NRGE {biogeom} | R Documentation |
The Narushin-Romanov-Griffin Equation (NRGE)
Description
NRGE
is used to calculate values at given
values using
the Narushin-Romanov-Griffin equation (NRGE).
Usage
NRGE(P, x)
Arguments
P |
the four parameters (i.e., |
x |
the given |
Details
The Narushin-Romanov-Griffin equation (Narushin et al., 2021) has four parameters in total, among which three parameters have clear geometric meanings.
Here, is the Narushin-Romanov-Griffin equation, which is used to predict the
coordinates
at the given
coordinates;
represents the egg's length;
represents the egg's maximum breadth;
is a parameter
to be estimated, and it can be expressed as
, where
is a parameter to
be estimated;
represents the egg's breadth associated with
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).
Value
The 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.
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, 169177. 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, 3442. 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, 751758. doi:10.1007/s11676-018-0770-y
See Also
curveNRGE
, fitNRGE
, SurfaceAreaNRGE
, VolumeNRGE
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()