Testing Better Entropy

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Previous: 'Switching to Cosine-weighted Poisson Sampling'

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0:01Recap and set the stage for the day

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0:01Recap and set the stage for the day

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0:01Recap and set the stage for the day

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0:49Hemisphere Integration

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0:49Hemisphere Integration

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0:49Hemisphere Integration

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12:38Our light reception function

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12:38Our light reception function

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12:38Our light reception function

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17:09Weighted sampling, as a way to optimise out the multiplication of a weighting coefficient

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17:09Weighted sampling, as a way to optimise out the multiplication of a weighting coefficient

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17:09Weighted sampling, as a way to optimise out the multiplication of a weighting coefficient

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29:18Writing the bias into the sampling equation

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29:18Writing the bias into the sampling equation

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29:18Writing the bias into the sampling equation

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33:10Review GenerateLightingPattern() from last stream

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33:10Review GenerateLightingPattern() from last stream

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33:10Review GenerateLightingPattern() from last stream

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33:59Make GenerateLightingPattern() take a much greater number of samples, to try and see if it converges

33:59Make GenerateLightingPattern() take a much greater number of samples, to try and see if it converges

34:50Run the game to see that it takes too long to compute

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34:50Run the game to see that it takes too long to compute

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34:50Run the game to see that it takes too long to compute

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35:56Make GenerateLightingPattern() take not quite that many samples

35:56Make GenerateLightingPattern() take not quite that many samples

35:56Make GenerateLightingPattern() take not quite that many samples

36:10Step in to GenerateLightingPattern() and inspect the test averages

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36:10Step in to GenerateLightingPattern() and inspect the test averages

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36:10Step in to GenerateLightingPattern() and inspect the test averages

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36:49Make GenerateLightingPattern() perform fewer tests and take more samples

36:49Make GenerateLightingPattern() perform fewer tests and take more samples

36:49Make GenerateLightingPattern() perform fewer tests and take more samples

37:12Step in to GenerateLightingPattern() and inspect the test averages

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37:12Step in to GenerateLightingPattern() and inspect the test averages

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37:12Step in to GenerateLightingPattern() and inspect the test averages

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37:23Further increase the sample count and lower the test count in GenerateLightingPattern()

37:23Further increase the sample count and lower the test count in GenerateLightingPattern()

37:23Further increase the sample count and lower the test count in GenerateLightingPattern()

37:48Step in to GenerateLightingPattern() and inspect the test averages

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37:48Step in to GenerateLightingPattern() and inspect the test averages

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37:48Step in to GenerateLightingPattern() and inspect the test averages

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38:00Increase the test count in GenerateLightingPattern()

38:00Increase the test count in GenerateLightingPattern()

38:00Increase the test count in GenerateLightingPattern()

38:16Step in to GenerateLightingPattern() and inspect the test averages, to find that we are starting to converge

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38:16Step in to GenerateLightingPattern() and inspect the test averages, to find that we are starting to converge

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38:49Consider replacing xorshift with PCG, specifically its notion of k-Dimensional Equidistribution^{1}

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38:49Consider replacing xorshift with PCG, specifically its notion of k-Dimensional Equidistribution^{1}

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44:46Determine to plot our random sampling points

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44:46Determine to plot our random sampling points

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44:46Determine to plot our random sampling points

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46:20Run the game to see our sample points

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46:20Run the game to see our sample points

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46:20Run the game to see our sample points

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46:37Enable LightingTest() to draw a random set of sampling points

46:37Enable LightingTest() to draw a random set of sampling points

46:37Enable LightingTest() to draw a random set of sampling points

49:41Run the game to see our random sample points

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49:41Run the game to see our random sample points

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49:41Run the game to see our random sample points

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50:33Research sphere point picking^{2}

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50:33Research sphere point picking^{2}

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50:33Research sphere point picking^{2}

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53:10Implement Marsaglia's method for uniform point picking on a sphere^{3}^{,4}

53:10Implement Marsaglia's method for uniform point picking on a sphere^{3}^{,4}

53:10Implement Marsaglia's method for uniform point picking on a sphere^{3}^{,4}

56:38Run the game to check out Marsaglia's sampling

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56:38Run the game to check out Marsaglia's sampling

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56:38Run the game to check out Marsaglia's sampling

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57:12Toggle between Marsaglia's method and our full random sampling in LightingTest()

57:12Toggle between Marsaglia's method and our full random sampling in LightingTest()

57:12Toggle between Marsaglia's method and our full random sampling in LightingTest()

58:04Run the game to check out the two sampling patterns

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58:04Run the game to check out the two sampling patterns

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58:04Run the game to check out the two sampling patterns

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58:47Modify Marsaglia's method in LightingTest() to sample only the upper hemisphere

58:47Modify Marsaglia's method in LightingTest() to sample only the upper hemisphere

58:47Modify Marsaglia's method in LightingTest() to sample only the upper hemisphere

59:52Run the game to check out the two hemisphere sampling patterns

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59:52Run the game to check out the two hemisphere sampling patterns

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59:52Run the game to check out the two hemisphere sampling patterns

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1:00:52Introduce random_series_pcg and versions of RandomNextU32(), RandomUnilateral() and RandomBilateral() that take this struct^{5}

1:00:52Introduce random_series_pcg and versions of RandomNextU32(), RandomUnilateral() and RandomBilateral() that take this struct^{5}

1:10:40Praise the compiler for figuring out that we'd never pass the check in Marsaglia's sampling routine, thus raising the "unreachable code" warning

1:10:40Praise the compiler for figuring out that we'd never pass the check in Marsaglia's sampling routine, thus raising the "unreachable code" warning

1:11:25Determine to enable the random_series_pcg version of RandomNextU32() to perform xorshift^{6}^{,7}

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1:11:25Determine to enable the random_series_pcg version of RandomNextU32() to perform xorshift^{6}^{,7}

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1:19:36Try to check out the example PCG code, but encounter a hang in File Explorer when clicking "New"

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1:19:36Try to check out the example PCG code, but encounter a hang in File Explorer when clicking "New"

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1:22:46Read through pcg_basic.c in conjunction with Melissa E. O'Neill's PCG paper^{8} and Pierre L'Ecuyer's 'Tables of linear congruential generators'^{9} with a view to understanding why the example code uses rng->inc or'd with 1 in the LCG update step

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1:22:46Read through pcg_basic.c in conjunction with Melissa E. O'Neill's PCG paper^{8} and Pierre L'Ecuyer's 'Tables of linear congruential generators'^{9} with a view to understanding why the example code uses rng->inc or'd with 1 in the LCG update step

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1:30:08Consult Wikipedia's article 'Linear congruential generator'^{10} to discover that O'Neill must be using Knuth's LCG style

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1:30:08Consult Wikipedia's article 'Linear congruential generator'^{10} to discover that O'Neill must be using Knuth's LCG style

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1:32:28Enable the random_series_pcg version of RandomNextU32() to perform the LCG update step, augmenting random_series_pcg to contain a Selector

1:32:28Enable the random_series_pcg version of RandomNextU32() to perform the LCG update step, augmenting random_series_pcg to contain a Selector

1:35:02Introduce RandomSeedPCG() for LightingTest() to use

1:35:02Introduce RandomSeedPCG() for LightingTest() to use

1:35:02Introduce RandomSeedPCG() for LightingTest() to use

1:37:01Run the game to see if we get any better random results

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1:37:01Run the game to see if we get any better random results

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1:37:01Run the game to see if we get any better random results

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1:38:05Fix RandomNextU32() to correctly cast the entire PreRotate computation

1:38:05Fix RandomNextU32() to correctly cast the entire PreRotate computation

1:38:05Fix RandomNextU32() to correctly cast the entire PreRotate computation

1:38:31Run the game to compare the PCG and Xorshift random sampling patterns

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1:38:31Run the game to compare the PCG and Xorshift random sampling patterns

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1:38:31Run the game to compare the PCG and Xorshift random sampling patterns

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1:39:23Make LightingTest() use a different random series for each axis

1:39:23Make LightingTest() use a different random series for each axis

1:39:23Make LightingTest() use a different random series for each axis

1:41:22Run the game to determine that the non-PCG random sampling looks fine

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1:41:22Run the game to determine that the non-PCG random sampling looks fine

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1:41:22Run the game to determine that the non-PCG random sampling looks fine

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1:42:21Q&A

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1:42:21Q&A

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1:42:21Q&A

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1:43:36Fix RandomSeedPCG() to correctly shift the Selector

1:43:36Fix RandomSeedPCG() to correctly shift the Selector

1:43:36Fix RandomSeedPCG() to correctly shift the Selector

1:43:56Run the game to see no significant difference

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1:43:56Run the game to see no significant difference

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1:43:56Run the game to see no significant difference

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1:52:15Generating blue noise cos(𝜃) distributed sampling points on a disc, for projection up to its hemisphere

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1:52:15Generating blue noise cos(𝜃) distributed sampling points on a disc, for projection up to its hemisphere

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1:57:37Show the lighting in the game

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1:57:37Show the lighting in the game

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1:57:37Show the lighting in the game

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2:00:21We are out of questions

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2:00:21We are out of questions

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2:00:21We are out of questions

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Next: 'Introduction to Function Approximation with Andrew Bromage'

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