DSGE {biogeom} | R Documentation |
Calculation of the First-Order Derivative of the Simplified Gielis Equation
Description
DSGE
is used to calculate the first-order derivative of the simplified Gielis equation at a given \varphi
-value.
Usage
DSGE(P, phi)
Arguments
P |
the parameters of the simplified Gielis equation, including |
phi |
the |
Details
The first-order derivative of the simplified Gielis equation with arguments simpver = 1
and m = 1
at a given \varphi
-value is:
g(x) = \frac{a}{4}\,\frac{n_{2}}{n_{1}}\,\left[\left(\cos{\frac{\varphi}{4}}\right)^{n_{2}-1}\left(\sin{\frac{\varphi}{4}}\right)-\left(\sin{\frac{\varphi}{4}}\right)^{n_{2}-1}\left(\cos{\frac{\varphi}{4}}\right)\right]\ \left[\left(\cos{\frac{\varphi}{4}}\right)^{n_{2}}+\left(\sin{\frac{\varphi}{4}}\right)^{n_{2}}\right]^{-\frac{1}{n_{1}}-1},
where P
has three parameters: a
, n_{1}
, and n_{2}
.
Note
The argument P
in the DSGE
function only has
the three parameters: a
, n_{1}
, and n_{2}
.
Author(s)
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
References
Chen, Z. (2012) Volume and area of revolution under polar coordinate system.
Studies in College Mathematics 15(6), 9-
11.
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
Examples
Par7 <- c(1.124, 14.86, 49.43)
phi1 <- seq(0, pi, len=2000)
g1 <- DSGE(P=Par7, phi=phi1)
dev.new()
plot(phi1, g1, type="l", col=4, cex.lab=1.5, cex.axis=1.5,
xlab=expression(italic(varphi)),
ylab=expression(paste(italic(g), "(", italic(varphi), ")", sep="")))
graphics.off()