disks: Sample (with noise) from disk

In tdaunif: Uniform Manifold Samplers for Topological Data Analysis

Sample (with noise) from disk

Description

These functions generate uniform samples from a disk in 2-dimensional space, optionally with noise.

Usage

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

Arguments

n	Number of observations.
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 disk. 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)

tdaunif documentation built on Sept. 10, 2023, 5:07 p.m.