-
-
Notifications
You must be signed in to change notification settings - Fork 3.4k
New issue
Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.
By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.
Already on GitHub? Sign in to your account
Use AHash to get color from entity in bevy_gizmos #8960
Conversation
`color_from_entity` uses the poor man's hash to get a fixed random color for an entity. While the poor man's hash is succinct, it has a tendency to clump. As a result, bevy_gizmos has a tendency to re-use very similar colors for different entities. This is bad, we would want non-similar colors that take the whole range of possible hues. This way, each bevy_gizmos aabb gizmo is easy to identify. AHash is a nice and fast hash that just so happen to be available to use, so we use it.
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
Do you happen to have any before/after screenshots of this fix?
My method was to print the hue value for about 30 entities. Let me setup something more scientific in any case. |
Here is the difference:
The height of the bars show how many entities ended up with the specific hue. You can see you only really get 9 different colors with the poor man's hash. While ahash's result is fairly well distributed across all hues. |
I love this graph, thank you! |
Eventually we may want to change this to quasi-random noise instead to optimize for "random but evenly spaced", but this is much better than the existing solution and simple. |
# Objective - #8960 isn't optimal for very distinct AABB colors, it can be improved ## Solution We want a function that maps sequential values (entities concurrently living in a scene _usually_ have ids that are sequential) into very different colors (the hue component of the color, to be specific) What we are looking for is a [so-called "low discrepancy" sequence](https://en.wikipedia.org/wiki/Low-discrepancy_sequence). ie: a function `f` such as for integers in a given range (eg: 101, 102, 103…), `f(i)` returns a rational number in the [0..1] range, such as `|f(i) - f(i±1)| ≈ 0.5` (maximum difference of images for neighboring preimages) AHash is a good random hasher, but it has relatively high discrepancy, so we need something else. Known good low discrepancy sequences are: #### The [Van Der Corput sequence](https://en.wikipedia.org/wiki/Van_der_Corput_sequence) <details><summary>Rust implementation</summary> ```rust fn van_der_corput(bits: u64) -> f32 { let leading_zeros = if bits == 0 { 0 } else { bits.leading_zeros() }; let nominator = bits.reverse_bits() >> leading_zeros; let denominator = bits.next_power_of_two(); nominator as f32 / denominator as f32 } ``` </details> #### The [Gold Kronecker sequence](https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/) <details><summary>Rust implementation</summary> Note that the implementation suggested in the linked post assumes floats, we have integers ```rust fn gold_kronecker(bits: u64) -> f32 { const U64_MAX_F: f32 = u64::MAX as f32; // (u64::MAX / Φ) rounded down const FRAC_U64MAX_GOLDEN_RATIO: u64 = 11400714819323198485; bits.wrapping_mul(FRAC_U64MAX_GOLDEN_RATIO) as f32 / U64_MAX_F } ``` </details> ### Comparison of the sequences So they are both pretty good. Both only have a single (!) division and two `u32 as f32` conversions. - Kronecker is resilient to regular sequence (eg: 100, 102, 104, 106) while this kills Van Der Corput (consider that potentially one entity out of two spawned might be a mesh) I made a small app to compare the two sequences, available at: https://gist.github.com/nicopap/5dd9bd6700c6a9a9cf90c9199941883e At the top, we have Van Der Corput, at the bottom we have the Gold Kronecker. In the video, we spawn a vertical line at the position on screen where the x coordinate is the image of the sequence. The preimages are 1,2,3,4,… The ideal algorithm would always have the largest possible gap between each line (imagine the screen x coordinate as the color hue): https://github.com/bevyengine/bevy/assets/26321040/349aa8f8-f669-43ba-9842-f9a46945e25c Here, we repeat the experiment, but with with `entity.to_bits()` instead of a sequence: https://github.com/bevyengine/bevy/assets/26321040/516cea27-7135-4daa-a4e7-edfd1781d119 Notice how Van Der Corput tend to bunch the lines on a single side of the screen. This is because we always skip odd-numbered entities. Gold Kronecker seems always worse than Van Der Corput, but it is resilient to finicky stuff like entity indices being multiples of a number rather than purely sequential, so I prefer it over Van Der Corput, since we can't really predict how distributed the entity indices will be. ### Chosen implementation You'll notice this PR's implementation is not the Golden ratio-based Kronecker sequence as described in [tueoqs](https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/). Why? tueoqs R function multiplies a rational/float and takes the fractional part of the result `(x/Φ) % 1`. We start with an integer `u32`. So instead of converting into float and dividing by Φ (mod 1) we directly divide by Φ as integer (mod 2³²) both operations are equivalent, the integer division (which is actually a multiplication by `u32::MAX / Φ`) is probably faster. ## Acknowledgements - `inspi` on discord linked me to https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/ and the wikipedia article. - [this blog post](https://probablydance.com/2018/06/16/fibonacci-hashing-the-optimization-that-the-world-forgot-or-a-better-alternative-to-integer-modulo/) for the idea of multiplying the `u32` rather than the `f32`. - `nakedible` for suggesting the `index()` over `to_bits()` which considerably reduces generated code (goes from 50 to 11 instructions)
# Objective - #8960 isn't optimal for very distinct AABB colors, it can be improved ## Solution We want a function that maps sequential values (entities concurrently living in a scene _usually_ have ids that are sequential) into very different colors (the hue component of the color, to be specific) What we are looking for is a [so-called "low discrepancy" sequence](https://en.wikipedia.org/wiki/Low-discrepancy_sequence). ie: a function `f` such as for integers in a given range (eg: 101, 102, 103…), `f(i)` returns a rational number in the [0..1] range, such as `|f(i) - f(i±1)| ≈ 0.5` (maximum difference of images for neighboring preimages) AHash is a good random hasher, but it has relatively high discrepancy, so we need something else. Known good low discrepancy sequences are: #### The [Van Der Corput sequence](https://en.wikipedia.org/wiki/Van_der_Corput_sequence) <details><summary>Rust implementation</summary> ```rust fn van_der_corput(bits: u64) -> f32 { let leading_zeros = if bits == 0 { 0 } else { bits.leading_zeros() }; let nominator = bits.reverse_bits() >> leading_zeros; let denominator = bits.next_power_of_two(); nominator as f32 / denominator as f32 } ``` </details> #### The [Gold Kronecker sequence](https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/) <details><summary>Rust implementation</summary> Note that the implementation suggested in the linked post assumes floats, we have integers ```rust fn gold_kronecker(bits: u64) -> f32 { const U64_MAX_F: f32 = u64::MAX as f32; // (u64::MAX / Φ) rounded down const FRAC_U64MAX_GOLDEN_RATIO: u64 = 11400714819323198485; bits.wrapping_mul(FRAC_U64MAX_GOLDEN_RATIO) as f32 / U64_MAX_F } ``` </details> ### Comparison of the sequences So they are both pretty good. Both only have a single (!) division and two `u32 as f32` conversions. - Kronecker is resilient to regular sequence (eg: 100, 102, 104, 106) while this kills Van Der Corput (consider that potentially one entity out of two spawned might be a mesh) I made a small app to compare the two sequences, available at: https://gist.github.com/nicopap/5dd9bd6700c6a9a9cf90c9199941883e At the top, we have Van Der Corput, at the bottom we have the Gold Kronecker. In the video, we spawn a vertical line at the position on screen where the x coordinate is the image of the sequence. The preimages are 1,2,3,4,… The ideal algorithm would always have the largest possible gap between each line (imagine the screen x coordinate as the color hue): https://github.com/bevyengine/bevy/assets/26321040/349aa8f8-f669-43ba-9842-f9a46945e25c Here, we repeat the experiment, but with with `entity.to_bits()` instead of a sequence: https://github.com/bevyengine/bevy/assets/26321040/516cea27-7135-4daa-a4e7-edfd1781d119 Notice how Van Der Corput tend to bunch the lines on a single side of the screen. This is because we always skip odd-numbered entities. Gold Kronecker seems always worse than Van Der Corput, but it is resilient to finicky stuff like entity indices being multiples of a number rather than purely sequential, so I prefer it over Van Der Corput, since we can't really predict how distributed the entity indices will be. ### Chosen implementation You'll notice this PR's implementation is not the Golden ratio-based Kronecker sequence as described in [tueoqs](https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/). Why? tueoqs R function multiplies a rational/float and takes the fractional part of the result `(x/Φ) % 1`. We start with an integer `u32`. So instead of converting into float and dividing by Φ (mod 1) we directly divide by Φ as integer (mod 2³²) both operations are equivalent, the integer division (which is actually a multiplication by `u32::MAX / Φ`) is probably faster. ## Acknowledgements - `inspi` on discord linked me to https://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/ and the wikipedia article. - [this blog post](https://probablydance.com/2018/06/16/fibonacci-hashing-the-optimization-that-the-world-forgot-or-a-better-alternative-to-integer-modulo/) for the idea of multiplying the `u32` rather than the `f32`. - `nakedible` for suggesting the `index()` over `to_bits()` which considerably reduces generated code (goes from 50 to 11 instructions)
Objective
color_from_entity
uses the poor man's hash to get a fixed random color for an entity.While the poor man's hash is succinct, it has a tendency to clump. As a result, bevy_gizmos has a tendency to re-use very similar colors for different entities.
This is bad, we would want non-similar colors that take the whole range of possible hues. This way, each bevy_gizmos aabb gizmo is easy to identify.
Solution
AHash is a nice and fast hash that just so happen to be available to use, so we use it.