# Drawing the Gielis Curve `curveGE` is used to draw the Gielis curve. UTF-8 ```r curveGE(expr, P, phi = seq(0, 2*pi, len = 2000), m = 1, simpver = NULL, nval = 1, fig.opt = FALSE, deform.fun = NULL, Par = NULL, xlim = NULL, ylim = NULL, unit = NULL, main="") ``` ## Arguments - `expr`: the original (or twin) Gielis equation or one of its simplified versions. - `P`: the three location parameters and the parameters of the original (or twin) Gielis equation or one of its simplified versions. - `phi`: the given polar angles at which we want to draw the Gielis curve. - `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 simplfied 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. - `fig.opt`: an optional argument to draw the Gielis curve. - `deform.fun`: the deformation function used to describe the deviation from a theoretical Gielis curve. - `Par`: the parameter(s) of the deformation function. - `xlim`: the range of the $x$-axis over which to plot the Gielis curve. - `ylim`: the range of the $y$-axis over which to plot the Gielis curve. - `unit`: the units of the $x$-axis and the $y$-axis when showing the Gielis curve. - `main`: the main title of the figure. ## Details The first three elements of `P` are location parameters. The first two are the planar coordinates of the transferred polar point, and the third is the angle between the major axis of the curve and the $x$-axis. The other arguments in `P` (except these first three location parameters), `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`. `deform.fun` should take the form as: `deform.fun <- function(Par, z){...}`, where `z` is a two-dimensional matrix related to the $x$ and $y$ values. And the return value of `deform.fun` should be a `list` with two variables `x` and `y`. ## Returns - **x**: the $x$ coordinates of the Gielis curve corresponding to the given polar angles `phi`. - **y**: the $y$ coordinates of the Gielis curve corresponding to the given polar angles `phi`. - **r**: the polar radii of the Gielis curve corresponding to the given polar angles `phi`. ## 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., 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, 34$-$42. tools:::Rd_expr_doi("10.1111/nyas.14799") Shi, P., Gielis, J., Quinn, B.K., Niklas, K.J., Ratkowsky, D.A., Schrader, J., Ruan, H., Wang, L., Niinemets, Ü. (2022) 'biogeom': An R package for simulating and fitting natural shapes. **Annals of the New York Academy of Sciences** 1516, 123$-$134. tools:::Rd_expr_doi("10.1111/nyas.14862") Shi, P., Ratkowsky, D.A., Gielis, J. (2020) The generalized Gielis geometric equation and its application. **Symmetry** 12, 645. tools:::Rd_expr_doi("10.3390/sym12040645") Shi, P., Xu, Q., Sandhu, H.S., Gielis, J., Ding, Y., Li, H., Dong, X. (2015) Comparison of dwarf bamboos (**Indocalamus** sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant. **Ecology and Evolution** 5, 4578-4589. tools:::Rd_expr_doi("10.1002/ece3.1728") ## See Also `areaGE`, `fitGE`, `GE`, `TGE` ## Examples ```r GE.par <- c(2, 1, 4, 6, 3) phi.vec <- seq(0, 2*pi, len=2000) r.theor <- GE(P=GE.par, phi=phi.vec, m=5) dev.new() plot( phi.vec, r.theor, cex.lab=1.5, cex.axis=1.5, xlab=expression(italic(phi)), ylab=expression(italic("r")), type="l", col=4 ) curve.par <- c(1, 1, pi/4, GE.par) GE.res <- curveGE(GE, P=curve.par, fig.opt=TRUE, deform.fun=NULL, Par=NULL, m=5) # GE.res$r GE.res <- curveGE( GE, P=c(0, 0, 0, 2, 4, 20), m=1, simpver=1, fig.opt=TRUE ) # GE.res$r GE.res <- curveGE( GE, P=c(1, 1, pi/4, 2, 1, 3), m=5, simpver=1, fig.opt=TRUE ) # GE.res$r GE.res <- curveGE( GE, P=c(1, 1, pi/4, 2, 1, 3), m=2, simpver=1, fig.opt=TRUE ) # GE.res$r GE.res <- curveGE( GE, P=c(1, 1, pi/4, 2, 0.05), m=1, simpver=2, fig.opt=TRUE ) # GE.res$r GE.res <- curveGE( GE, P=c(1, 1, pi/4, 2), m=4, simpver=3, nval=2, fig.opt=TRUE ) # GE.res$r GE.res <- curveGE( GE, P=c(1, 1, pi/4, 2, 0.6), m=4, simpver=8, nval=2, fig.opt=TRUE ) # GE.res$r graphics.off() ```

curveGE function