ellipses {tdaunif}

Sample (with noise) from ellipses

Description

These functions generate uniform samples from configurations of ellipses of major or minor radius 1 in 2- or 3-dimensional space, optionally with noise.

Usage

sample_ellipse(n, ar = 1, sd = 0)

sample_cylinder_elliptical(n, ar = 1, width = 1, sd = 0)

Arguments

n

Number of observations.

ar

Aspect ratio for an ellipse (ratio of major and minor radii).

sd

Standard deviation of (independent multivariate) Gaussian noise.

width

Width of the cylinder (with respect to the fixed radius of the ellipse).

Details

The function sample_ellipse() uses the usual sinusoidal parameterization from the unit interval to an ellipse with radii 1 and 1/ar. The uniform sample is generated through a rejection sampling process as described by Diaconis, Holmes, and Shahshahani (2013).

Examples

set.seed(97205L)

# ellipses in 2-space
x <- sample_ellipse(120, ar = 6)
plot(x, asp = 1, pch = 19, cex = .5)
x <- sample_ellipse(120, ar = 1/6)
plot(x, asp = 1, pch = 19, cex = .5)

# ellipses in 2-space
x <- sample_ellipse(120, ar = 6, sd = .1/6)
plot(x, asp = 1, pch = 19, cex = .5)
x <- sample_ellipse(120, ar = 1/6, sd = .1)
plot(x, asp = 1, pch = 19, cex = .5)

# cylinders in 3-space
x <- sample_cylinder_elliptical(120, ar = 1)
pairs(x, asp = 1, pch = 19, cex = .5)
x <- sample_cylinder_elliptical(120, ar = 3, width = 2*pi)
pairs(x, asp = 1, pch = 19, cex = .5)