VolumeEPE | R Documentation |
VolumeEPE
is used to calculate the volume of an egg that follows the explicit Preston equation.
VolumeEPE(P, simpver = NULL)
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. |
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}
.
The argument P
in the VolumeEPE
function has the same parameters, as those in the
EPE
function.
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/nyas.15000")}
EPE
, fitEPE
, SurfaceAreaEPE
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
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