DSGE function

Calculation of the First-Order Derivative of the Simplified Gielis Equation

DSGE is used to calculate the first-order derivative of the simplified Gielis equation at a given $\varphi$-value. UTF-8

DSGE(P, phi)

Arguments

• P: the parameters of the simplified Gielis equation, including $a$, $n_{1}$, and $n_{2}$.
• phi: the $\varphi$-value used in the simplified Gielis equation.

Details

The first-order derivative of the simplified Gielis equation with arguments simpver = 1 and m = 1 at a given $\varphi$-value is:

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. tools:::Rd_expr_doi("10.1111/nyas.15000")

See Also

GE, fitGE, SurfaceAreaSGE

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()