areaGE {biogeom}

Area Calculation for the Gielis Curve Within [0, 2\pi)

Description

areaGE is used to calculate the area of the polygon generated by the Gielis curve within [0, 2\pi).

Usage

areaGE(expr, P, m = 1, simpver = NULL,  
       nval = 1, subdivisions = 100L,
       rel.tol = .Machine$double.eps^0.25, 
       abs.tol = rel.tol, stop.on.error = TRUE, 
       keep.xy = FALSE, aux = NULL)

Arguments

expr

the original (or twin) Gielis equation or one of its simplified versions.

P

the parameters of the original (or twin) Gielis equation or one of its simplified versions.

m

the given m value that determines the number of angles of the Gielis curve within [0, 2\pi).

simpver

an optional argument to use the simplified version of the original (or twin) Gielis equation.

nval

the specified value for n_{1} or n_{2} or n_{3} in the simplified versions.

subdivisions

please see the arguments for the integrate function in package stats.

rel.tol

please see the arguments for the integrate function in package stats.

abs.tol

please see the arguments for the integrate function in package stats.

stop.on.error

please see the arguments for the integrate function in package stats.

keep.xy

please see the arguments for the integrate function in package stats.

aux

please see the arguments for the integrate function in package stats.

Details

The arguments of P, m, simpver, and nval should correspond to expr (i.e., GE or TGE). Please note the differences in the simplified version number and the number of parameters between GE and TGE.

Value

The area of the polygon within [0, 2\pi) generated by the original (or twin) Gielis equation or one of its simplified versions.

Note

simpver in GE is different from that in TGE.

Author(s)

Peijian Shi [e-mail], Johan Gielis [e-mail], Brady K. Quinn [e-mail].

References

Gielis, J. (2003) A generic geometric transformation that unifies a wide range of natural and abstract shapes. American Journal of Botany 90, 333-338. doi:10.3732/ajb.90.3.333

Li, Y., Quinn, B.K., Gielis, J., Li, Y., Shi, P. (2022) Evidence that supertriangles exist in nature from the vertical projections of Koelreuteria paniculata fruit. Symmetry 14, 23. doi:10.3390/sym14010023

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. doi:10.1111/nyas.14862

Shi, P., Ratkowsky, D.A., Gielis, J. (2020) The generalized Gielis geometric equation and its application. Symmetry 12, 645. doi:10.3390/sym12040645

Shi, P., Xu, Q., Sandhu, H.S., Gielis, J., Ding, Y., Li, H., Dong, X. (2015) Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant. Ecology and Evolution 5, 4578-4589. doi:10.1002/ece3.1728

See Also

curveGE, fitGE, GE, TGE

Examples

Para1 <- c(1.7170, 5.2258, 7.9802)
areaGE(GE, P = Para1, m=5, simpver=1)

Para2 <- c(2.1066, 3.5449, 0.4619, 10.5697)
areaGE(TGE, P = Para2, m=5, simpver=1)