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Numerical Integration

Source Code: /src/families/_2d/tests/integration/

This is the same as the 1d integration test, but integrating over 2d functions instead of 1d functions.

1D Integration Test

The functions being integrated over are:

  • Disk: the inside of a circle with radius 2/pi

  • Triangle: y > x

  • Step: x < 1/pi

  • Gaussian: z = e^(-x^2-y^2)

  • Bilinear: z = x * y

Disk

Triangle

Step

Gaussian

Bilinear

Test Results

tests done:

  • Disk

  • Triangle

  • Step

  • Gaussian

  • Bilinear

Disk

Blue Noise Sequences

blue_noise

Irrational Number Sampling

irrational_numbers

Low Discrepancy Sequences

lds

Hammersley Low Discrepancy Sequence

lds_hammersley

Regular Sampling

regular

Uniform Random Number Sampling

uniform_random

Triangle

Blue Noise Sequences

blue_noise

Irrational Number Sampling

irrational_numbers

Low Discrepancy Sequences

lds

Hammersley Low Discrepancy Sequence

lds_hammersley

Regular Sampling

regular

Uniform Random Number Sampling

uniform_random

Step

Blue Noise Sequences

blue_noise

Irrational Number Sampling

irrational_numbers

Low Discrepancy Sequences

lds

Hammersley Low Discrepancy Sequence

lds_hammersley

Regular Sampling

regular

Uniform Random Number Sampling

uniform_random

Gaussian

Blue Noise Sequences

blue_noise

Irrational Number Sampling

irrational_numbers

Low Discrepancy Sequences

lds

Hammersley Low Discrepancy Sequence

lds_hammersley

Regular Sampling

regular

Uniform Random Number Sampling

uniform_random

Bilinear

Blue Noise Sequences

blue_noise

Irrational Number Sampling

irrational_numbers

Low Discrepancy Sequences

lds

Hammersley Low Discrepancy Sequence

lds_hammersley

Regular Sampling

regular

Uniform Random Number Sampling

uniform_random