Biological Geometries
Calculation of the Surface Area of An Egg Based on the Explicit Trosci...
Boundary Data Adjustment of A Polygon
Area Calculation for the Gielis Curve Within
Area Calculation for an Ovate Polygon
Measure of the Extent of Bilateral Symmetry of A Polygon
Biological Geometries
Drawing the Preston Curve Produced by the the Explicit Preston Equatio...
Drawing the Troscianko Curve Produced by the Explicit Troscianko Equat...
Drawing the Gielis Curve
Drawing the Egg Shape Predicted by the Narushin-Romanov-Griffin Equati...
Drawing the Ovate Leaf-Shape Curve
Calculation of the First-Order Derivative of the Explicit Preston Equa...
Calculation of the First-Order Derivative of the Explicit Troscianko E...
Calculation of the First-Order Derivative of the Narushin-Romanov-Grif...
Calculation of the First-Order Derivative of the Simplified Gielis Equ...
Calculation of the Ordinate For an Arbitrary Point on the Preston Curv...
Calculation of the Ordinate For an Arbitrary Point on the Troscianko C...
Data-Fitting Function for the Explicit Preston Equation
Data-Fitting Function for the Explicit Troscianko Equation
Data-Fitting Function for the Gielis Equation
Data-Fitting Function for the Rotated and Right-Shifted Lorenz Curve
Parameter Estimation for the Narushin-Romanov-Griffin Equation
Data-Fitting Function for the Ovate Leaf-Shape Equation
Data-Fitting Function for the Sigmoid Growth Equation
Data-Fitting Function for the Superellipse Equation
Calculation of Fractal Dimension of Lef Veins Based on the Box-Countin...
Calculation of the Polar Radius of the Gielis Curve
Parameter Estimation for the Todd-Smart Equation
Parameter Estimation for the Troscianko Equation
Modified Beta Equation
Modified Briere Equation
Modified Lobry-Rosso-Flandrois (LRF) Equation
Modified Performance Equation
The Narushin-Romanov-Griffin Equation (NRGE)
Calculation of the Abscissa, Ordinate and Distance From the Origin For...
Sarabia Equation
Sarabia-Castillo-Slottje Equation (SCSE)
Sitthiyot-Holasut Equation
Sigmoid Growth Equation
Calculation of the Surface Area of An Egg Based on the Explicit Presto...
Calculation of the Surface Area of An Egg Based on the Narushin-Romano...
Calculation of the Surface Area of An Egg Based on the Simplified Giel...
The Troscianko Equation (TE)
Calculation of the Polar Radius of the Twin Gielis Curve
The Todd-Smart Equation (TSE)
Calculation of the Volume of An Egg Based on the Explicit Preston Equa...
Calculation of the Volume of An Egg Based on the Explicit Troscianko E...
Calculation of the Volume of An Egg Based on the Narushin-Romanov-Grif...
Calculation of the Volume of An Egg Based on the Simplified Gielis Equ...
Is used to simulate and fit biological geometries. 'biogeom' incorporates several novel universal parametric equations that can generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings (Gielis (2003) <doi:10.3732/ajb.90.3.333>; Shi et al. (2020) <doi:10.3390/sym12040645>), three growth-rate curves representing the ontogenetic growth trajectories of animals and plants against time, and the axially symmetrical and integral forms of all these functions (Shi et al. (2017) <doi:10.1016/j.ecolmodel.2017.01.012>; Shi et al. (2021) <doi:10.3390/sym13081524>). The optimization method proposed by Nelder and Mead (1965) <doi:10.1093/comjnl/7.4.308> was used to estimate model parameters. 'biogeom' includes several real data sets of the boundary coordinates of natural shapes, including avian eggs, fruit, lanceolate and ovate leaves, tree rings, seeds, and sea stars,and can be potentially applied to other natural shapes. 'biogeom' can quantify the conspecific or interspecific similarity of natural outlines, and provides information with important ecological and evolutionary implications for the growth and form of living organisms. Please see Shi et al. (2022) <doi:10.1111/nyas.14862> for details.