VolumeNRGE function

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

VolumeNRGE is used to calculate the volume of an egg that follows the Narushin-Romanov-Griffin equation. UTF-8

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:

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

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. tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_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