I present a new low discrepancy quasirandom sequence that offers many substantial improvements over other popular sequences such as the Sobol and Halton sequences.

Continue reading “The Unreasonable Effectiveness of Quasirandom Sequences”

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## The Unreasonable Effectiveness

of Quasirandom Sequences

## A simple method to construct isotropic quasirandom

blue noise point sequences

## The Theil-Sen and Siegel non-parametric estimators

for linear regression

## A new method to construct isotropic blue-noise

sample point sets with uniform projections

## Evenly Distributing Points in a Triangle.

## A probabilistic approach

to fractional factorial design

## The Fisher-Yates Algorithm

## Evenly distributing points on a sphere

Always curious. Always learning.

of Quasirandom Sequences

I present a new low discrepancy quasirandom sequence that offers many substantial improvements over other popular sequences such as the Sobol and Halton sequences.

Continue reading “The Unreasonable Effectiveness of Quasirandom Sequences”

blue noise point sequences

** **I describe a simple method for constructing a sequence of points, that is based on a low discrepancy quasirandom sequence but exhibits enhanced isotropic blue noise properties. This results in fast convergence rates with minimal aliasing artifacts.

Continue reading “A simple method to construct isotropic quasirandom blue noise point sequences”

for linear regression

The Theil-Sen (Kendall) and Siegel estimators are non-parametric distribution-free methods used to fit a line to data, in ways that are very robust to large levels of noise and outliers. We briefly illustrate how the lesser-known Siegel estimator is typically better than the more commonly used Theil-Sen estimator.

Continue reading “The Theil-Sen and Siegel non-parametric estimators

for linear regression”

sample point sets with uniform projections

I describe a how a small but critical modification to correlated multi-jittered sampling can significantly improve its blue noise spectral characteristics whilst maintaining its uniform projections. This is an exact and direct grid-based construction method that guarantees a minimum neighbor point separation of at least $0.707/n$ and has an average point separation of $0.965/n$*.*

Most two dimensional quasirandom methods focus on sampling over a unit square. However, sampling evenly over the triangle is also very important in computer graphics. Therefore, I describe a simple and direct construction method for a point sequence to evenly cover an arbitrary shaped triangle.

Continue reading “Evenly Distributing Points in a Triangle.”

to fractional factorial design

I describe a probabilistic alternative to fractional factorial design based on the Sobol’ low discrepancy quasirandom sequence. This method is robust to aliasing (confounders), is often simpler to implement than traditional fractional factorial sample designs, and produces more accurate results than simple random sampling.

Continue reading “A probabilistic approach

to fractional factorial design”

Creating unbiased random permutations of lists is often crucial to sampling. The Fisher-Yates shuffle is the definitive method to shuffle a sequence of items. Popularised by Knuth, it is unbiased, has optimal linear time efficiency; uses constant space; and is incremental.

How to distribute points on the surface of a sphere as evenly as possibly is an incredibly important problem in maths, science and computing, and mapping the Fibonacci lattice onto the surface of a sphere via equal-area projection is an extremely fast and effective approximate method to achieve this. I show that with only minor modifications it can be made even better.