# 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 ```r 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 ```r 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() ```

curveEPE function