curveEPE function

Drawing the Preston Curve Produced by the the Explicit Preston Equation

curveEPE is used to draw the Preston curve that is produced by the explicit Preston equation. UTF-8

curveEPE(P, np = 5000, simpver = NULL,
        fig.opt = FALSE, deform.fun = NULL, Par = NULL,
        xlim = NULL, ylim = NULL, unit = NULL, main="")

Arguments

• P: the three location parameters and the parameters of the explicit Preston equation or one of its simplified versions.
• np: the number of data points on the Preston curve.
• simpver: an optional argument to use the simplfied version of the explicit Preston equation.
• fig.opt: an optional argument to draw the Preston curve.
• deform.fun: the deformation function used to describe the deviation from a theoretical Preston curve.
• Par: the parameter(s) of the deformation function.
• xlim: the range of the $x$-axis over which to plot the Preston curve.
• ylim: the range of the $y$-axis over which to plot the Preston curve.
• unit: the units of the $x$-axis and the $y$-axis when showing the Preston curve.
• main: the main title of the figure.

Details

The first three elements of P are location parameters. The first two are the planar coordinates of the transferred origin, and the third is the angle between the major axis of the curve and the $x$-axis. Here, the major axis is a straight line through the two ends of an egg's profile (i.e., the mid-line of the egg's profile). The other arguments in P

(except these first three location parameters), and simpver should correspond to those of P in EPE. deform.fun should take the form as: deform.fun <- function(Par, z){...}, where z is a two-dimensional matrix related to the $x$ and $y$ values. And the return value of deform.fun should be a list with two variables x and y.

Returns

• x: the $x$ coordinates of the Preston curve.

• y: the $y$ coordinates of the Preston curve.

Note

When the rotation angle is zero (i.e., the third element in P is zero), np data points are distributed counterclockwise on the Preston curve from the rightmost end of the egg's profile to itself.

Author(s)

Peijian Shi pjshi@njfu.edu.cn , Johan Gielis johan.gielis@uantwerpen.be , Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca .

References

Preston, F.W. (1953) The shapes of birds' eggs. The Auk 70, 160$-$182.

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., Gielis, J., Quinn, B.K., Niklas, K.J., Ratkowsky, D.A., Schrader, J., Ruan, H., Wang, L., Niinemets, Ü. (2022) 'biogeom': An R package for simulating and fitting natural shapes. Annals of the New York Academy of Sciences 1516, 123$-$134. tools:::Rd_expr_doi("10.1111/nyas.14862")

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")

Todd, P.H., Smart, I.H.M. (1984) The shape of birds' eggs. Journal of Theoretical Biology

106, 239$-$243. tools:::Rd_expr_doi("10.1016/0022-5193(84)90021-3")

See Also

EPE, fitEPE, lmPE, PE, TSE

Examples

Para1 <- c(0, 0, 0, 10, 6, 0.325, -0.0415)
  curveEPE(P=Para1, simpver=1, fig.opt=TRUE)
  Para2 <- c(0, 0, pi, 10, 6, -0.325, -0.0415)
  curveEPE(P=Para2, simpver=1, fig.opt=TRUE)

  Para3 <- c(0, 0, 0, 10, 6, 0.325, -0.0415, 0.2)
  curveEPE(P=Para3, simpver=NULL, fig.opt=TRUE)
  Para4 <- c(0, 0, pi, 10, 6, -0.325, -0.0415, 0.2)
  curveEPE(P=Para4, simpver=NULL, fig.opt=TRUE)

  Para5 <- c(0, 0, pi/4, 10, 6, 0.325, -0.0415)
  curveEPE(P=Para5, simpver=1, 
          fig.opt=TRUE, main="A rotated egg shape")

  # There is an example that introduces a deformation function in the egg-shape equation
  myfun <- function(Par, z){
    x  <- z[,1]
    y  <- z[,2]
    k1 <- Par[1]
    k2 <- Par[2]
    y  <- y - k1*(y+k2)^2
    list(x=x, y=y)
  }
  deform.op <- curveEPE(P=Para1, np=5000, simpver=1, 
                       fig.opt=TRUE, deform.fun=myfun, Par=c(0.05, 8))

  graphics.off()