biogeom (version 1.4.3)

VolumeEPE: Calculation of the Volume of An Egg Based on the Explicit Preston Equation

Description

VolumeEPE is used to calculate the volume of an egg that follows the explicit Preston equation.

Usage

VolumeEPE(P, simpver = 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.

Author

Peijian Shi , Johan Gielis , Brady K. Quinn .

Details

When simpver = NULL, the volume formula (\(V\)) of the explicit Preston equation is selected: $$ V(x) = \frac{4\,\pi}{315}a\,b^{2}\left(105+21\,c_{1}^{2}+42\,c_{2}+9\,c_{2}^2+18\,c_{1}\,c_{3}+5\,c_{3}^2\right), $$ where P has five parameters: \(a\), \(b\), \(c_{1}\), \(c_{2}\), and \(c_{3}\).

\(\quad\) When simpver = 1, the volume formula of the simplified version 1 is selected: $$ V(x) = \frac{4\,\pi}{315}a\,b^{2}\left(105+21\,c_{1}^{2}+42\,c_{2}+9\,c_{2}^2\right), $$ where P has four parameters: \(a\), \(b\), \(c_{1}\), and \(c_{2}\).

\(\quad\) When simpver = 2, the volume formula of the simplified version 2 is selected: $$ V(x) = \frac{4\,\pi}{315}a\,b^{2}\left(105+21\,c_{1}^{2}\right), $$ where P has three parameters: \(a\), \(b\), and \(c_{1}\).

\(\quad\) When simpver = 3, the volume formula of the simplified version 3 is selected: $$ V(x) = \frac{4\,\pi}{315}a\,b^{2}\left(105+42\,c_{2}+9\,c_{2}^2\right), $$ where P has three parameters: \(a\), \(b\), and \(c_{2}\).

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. 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

EPE, fitEPE, SurfaceAreaEPE

Examples

  Par3 <- c(4.27, 2.90, 0.0868, 0.0224, -0.0287)
  VolumeEPE(P=Par3, simpver=NULL)

  # Test the case when simpver = NULL
  a    <- Par3[1]
  b    <- Par3[2]
  c1   <- Par3[3]
  c2   <- Par3[4]
  c3   <- Par3[5]
  pi*4/315*a*b^2*(105+21*c1^2+42*c2+9*c2^2+18*c1*c3+5*c3^2)

  myfun <- function(x){
    pi*EPE(P=Par3, x=x, simpver=NULL)^2
  }
  integrate(myfun, -4.27, 4.27)$value