biogeom (version 1.4.4)

EPE: Calculation of the Ordinate For an Arbitrary Point on the Preston Curve in the Plane

Description

EPE is used to calculate the y-value for an arbitrary point on the Preston curve that was generated by the explicit Preston equation or one of its simplified versions for a given x-value.

Usage

EPE(P, x, simpver = NULL)

Value

The \(y\) values predicted by the explicit Preston equation.

Arguments

P

the parameters of the explicit Preston equation or one of its simplified versions.

x

the x-value used in the explicit Preston equation.

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 explicit Preston equation is selected: $$ y = b\ \sqrt{1-\left(\frac{x}{a}\right)^2}\left(1+c_{1}\ \frac{x}{a}+c_{2}\left(\frac{x}{a}\right)^2+c_{3}\left(\frac{x}{a}\right)^3\right), $$ where P has five parameters: \(a\), \(b\), \(c_{1}\), \(c_{2}\), and \(c_{3}\).

\(\quad\) When simpver = 1, the simplified version 1 is selected: $$ y = b\ \sqrt{1-\left(\frac{x}{a}\right)^2}\left(1+c_{1}\ \frac{x}{a}+c_{2}\left(\frac{x}{a}\right)^2\right), $$ where P has four parameters: \(a\), \(b\), \(c_{1}\), and \(c_{2}\).

\(\quad\) When simpver = 2, the simplified version 2 is selected: $$ y = b\ \sqrt{1-\left(\frac{x}{a}\right)^2}\left(1+c_{1}\ \frac{x}{a}\right), $$ where P has three parameters: \(a\), \(b\), and \(c_{1}\).

\(\quad\) When simpver = 3, the simplified version 3 is selected: $$ y = b\ \sqrt{1-\left(\frac{x}{a}\right)^2}\left(1+c_{2}\left(\frac{x}{a}\right)^2\right), $$ where P has three parameters: \(a\), \(b\), and \(c_{2}\).

References

Lian, M., He, K., Ratkowsky, D.A., Chen, L., Wang, J., Wang, L., Yao, W., Shi, P. (2024) Comparison of egg-shape equations using relative curvature measures of nonlinearity. Poultry Science 103, 104069. tools:::Rd_expr_doi("10.1016/j.psj.2024.104069")

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")

Shi, P., Wang, L., Quinn, B.K., Gielis, J. (2023) A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds. Symmetry 15, 231. tools:::Rd_expr_doi("10.3390/sym15010231")

See Also

curveEPE, fitEPE, PE, SurfaceAreaEPE, VolumeEPE

Examples

  Par3 <- c(4.27, 2.90, 0.0868, 0.0224, -0.0287)
  xx1  <- seq(-4.27, 4.27, by=0.001)
  yy1  <- EPE(P=Par3, x=xx1, simpver=NULL)
  yy2  <- -EPE(P=Par3, x=xx1, simpver=NULL)

  dev.new()
  plot(xx1, yy1, asp=1, type="l", col=4, cex.lab=1.5, cex.axis=1.5,
       xlim=c(-5, 5), ylim=c(-5, 5), 
       xlab=expression(italic(x)), ylab=expression(italic(y)))
  lines(xx1, yy2, col=2) 

  graphics.off()