SurfaceAreaEPE function

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

SurfaceAreaEPE is used to calculate the surface area of an egg that follows the explicit Preston equation. UTF-8

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:

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 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., 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

DEPE, EPE, fitEPE, VolumeEPE

Examples

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