SurfaceAreaAM: Calculation of the Lateral Surface Area of an Apical...

View source: R/SurfaceAreaAM.R

SurfaceAreaAMR Documentation

Calculation of the Lateral Surface Area of an Apical meristem.

Description

SurfaceAreaAM is used to calculate the lateral surface area of an apical meristem that follows the the hybrid catenary-parabolic equation or the superparabolic equation.

Usage

SurfaceAreaAM(model = "Hybrid", P, upper = Inf, subdivisions = 100L,
          rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
          stop.on.error = TRUE, keep.xy = FALSE, aux = NULL)

Arguments

model

an optional argument to select a model to calculate the surface area.

P

the parameters of the hybrid catenary-parabolic equation or the superparabolic equation.

upper

the upper limit of integration in x.

subdivisions

please see the arguments for the integrate function in package stats.

rel.tol

please see the arguments for the integrate function in package stats.

abs.tol

please see the arguments for the integrate function in package stats.

stop.on.error

please see the arguments for the integrate function in package stats.

keep.xy

please see the arguments for the integrate function in package stats.

aux

please see the arguments for the integrate function in package stats.

Details

The formula of the lateral surface area (S) of an apical meristem based on the hybrid catenary-parabolic equation or the superparabolic equation:

S(x)=2 \, \pi \int_{0}^{a} x \,\sqrt{1+\left(\frac{dy}{dx}\right)^2}\,dx,

where a is the upper limit of integration in x. The lower limit of integration in x is 0.

\quad If model = "Hybrid", y denotes the hybrid catenary-parabolic equation, which equals y\left(x\right) = \alpha\,\mbox{cosh}(\beta x) + \gamma x^{2}-\alpha, and \frac{dy}{dx} = \alpha\,\beta\,\mbox{sinh}(\beta x) + 2\gamma x. Here, \alpha, \beta and \gamma are model parameters provided by the argument P.

\quad If model = "Superparabola", y denotes the superparabolic equation, which equals y\left(x\right) = \beta_{1}\, {\left|x\right|}^{\beta_{2}}, and \frac{dy}{dx} = \beta_{1}\,\beta_{2}\,x \left|x\right|^{\beta_{2}-2}. Here, \beta_{1} and \beta_{2} are model parameters provided by the argument P.

Note

The SurfaceAreaAM function actually calculates the lateral surface area regardless of the area of the 'base' circle. The argument P in the SurfaceAreaAM function has three parameters for model = "Hybrid", and two parameters for model = "Superparabola".

Author(s)

Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.

References

Shi, P., Gielis, J., Quinn, B.K., Niklas, K.J., Ratkowsky, D.A., Schrader, J., Ruan, H., Wang, L., Niinemets, Ü. (2022) 'biogeom': An R package for simulating and fitting natural shapes. Annals of the New York Academy of Sciences 1516, 123-134. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/nyas.14862")}

See Also

fitAM, PlanCoor, SAMs, VolumeAM

Examples

  par3 <- c(-20, 0.9695, 11.40)
  SurfaceAreaAM(model = "Hybrid", P = par3, upper=1)
  
  par5 <- c(1.3807, 1.3173)
  SurfaceAreaAM(model = "Superparabola", P = par5, upper=1)

biogeom documentation built on Aug. 24, 2025, 5:08 p.m.