Spiral and Blue Noise Distributions on the Sphere

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Previous: 'Removing the CRT from the Win32 Loader'

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0:03Recap and set the stage for the day using sine and cosine to improve the lighting sampling quality

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0:03Recap and set the stage for the day using sine and cosine to improve the lighting sampling quality

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2:08Run the game to show the debug visualisation of our lighting's hemisphere sampling

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2:08Run the game to show the debug visualisation of our lighting's hemisphere sampling

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2:08Run the game to show the debug visualisation of our lighting's hemisphere sampling

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4:27Describe the hemisphere sampling in ComputeLightPropagation()

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4:27Describe the hemisphere sampling in ComputeLightPropagation()

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4:27Describe the hemisphere sampling in ComputeLightPropagation()

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5:33Hemisphere sample distribution

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5:33Hemisphere sample distribution

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5:33Hemisphere sample distribution

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7:26Run the game to show our hemisphere sampling

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7:26Run the game to show our hemisphere sampling

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7:26Run the game to show our hemisphere sampling

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8:52Begin to change ComputeLightPropagation() to perform spiral sampling

^{1}^{,2}of the lighting, as suggested by Kelimion8:52Begin to change ComputeLightPropagation() to perform spiral sampling

^{1}^{,2}of the lighting, as suggested by Kelimion^{1}

^{,2}of the lighting, as suggested by Kelimion

17:20Change ComputeLightPropagation() to use polar coordinates for our randomly sampled hemisphere

17:20Change ComputeLightPropagation() to use polar coordinates for our randomly sampled hemisphere

17:20Change ComputeLightPropagation() to use polar coordinates for our randomly sampled hemisphere

18:29Run the game to see our hemisphere sampling

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18:29Run the game to see our hemisphere sampling

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18:29Run the game to see our hemisphere sampling

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18:50Change ComputeLightPropagation() to produce spiral sampling around a sphere

^{3}with a note about Vogel's method^{4}18:50Change ComputeLightPropagation() to produce spiral sampling around a sphere

^{3}with a note about Vogel's method^{4}^{3}with a note about Vogel's method

^{4}

29:53Run the game to see the sample distribution

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29:53Run the game to see the sample distribution

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29:53Run the game to see the sample distribution

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30:13Increase the sample count from 16 to 64 in ComputeLightPropagation()

30:13Increase the sample count from 16 to 64 in ComputeLightPropagation()

30:13Increase the sample count from 16 to 64 in ComputeLightPropagation()

30:25Run the game to see the nice covering of the sphere

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30:25Run the game to see the nice covering of the sphere

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30:25Run the game to see the nice covering of the sphere

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30:49Make ComputeLightPropagation() produce hemispherical data

30:49Make ComputeLightPropagation() produce hemispherical data

30:49Make ComputeLightPropagation() produce hemispherical data

31:24Run the game to see the hemispherical data

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31:24Run the game to see the hemispherical data

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31:24Run the game to see the hemispherical data

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32:01Reduce the sample count back to 16 and randomly jitter them in ComputeLightPropagation()

32:01Reduce the sample count back to 16 and randomly jitter them in ComputeLightPropagation()

32:01Reduce the sample count back to 16 and randomly jitter them in ComputeLightPropagation()

33:50Run the game to see that this is back to being clumpy

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33:50Run the game to see that this is back to being clumpy

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33:50Run the game to see that this is back to being clumpy

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34:04Try to alleviate the clumpiness in ComputeLightPropagation()

34:04Try to alleviate the clumpiness in ComputeLightPropagation()

34:04Try to alleviate the clumpiness in ComputeLightPropagation()

36:05Run the game to see the varying samples

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36:05Run the game to see the varying samples

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36:05Run the game to see the varying samples

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36:53Make ComputeLightPropagation() only randomise the Rho value

36:53Make ComputeLightPropagation() only randomise the Rho value

36:53Make ComputeLightPropagation() only randomise the Rho value

37:33Run the game to see this coverage

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37:33Run the game to see this coverage

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37:33Run the game to see this coverage

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37:40Make ComputeLightPropagation() use one randomised RhoOffset for the whole sphere

37:40Make ComputeLightPropagation() use one randomised RhoOffset for the whole sphere

37:40Make ComputeLightPropagation() use one randomised RhoOffset for the whole sphere

38:48Run the game to see this coverage

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38:48Run the game to see this coverage

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38:48Run the game to see this coverage

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38:55Let ComputeLightPropagation() run the sampling over 20 frames for us to visualise the coverage

38:55Let ComputeLightPropagation() run the sampling over 20 frames for us to visualise the coverage

38:55Let ComputeLightPropagation() run the sampling over 20 frames for us to visualise the coverage

39:56Run the game to see this extended coverage

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39:56Run the game to see this extended coverage

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39:56Run the game to see this extended coverage

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40:26Make ComputeLightPropagation() multiple Theta, rather than Tau, in to the RhoOffset

40:26Make ComputeLightPropagation() multiple Theta, rather than Tau, in to the RhoOffset

40:26Make ComputeLightPropagation() multiple Theta, rather than Tau, in to the RhoOffset

40:46Run the game to see this extended coverage

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40:46Run the game to see this extended coverage

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40:46Run the game to see this extended coverage

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41:09Change ComputeLightPropagation() to jitter the 64 points sampling more fairly

41:09Change ComputeLightPropagation() to jitter the 64 points sampling more fairly

41:09Change ComputeLightPropagation() to jitter the 64 points sampling more fairly

42:50Run the game to see this jittered coverage

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42:50Run the game to see this jittered coverage

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42:50Run the game to see this jittered coverage

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43:01Make ComputeLightPropagation() jitter the i value

43:01Make ComputeLightPropagation() jitter the i value

43:01Make ComputeLightPropagation() jitter the i value

43:29Run the game to see this coverage biasing towards the spiral

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43:29Run the game to see this coverage biasing towards the spiral

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43:29Run the game to see this coverage biasing towards the spiral

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44:48Make ComputeLightPropagation() jitter the normal of each ray

44:48Make ComputeLightPropagation() jitter the normal of each ray

44:48Make ComputeLightPropagation() jitter the normal of each ray

46:18Run the game to see this distribution

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46:18Run the game to see this distribution

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46:18Run the game to see this distribution

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47:19Make ComputeLightPropagation() bias the distribution towards upwards

47:19Make ComputeLightPropagation() bias the distribution towards upwards

47:19Make ComputeLightPropagation() bias the distribution towards upwards

49:02Run the game to see this more upwards facing distribution, and consider how to concentrate the samples at the top

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49:02Run the game to see this more upwards facing distribution, and consider how to concentrate the samples at the top

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52:01Make ComputeLightPropagation() produce a handwritten distribution of 64 points

52:01Make ComputeLightPropagation() produce a handwritten distribution of 64 points

52:01Make ComputeLightPropagation() produce a handwritten distribution of 64 points

56:49Run the game to see this distribution, tweaking the MinimumDistanceSq until we crash

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56:49Run the game to see this distribution, tweaking the MinimumDistanceSq until we crash

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56:49Run the game to see this distribution, tweaking the MinimumDistanceSq until we crash

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57:17Make ComputeLightPropagation set MinimumDistanceSq to 0.25²

57:17Make ComputeLightPropagation set MinimumDistanceSq to 0.25²

57:17Make ComputeLightPropagation set MinimumDistanceSq to 0.25²

57:28Run the game see to see our uniformly covered sphere

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57:28Run the game see to see our uniformly covered sphere

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57:28Run the game see to see our uniformly covered sphere

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57:45Make ComputeLightPropagation() concentrate our distribution towards the top

57:45Make ComputeLightPropagation() concentrate our distribution towards the top

57:45Make ComputeLightPropagation() concentrate our distribution towards the top

1:03:23Run the game to see our tighter distribution

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1:03:23Run the game to see our tighter distribution

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1:03:23Run the game to see our tighter distribution

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1:03:34Let ComputeLightPropagation() run the sampling over 20 frames for us to visualise the coverage

1:03:34Let ComputeLightPropagation() run the sampling over 20 frames for us to visualise the coverage

1:04:12Run the game to see this extended coverage, and consider how to produce bundles of 4 points, accounting for the spread

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1:04:12Run the game to see this extended coverage, and consider how to produce bundles of 4 points, accounting for the spread

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1:06:12Euclidean straight-line vs "great arc" parabolic distance

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1:06:12Euclidean straight-line vs "great arc" parabolic distance

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1:06:12Euclidean straight-line vs "great arc" parabolic distance

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1:08:17Change ComputeLightPropagation() to distribute the sampling points by their parabolic rather than straight-line distance

1:08:17Change ComputeLightPropagation() to distribute the sampling points by their parabolic rather than straight-line distance

1:22:50Run the game to see our extended parabolic distribution

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1:22:50Run the game to see our extended parabolic distribution

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1:22:50Run the game to see our extended parabolic distribution

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1:22:59Make ComputeLightPropagation() jitter our randomly distributed sampling points over 20 frames

1:22:59Make ComputeLightPropagation() jitter our randomly distributed sampling points over 20 frames

1:22:59Make ComputeLightPropagation() jitter our randomly distributed sampling points over 20 frames

1:25:41Run the game to see the random patches

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1:25:41Run the game to see the random patches

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1:25:41Run the game to see the random patches

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1:26:09Make ComputeLightPropagation() concentrate the points towards the top

1:26:09Make ComputeLightPropagation() concentrate the points towards the top

1:26:09Make ComputeLightPropagation() concentrate the points towards the top

1:28:10Run the game to see our distribution, and consider distributing all 64 separately

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1:28:10Run the game to see our distribution, and consider distributing all 64 separately

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1:28:10Run the game to see our distribution, and consider distributing all 64 separately

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1:28:19Make ComputeLightPropagation() distribute all 64 points unbundled

1:28:19Make ComputeLightPropagation() distribute all 64 points unbundled

1:28:19Make ComputeLightPropagation() distribute all 64 points unbundled

1:31:15Run the game to see our 64 distributed points

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1:31:15Run the game to see our 64 distributed points

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1:31:15Run the game to see our 64 distributed points

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1:33:19Q&A

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1:33:19Q&A

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1:33:19Q&A

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1:35:39Lateral distribution

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1:35:39Lateral distribution

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1:35:39Lateral distribution

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1:38:02Consider doing quadrant-based distribution

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1:38:02Consider doing quadrant-based distribution

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1:38:02Consider doing quadrant-based distribution

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1:41:53Step in to the asm of rand() from the CRT

^{5}🏃

1:41:53Step in to the asm of rand() from the CRT

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1:41:53Step in to the asm of rand() from the CRT

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1:45:54Point out the blue noise graph in 'The Color of Noise'

^{6}📖

1:45:54Point out the blue noise graph in 'The Color of Noise'

^{6}📖

1:45:54Point out the blue noise graph in 'The Color of Noise'

^{6}📖

1:47:23Wrap things up

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1:47:23Wrap things up

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1:47:23Wrap things up

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Next: 'Switching to Precomputed Hemisphere Distributions'

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