# How to do logarithmic shading with TikZ?

TeX - LaTeX Asked by Tobard on January 5, 2021

Using TikZ, the shade option is very convenient to produce color shadings, but it produces only linear color gradients. Is it possible to obtain other transitions, and especially a logarithmic one?

Thanks!

# Edit:

Here is an example for the linear case:

documentclass[border=5mm]{standalone}
usepackage{tikz}
begin{document}

begin{tikzpicture}
shade[left color=black, right color=white] (0,0) rectangle (10,1);
end{tikzpicture}

end{document}

Here are some examples.

• R=G=B=x
• R=G=B=x²
• R=G=B=√x
• R=G=B=log(1+x)
• R=G=B=log(1+9x)
• R=G=B= ... well ...

documentclass{article}
usepackage[a3paper]{geometry}
usepackage{tikz}
begin{document}

begin{tikzpicture}
fill(-11,0)|-(0,-2)|-(11,2)|-cycle;
end{tikzpicture}

pop 50 div .5 sub % u
dup dup % u u u
}
begin{tikzpicture}
fill(-11,0)|-(0,-2)|-(11,2)|-cycle;
end{tikzpicture}

pop 50 div .5 sub % u
dup mul % u²
dup dup % u² u² u²
}
begin{tikzpicture}
fill(-11,0)|-(0,-2)|-(11,2)|-cycle;
end{tikzpicture}

pop 50 div .5 sub % u
sqrt % √u
dup dup % √u √u √u
}
begin{tikzpicture}
fill(-11,0)|-(0,-2)|-(11,2)|-cycle;
end{tikzpicture}

pop 50 div .5 sub % u
dup dup % ㏒(1+u) ㏒(1+u) ㏒(1+u)
}
begin{tikzpicture}
fill(-11,0)|-(0,-2)|-(11,2)|-cycle;
end{tikzpicture}

pop 50 div .5 sub % u
9 mul 1 add log % ㏒(1+9u)
dup dup % ㏒(1+9u) ㏒(1+9u) ㏒(1+9u)
}
begin{tikzpicture}
fill(-11,0)|-(0,-2)|-(11,2)|-cycle;
end{tikzpicture}

50 div .5 sub exch % v U
50 div .5 sub 4 mul exch % 4u v
dup 1 exch sub % 4u v 1-v
2 index % 4u v (1-v) 4u
mul mul % u 4uv(1-v)
dup 1 exch sub 2 index mul mul
dup 1 exch sub 2 index mul mul
dup 1 exch sub 2 index mul mul
dup 1 exch sub 2 index mul mul
dup 1 exch sub 2 index mul mul
exch pop dup dup
}
begin{tikzpicture}
fill(-11,0)|-(0,-2)|-(11,2)|-cycle;
end{tikzpicture}

end{document}

### Remarks

• dup duplicates the topmost element.
• The dup dup at every very end is actually unnecessary.
• If you leave only a single number in the stack, PDF-renderer will treat it as the grayscale.
• If there are three, they are R, G, B respectively.
• If there are 0 or 2 or 4, 5, 6, ... I do not know.
• pop discards the topmost element.
• The pop at every very beginning throws away the y-coordinate, which is useless except the last case.
• Replacing pop by swap, you can leave the y-coordinate at the bottom alone. But then dup dup becomes necessary.