | article in journal/newspaper |
| Language: | English |
| Relation: | https://www.mdpi.com/1999-4907/14/6/1102; https://doaj.org/toc/1999-4907; https://doaj.org/article/81656d7b834f43c1b2270be74c133f94 |
| DOI: | 10.3390/f14061102 |
| Availability: | https://doi.org/10.3390/f14061102 https://doaj.org/article/81656d7b834f43c1b2270be74c133f94 |
| Accession Number: | edsbas.36D48C32 |
| Database: | BASE |
Nájsť tento článok vo Web of Science | 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. |
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| DOI: | 10.3390/f14061102 |