areaGE function

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

areaGE is used to calculate the area of the polygon generated by the Gielis curve within $[0, 2\pi)$. UTF-8

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.

Returns

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

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. tools:::Rd_expr_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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1111/nyas.14862")

Shi, P., Ratkowsky, D.A., Gielis, J. (2020) The generalized Gielis geometric equation and its application. Symmetry 12, 645. tools:::Rd_expr_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. tools:::Rd_expr_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)