View source: R/SurfaceAreaAM.R
SurfaceAreaAM | R Documentation |
SurfaceAreaAM
is used to calculate the lateral surface area of an apical meristem
that follows the the hybrid catenary-parabolic equation or the superparabolic equation.
SurfaceAreaAM(model = "Hybrid", P, upper = Inf, subdivisions = 100L,
rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
stop.on.error = TRUE, keep.xy = FALSE, aux = NULL)
model |
an optional argument to select a model to calculate the surface area. |
P |
the parameters of the hybrid catenary-parabolic equation or the superparabolic equation. |
upper |
the upper limit of integration in |
subdivisions |
please see the arguments for the |
rel.tol |
please see the arguments for the |
abs.tol |
please see the arguments for the |
stop.on.error |
please see the arguments for the |
keep.xy |
please see the arguments for the |
aux |
please see the arguments for the |
The formula of the lateral surface area (S
) of an apical meristem
based on the hybrid catenary-parabolic equation or the superparabolic equation:
S(x)=2 \, \pi \int_{0}^{a} x \,\sqrt{1+\left(\frac{dy}{dx}\right)^2}\,dx,
where a
is the upper limit of integration in x
. The lower limit of integration in x
is 0.
\quad
If model = "Hybrid"
, y
denotes the hybrid catenary-parabolic equation,
which equals y\left(x\right) = \alpha\,\mbox{cosh}(\beta x) + \gamma x^{2}-\alpha
,
and \frac{dy}{dx} = \alpha\,\beta\,\mbox{sinh}(\beta x) + 2\gamma x
.
Here, \alpha
, \beta
and \gamma
are
model parameters provided by the argument P
.
\quad
If model = "Superparabola"
, y
denotes the superparabolic equation,
which equals y\left(x\right) = \beta_{1}\, {\left|x\right|}^{\beta_{2}}
,
and \frac{dy}{dx} = \beta_{1}\,\beta_{2}\,x \left|x\right|^{\beta_{2}-2}
. Here, \beta_{1}
and \beta_{2}
are
model parameters provided by the argument P
.
The SurfaceAreaAM
function actually calculates
the lateral surface area regardless of the area of the 'base' circle.
The argument P
in the SurfaceAreaAM
function has three parameters for model = "Hybrid"
,
and two parameters for model = "Superparabola"
.
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/nyas.14862")}
fitAM
, PlanCoor
, SAMs
, VolumeAM
par3 <- c(-20, 0.9695, 11.40)
SurfaceAreaAM(model = "Hybrid", P = par3, upper=1)
par5 <- c(1.3807, 1.3173)
SurfaceAreaAM(model = "Superparabola", P = par5, upper=1)
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