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Regular Sampling

Source Code: src/families/_2d/samples/regular/

The 2d regular sampling sequences are direct extensions of the 1d regular sampling sequences.

1D Regular Sampling

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:

  • Regular (Not Progressive, Deterministic)

  • RegularCentered (Not Progressive, Deterministic)

  • RegularCenteredOffset (Not Progressive, Deterministic)

  • RegularJittered (Not Progressive, Randomized)

Regular

Discrete Fourier Transform

Regular

Plot

Regular

RegularCentered

Discrete Fourier Transform

RegularCentered

Plot

RegularCentered

RegularCenteredOffset

Discrete Fourier Transform

RegularCenteredOffset

Plot

RegularCenteredOffset

RegularJittered

Discrete Fourier Transform

RegularJittered

Plot

RegularJittered

Discrepancy Test

regular

Numerical Integration

Disk

regular

Triangle

regular

Step

regular

Gaussian

regular

Bilinear

regular