VolumeETE {biogeom}

Calculation of the Volume of An Egg Based on the Explicit Troscianko Equation

Description

VolumeETE is used to calculate the volume of an egg that follows the explicit Troscianko equation.

Usage

VolumeETE(P, 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 Troscianko 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 volume (V) of an egg based on the explicit Troscianko equation is:

V(x)=\pi\int_{-a}^{a}y^2\,dx,

where y denotes the explicit Troscianko equation (i.e., ETE), and a denotes half the egg's length.

Note

The argument P in the VolumeETE function has the same parameters, as those in the ETE 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

ETE, fitETE, SurfaceAreaETE

Examples

  Par5 <- c(2.25, -0.38, -0.29, -0.16)
  VolumeETE(P=Par5)

  myfun <- function(x){
    pi*ETE(P=Par5, x=x)^2
  }
  integrate(myfun, -2.25, 2.25)$value