NRGE() R function from [biogeom]

The Narushin-Romanov-Griffin Equation (NRGE)

NRGE is used to calculate $y$ values at given $x$ values using the Narushin-Romanov-Griffin equation (NRGE). UTF-8


NRGE(P, x)

Arguments

P: the four parameters (i.e., $A$ , $B$ , $C$ , and $D$ ) of the Narushin-Romanov-Griffin equation.
x: the given $x$ values.

Details

The Narushin-Romanov-Griffin equation (Narushin et al., 2021) has four parameters in total, among which three parameters have clear geometric meanings.

f_{1}(x)=\frac{B}{2}\sqrt{\frac{A^2-4x^2}{A^2+8Cx+4C^2}},

E = \frac{\sqrt{5.5A^{2}+11AC+4C^{2}} \cdot \left(\sqrt{3}AB-2D\sqrt{A^{2}+2AC+4C^{2}}\right)}{\sqrt{3}AB\left(\sqrt{5.5A^{2}+11AC+4C^{2}}-2\sqrt{A^{2}+2AC+4C^{2}}\right)},

f_{2}(x)=\sqrt{\frac{A\left(A^{2}+8Cx+4C^{2}\right)}{2(A-2C)x^{2}+\left(A^{2}+8AC-4C^{2}\right)x+2AC^{2}+A^{2}C+A^{3}}},

f(x)=\pm f_{1}(x) \cdot \left\{1-E \cdot \left[1-f_{2}(x)\right]\right\}.

Here, $f(x)$ is the Narushin-Romanov-Griffin equation, which is used to predict the $y$ coordinates at the given $x$ coordinates; $A$ represents the egg's length; $B$ represents the egg's maximum breadth; $C$ is a parameter to be estimated, and it can be expressed as $\left(A-B\right)/(2q)$ , where $q$ is a parameter to be estimated; $D$ represents the egg's breadth associated with $(3/4)L$ from the egg base (to the egg tip) on the egg length axis (which can be regarded as the major axis of the egg shape).

Returns

The $y$ values predicted by the Narushin-Romanov-Griffin equation.

Note

Here, parameter C is a parameter to be estimated, which can be directly calculated numerically based on the egg-shape data.

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")

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")

Author(s)

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

Examples


P0 <- c(11.5, 7.8, 1.1, 5.6)
x  <- seq(-11.5/2, 11.5/2, len=2000)
y1 <- NRGE(P=P0, x=x)
y2 <- -NRGE(P=P0, x=x)

dev.new()
plot(x, y1, cex.lab=1.5, cex.axis=1.5, type="l", 
     col=4, ylim=c(-4, 4), asp=1, 
     xlab=expression(italic(x)), ylab=expression(italic(y)) )
lines(x, y2, col=2)

graphics.off()

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Maintainer: Peijian Shi
License: GPL (>= 2)
Last published: 2024-03-29

Useful links

NRGE function