annuli {tdaunif}

Sample (with noise) from annuli

Description

These functions generate uniform samples from annuli with in 2-dimensional space with major radius 1, optionally with noise.

Usage

sample_annulus(n, r = 0.5, bins = 1L, sd = 0)

sample_disk(n, bins = 1L, sd = 0)

Arguments

n

Number of observations.

r

Minor radius of the annulus; 0 yields the disk.

bins

Number of intervals per dimension to stratify by. Default set to 1, which generates a uniform sample.

sd

Standard deviation of (independent multivariate) Gaussian noise.

Details

The sample is generated by an area-preserving parameterization of the annulus. This parameterization was derived through the method for sampling 2-manifolds as described by Arvo (2001).

References

J Arvo (2001) Stratified Sampling of 2-Manifolds. SIGRAPH 2001 (State of the Art in Monte Carlo Ray Tracing for Realistic Image Synthesis), Course Notes, Vol. 29. https://www.cs.princeton.edu/courses/archive/fall04/cos526/papers/course29sig01.pdf

Examples

set.seed(99812L)

# Uniformly sampled unit disk in 2-space
x <- sample_disk(1800, sd = 0)
plot(x, asp = 1, pch = 19, cex = .5)

# Uniformly sampled unit disk in 2-space with Gaussian noise
x <- sample_disk(1800, sd = .1)
plot(x, asp = 1, pch = 19, cex = .5)

# Uniformly sampled annulus
x <- sample_annulus(100, r = .4, sd = 0)
plot(x, asp = 1, pch = 19, cex = .5)