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Updated theory (code is not up to date with theory yet)

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Klemek
2019-05-28 19:19:38 +02:00
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@@ -23,7 +23,30 @@ Optional arguments :
It gives you something like this :
![example](wallpaper.jpg)
## Theory
Generate a matrix of random 3-tuples as following :
![0<R_{x,y,z}<1](https://latex.codecogs.com/svg.latex?%5Cdpi%7B150%7D%20%5CLARGE%200%3CR_%7Bx%2Cy%2Cz%7D%3C1)
Initialize with a starting color, a slope vector and a variation vector :
![V_{0,0}=\[r_{0,0},g_{0,0},b_{0,0}\]](https://latex.codecogs.com/svg.latex?%5CLARGE%20V_%7B0%2C0%7D%3D%5Br_%7B0%2C0%7D%2Cg_%7B0%2C0%7D%2Cb_%7B0%2C0%7D%5D)
![S=\[s_{x},s_{y}\],s_{x}+s_{y}=1](https://latex.codecogs.com/svg.latex?%5CLARGE%20S%3D%5C%5Bs_%7Bx%7D%2Cs_%7By%7D%5C%5D%2Cs_%7Bx%7D&plus;s_%7By%7D%3D1)
![K=\[k_{r},k_{g},k_{b}\]](https://latex.codecogs.com/svg.latex?%5CLARGE%20K%3D%5C%5Bk_%7Br%7D%2Ck_%7Bg%7D%2Ck_%7Bb%7D%5C%5D)
Given a sigma function as following :
![0<\sigma (x)<1](https://latex.codecogs.com/svg.latex?%5Cdpi%7B150%7D%20%5CLARGE%200%3C%5Csigma%28x%29%3C1)
Compute each pixels with :
![V_{x,y,z}=\sigma (R_{x,y,z}*K_{z}+V_{x-1,y,z}*s_{x}+V_{x,y-1,z}*s_{y})](https://latex.codecogs.com/svg.latex?%5Clarge%20V_%7Bx%2Cy%2Cz%7D%3D%5Csigma%20%28R_%7Bx%2Cy%2Cz%7D*K_%7Bz%7D&plus;V_%7Bx-1%2Cy%2Cz%7D*s_%7Bx%7D&plus;V_%7Bx%2Cy-1%2Cz%7D*s_%7By%7D%29)
Compute output 3-tuples as color vectors and you have your final image.
![V_{x,y}=\[r_{x,y},g_{x,y},b_{x,y}\]](https://latex.codecogs.com/svg.latex?%5CLARGE%20V_%7Bx%2Cy%7D%3D%5C%5Br_%7Bx%2Cy%7D%2Cg_%7Bx%2Cy%7D%2Cb_%7Bx%2Cy%7D%5C%5D)