curveNRGE function

Drawing the Egg Shape Predicted by the Narushin-Romanov-Griffin Equation

curveNRGE is used to draw the egg shape predicted by the Narushin-Romanov-Griffin equation. UTF-8

curveNRGE(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 four parameters of the Narushin-Romanov-Griffin equation (Narushin et al., 2021).
• np: the number of data points on the Narushin-Romanov-Griffin curve.
• fig.opt: an optional argument to draw the Narushin-Romanov-Griffin curve.
• deform.fun: the deformation function used to describe the deviation from a theoretical Narushin-Romanov-Griffin curve.
• Par: the parameter(s) of the deformation function.
• xlim: the range of the $x$-axis over which to plot the Narushin-Romanov-Griffin curve.
• ylim: the range of the $y$-axis over which to plot the Narushin-Romanov-Griffin curve.
• unit: the units of the $x$-axis and the $y$-axis when showing the Narushin-Romanov-Griffin 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. The other arguments in P

should be the same as those in NRGE. 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 Narushin-Romanov-Griffin curve.

• y: the $y$ coordinates of the Narushin-Romanov-Griffin 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 Narushin-Romanov-Griffin 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

Narushin, V.G., Romanov, M.N., Griffin, D.K. (2021) Egg and math: introducing a universal formula for egg shape. Annals of the New York Academy of Sciences 1505, 169$-$177. tools:::Rd_expr_doi("10.1111/nyas.14680")

Shi, P., Gielis, J., Niklas, K.J. (2022) Comparison of a universal (but complex) model for avian egg shape with a simpler model. Annals of the New York Academy of Sciences 1514, 34$-$42. tools:::Rd_expr_doi("10.1111/nyas.14799")

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")

Tian, F., Wang, Y., Sandhu, H.S., Gielis, J., Shi, P. (2020) Comparison of seed morphology of two ginkgo cultivars. Journal of Forestry Research 31, 751$-$758. tools:::Rd_expr_doi("10.1007/s11676-018-0770-y")

See Also

fitNRGE, NRGE

Examples

PA   <- c(1, 1, pi/4, 11.5, 7.8, 1.1, 5.6)
resA <- curveNRGE(PA, np=5000, fig.opt=TRUE)
resB <- curveNRGE(PA, np=5000, fig.opt=TRUE, xlim=c(-6, 6), 
                  ylim=c(-6, 6), main="A pear-shaped egg") 
cbind(resB$x, resB$y)

graphics.off()