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)
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.
Value
- Returns a matrix of coordinates
cbind(x,y) to plot a 2-dimensional ellipse.
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 $C=\code{qchisq(alpha, df = 2)}$.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 = "+")