VolumeNRGE {biogeom}

Calculation of the Volume of An Egg Based on the Narushin-Romanov-Griffin Equation

Description

VolumeNRGE is used to calculate the volume of an egg that follows the Narushin-Romanov-Griffin equation.

Usage

VolumeNRGE(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 Narushin-Romanov-Griffin 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 Narushin-Romanov-Griffin equation is:

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

where y denotes the Narushin-Romanov-Griffin equation (i.e., NRGE), and A denotes the egg's length, which is the first element in the parameter vector, P.

Note

The argument P in the VolumeNRGE function has the same parameters, as those in the NRGE function.

Author(s)

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

References

Narushin, V.G., Romanov, M.N., Griffin, D.K. (2021) Egg and math: introducing a universal formula for egg shape. Annals of the New York Academy of Sciences 1505, 169-177. doi:10.1111/nyas.14680

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

curveNRGE, fitNRGE, NRGE, SurfaceAreaNRGE

Examples

  Par6 <- c(4.51, 3.18, 0.1227, 2.2284)
  VolumeNRGE(P=Par6)

  myfun <- function(x){
    pi*NRGE(P=Par6, x=x)^2
  }
  integrate(myfun, -4.51/2, 4.51/2)$value