Contents
What is the difference between high and low discrepancy?
In this context, discrepancy is a measurement of the highest or lowest density of points in a sequence. High discrepancy means that there is either a large area of empty space, or that there is an area that has a high density of points. Low discrepancy means that there are neither, and that your points are more or less pretty evenly distributed.
When to use lower or higher dimensions for noise?
Evaluate the noise in 4D space at the input Vector and the input W as the fourth dimension. Higher dimensions corresponds to higher render time, so lower dimensions should be used unless higher dimensions are necessary. Value of fractal noise.
How is random noise used to create textures?
In nature, everything has a random look, while mathematical formulas typically don’t generate random looking results, unless you use them well. Random noise, such as Perlin noise invented by Ken Perlin, uses random numbers to generate natural looking textures. Smooth Noise
When do random numbers are too random, low discrepancy sequences?
Low Discrepancy: Low Discrepancy Sequences – In lower numbers of samples, this will have faster convergence by having better coverage of the sampling space, but will use randomness to get rid of aliasing by introducing noise. Also interesting to note, Quasi Monte Carlo has provably better asymptotic convergence than regular monte carlo integration.
When do you need a low discrepancy in Monte Carlo?
The lowest discrepancy possible has no randomness at all, and in the 1 dimensional case means that the points are evenly distributed on a grid. For monte carlo integration and the game dev usage cases I mentioned, we do want some randomness, we just want the random points to be spread out a little more evenly.
How are subrandom numbers used to reduce white noise?
Subrandom numbers are ways to decrease the discrepancy of white noise. One way to do this is to break the sampling space in half. You then generate even numbered samples in the first half of the space, and odd numbered samples in the second half of the space.