Regular Sampling
August 1, 2019 ยท View on GitHub
Source Code: src/families/_2d/samples/regular/
The 2d regular sampling sequences are direct extensions of the 1d regular sampling sequences.
It might be odd to see that RegularJittered has the lowest discrepancy of these sequences, but discrepancy gets a bit more complex in 2d. Basically, those big empty rows and columns between samples in regular sampling contribute to making larger discrepancy for those sequences. Adding random jitter causes those regions to get broken up.
The lower discrepancy means that it also does better at integration.
Test Results
samples tested:
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Regular (Not Progressive, Deterministic)
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RegularCentered (Not Progressive, Deterministic)
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RegularCenteredOffset (Not Progressive, Deterministic)
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RegularJittered (Not Progressive, Randomized)
Regular
Discrete Fourier Transform

Plot

RegularCentered
Discrete Fourier Transform

Plot

RegularCenteredOffset
Discrete Fourier Transform

Plot

RegularJittered
Discrete Fourier Transform

Plot

Discrepancy Test

Numerical Integration
Disk

Triangle

Step

Gaussian

Bilinear
