SurfaceAreaEPE {biogeom}

Calculation of the Surface Area of An Egg Based on the Explicit Preston Equation

Description

SurfaceAreaEPE is used to calculate the surface area of an egg that follows the explicit Preston equation.

Usage

SurfaceAreaEPE(P, simpver = NULL, subdivisions = 100L,
          rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
          stop.on.error = TRUE, keep.xy = FALSE, aux = NULL)

Arguments

P

the parameters of the explicit Preston equation or one of its simplified versions.

simpver

an optional argument to use the simplified version of the explicit Preston equation.

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 surface area (S) of an egg based on the explicit Preston equation or one of its simplified versions is:

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

where y denotes the explicit Preston equation (i.e., EPE), and a denotes half the egg's length. When simpver = NULL, P has five parameters: a, b, c_{1}, c_{2}, and c_{3}; when simpver = 1, P has four parameters: a, b, c_{1}, and c_{2}; when simpver = 2, P has three parameters: a, b, and c_{1}; when simpver = 3, P has three parameters: a, b, and c_{2}.

Note

The argument P in the SurfaceAreaEPE function has the same parameters, as those in the EPE function.

Author(s)

Peijian Shi [e-mail], Johan Gielis [e-mail], Brady K. Quinn [e-mail].

References

Narushin, V.G., Romanov, M.N., Mishra, B., Griffin, D.K. (2022) Mathematical progression of avian egg shape with associated area and volume determinations. Annals of the New York Academy of Sciences 1513, 65-78. doi:10.1111/nyas.14771

Shi, P., Chen, L., Quinn, B.K., Yu, K., Miao, Q., Guo, X., Lian, M., Gielis, J., Niklas, K.J. (2023) A simple way to calculate the volume and surface area of avian eggs. Annals of the New York Academy of Sciences 1524, 118-131. doi:10.1111/nyas.15000

See Also

DEPE, EPE, fitEPE, VolumeEPE

Examples

  Par4 <- c(4.27, 2.90, 0.0868, 0.0224, -0.0287)
  SurfaceAreaEPE(P = Par4, simpver = NULL)