curveETE {biogeom}

Drawing the Troscianko Curve Produced by the Explicit Troscianko Equation

Description

curveETE is used to draw the Troscianko curve that is produced by the explicit Troscianko equation.

Usage

curveETE(P, np = 5000, 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 Troscianko equation.

np

the number of data points on the Troscianko curve.

fig.opt

an optional argument to draw the Troscianko curve.

deform.fun

the deformation function used to describe the deviation from a theoretical Troscianko curve.

Par

the parameter(s) of the deformation function.

xlim

the range of the x-axis over which to plot the Troscianko curve.

ylim

the range of the y-axis over which to plot the Troscianko curve.

unit

the units of the x-axis and the y-axis when showing the Troscianko 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) should correspond to those of P in ETE. 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.

Value

x

the x coordinates of the Troscianko curve.

y

the y coordinates of the Troscianko 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 Troscianko curve from the rightmost end of the egg's profile to itself.

Author(s)

Peijian Shi [e-mail], Johan Gielis [e-mail], Brady K. Quinn [e-mail].

References

Biggins, J.D., Montgomeries, R.M., Thompson, J.E., Birkhead, T.R. (2022) Preston’s universal formula for avian egg shape. Ornithology 139, ukac028. doi:10.1093/ornithology/ukac028

Biggins, J.D., Thompson, J.E., Birkhead, T.R. (2018) Accurately quantifying the shape of birds' eggs. Ecology and Evolution 8, 9728-9738. doi:10.1002/ece3.4412

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. 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. doi:10.3390/sym15010231

See Also

ETE, fitETE

Examples

  Para1 <- c(0, 0, 0, 2.25, -0.377, -0.29, -0.16)
  curveETE(P=Para1, fig.opt=TRUE)

  # 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 <- curveETE(P=Para1, np=5000, fig.opt=TRUE, deform.fun=myfun, Par=c(0.05, 8))

  graphics.off()