nicheROVER (version 1.1.2)

ellipse: Point coordinates for a 2-D ellipse.

Description

Calculates coordinates of points for plotting a 2-dimensional ellipse based on user-defined parameters. Can be used for exploratory data analysis to produce ellipses at a given niche region size (e.g., \(\alpha = 95\%\)).

Usage

ellipse(mu, V, alpha = 0.95, n = 100)

Value

Returns a matrix of coordinates cbind(x,y) to plot a 2-dimensional ellipse.

Arguments

mu

Centre of ellipse. A vector of length 2.

V

Scale of ellipse. A 2x2 matrix. See 'Details'.

alpha

Niche region size. See 'Details'.

n

Number of points to return for plotting.

Details

This function provides the coordinates needed to plot a 2-dimensional ellipse based on user-defined parameters, such that X = c(x,y) satisfies the equation $$ (X-\mu)' V^{-1} (X-\mu) = C, $$ where \(C=\code{qchisq(alpha, df = 2)}\).

See Also

niche.plot() for plotting.

Examples

mu <- rnorm(2)
V <- crossprod(matrix(rnorm(4), 2, 2))
ell.pts <- ellipse(mu = mu, V = V, alpha = .9, n = 100)
plot(ell.pts, col = rainbow(110)[1:100], type = "o")
points(mu[1], mu[2], pch = "+")