biogeom (version 1.4.3)

VolumeSGE: Calculation of the Volume of An Egg Based on the Simplified Gielis Equation

Description

VolumeSGE is used to calculate the volume of an egg that follows the simplified Gielis equation.

Usage

VolumeSGE(P, subdivisions = 100L,
          rel.tol = .Machine$double.eps^0.25, abs.tol = rel.tol,
          stop.on.error = TRUE, keep.xy = FALSE, aux = NULL)

Arguments

P

the parameters of the simplified Gielis equation, including \(a\), \(n_{1}\), and \(n_{2}\).

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.

Author

Peijian Shi , Johan Gielis , Brady K. Quinn .

Details

The formula of the volume (\(V\)) of an egg based on the simplified Gielis equation is: $$V\left(\varphi\right)=\frac{2}{3}\,\pi\int_{0}^{\pi}\sin{\left(\varphi\right)}\ r^3\left(\varphi\right)\,d\varphi,$$

where the polar raidus (\(r\)) is the function of the polar angle (\(\varphi\)):

$$r\left(\varphi\right) = a\left(\left|\mathrm{cos}\left(\frac{m}{4}\varphi\right)\right|^{n_{2}}+ \left|\mathrm{sin}\left(\frac{m}{4}\varphi\right)\right|^{n_{2}}\right)^{-\frac{1}{n_{1}}},$$

namely the simplified Gielis equation (i.e., GE) with arguments simpver = 1 and m = 1.

References

Chen, Z. (2012) Volume and area of revolution under polar coordinate system. Studies in College Mathematics 15(6), 9\(-\)11.

Shi, P., Chen, L., Quinn, B.K., Yu, K., Miao, Q., Guo, X., Lian, M., Gielis, J., Niklas, K.J. (2023) A simple way to calculate the volume and surface area of avian eggs. Annals of the New York Academy of Sciences 1524, 118\(-\)131. tools:::Rd_expr_doi("10.1111/nyas.15000")

See Also

fitGE, GE, SurfaceAreaSGE

Examples

  Par7 <- c(1.124, 14.86, 49.43)
  VolumeSGE(P = Par7)