biogeom (version 1.5.0)

SurfaceAreaAM: 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.

Author

Peijian Shi , Johan Gielis , Brady K. Quinn .

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.

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. 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)