areaGE | R Documentation |
[0, 2\pi)
areaGE
is used to calculate the area of the polygon
generated by the Gielis curve within [0, 2\pi)
.
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)
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 |
simpver |
an optional argument to use the simplified version of the original (or twin) Gielis equation. |
nval |
the specified value for |
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 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
.
The area of the polygon within [0, 2\pi)
generated by the original (or twin) Gielis equation
or one of its simplified versions.
simpver
in GE
is different from that in TGE
.
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
Gielis, J. (2003) A generic geometric transformation that unifies a wide range of natural
and abstract shapes. American Journal of Botany 90, 333-
338. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/ece3.1728")}
curveGE
, fitGE
, GE
, TGE
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)
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