drummyfish/less_retarded_wiki
5
1
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity

Update

Browse source
This commit is contained in:
Miloslav Ciz 2023-12-17 18:21:35 +01:00
parent 3eaceb1bb7
commit 3461c669cf
5 changed files with 38 additions and 31 deletions
Download patch file Download diff file Expand all files Collapse all files

8
bilinear.md
View file

@ -1,6 +1,6 @@
# Bilinear Interpolation
Bilinear interpolation (also bilinear filtering) is a simple way of creating a smooth transition ([interpolation](interpolation.md)) between [discrete](discrete.md) samples (values) in 2D, it is a [generalization](generalization.md) of [linear interpolation](lerp.md) to 2 dimensions. It is used in many places, popularly e.g. in 3D [computer graphics](graphics.md) for [texture](texture.md) filtering; bilinear interpolation allows to upscale textures to higher resolutions (i.e. compute new pixels between existing pixels) while keeping their look smooth and "non-blocky" (even though blurry). On the scale of quality vs simplicity it is kind of a middle way between a simpler [nearest neighbour](nearest_neighbour.md) interpolation (which creates the "blocky" look) and more complex [bicubic interpolation](bicubic.md) (which uses yet smoother curves but also requires more samples). Bilinear interpolation can further be generalized to [trilinear interpolation](trilinear.md) (in computer graphics trilinear interpolation is used to also additionally interpolate between different levels of a texture's [mipamap](mipamp.md)) and perhaps even bilinear [extrapolation](extrapolation.md). Many frameworks/libraries/engines have bilinear filtering built-in (e.g. `GL_LINEAR` in [OpenGL](ogl.md)).
Bilinear interpolation (also bilinear filtering) is a simple way of creating a smooth transition ([interpolation](interpolation.md)) between [discrete](discrete.md) samples (values) in 2D, it is a [generalization](generalization.md) of [linear interpolation](lerp.md) to 2 dimensions. It is used in many places, popularly e.g. in 3D [computer graphics](graphics.md) for **[texture](texture.md) filtering**; bilinear interpolation allows to upscale textures to higher resolutions (i.e. compute new pixels between existing pixels) while keeping their look smooth and "non-blocky" (even though blurry). On the scale of quality vs simplicity it is kind of a middle way between a simpler [nearest neighbour](nearest_neighbour.md) interpolation (which creates the "blocky" look) and more complex [bicubic interpolation](bicubic.md) (which uses yet smoother curves but also requires more samples). Bilinear interpolation can further be generalized to [trilinear interpolation](trilinear.md) (in computer graphics trilinear interpolation is used to also additionally interpolate between different levels of a texture's [mipamap](mipamp.md)) and perhaps even bilinear [extrapolation](extrapolation.md). Many frameworks/libraries/engines have bilinear filtering built-in (e.g. `GL_LINEAR` in [OpenGL](ogl.md)). Of course this method may be used to smooth not just textures but anything, for example terrain [heightmaps](heightmap.md) or just any discrete mathematical function that we simply want to have defined everywhere, it's not just graphics thing, but here we will focus on its application in [graphics](graphics.md).
```
####OOOOVVVVaaaaxxxxssssffffllllcccc////!!!!;;;;,,,,....----
@ -111,4 +111,8 @@ The program outputs:
6 6 6 6 5 5 5 4
7 7 7 6 6 5 5 4
8 8 7 6 6 5 4 3
```
```
**Cool [hack](hacking.md) to improve bilinear interpolation** (from https://iquilezles.org/articles/texture): bilinear interpolation doesn't looks as good as bicubic but bicubic is a lot more complex on hardware and bandwidth as it requires fetching more texels -- there is one trick which [shader](shader.md) programmers use to improve the look of bilinear filtering while not requiring fetching more texels. They use the `smoothstep` function on the interpolation parameter which eliminates instant "jumps" at edges between texels, it replaces straight lines with a smoother curve and so makes the [derivative](derivative.md) of the result continuous -- basically it looks a lot better. Still not as good as bicubic but close enough.
TODO: code for the above