TiKz/PS Blending at the pixel level

Question

To do proper blending easily in TiKz, I need to do be able to have a special blend mode. (this is relevant to anything dealing with graphics and not tiks/tex)

• When you plot a pixel with an alpha channel the graphics package or graphics card will mix the pixel color below it with the new one. eg., suppose we have (100,0,0,255) and we plot (50,50,0,50) on top of it. The new pixel will be (100*(255 - 50)/255 + 50*50/255, 50*50/255, 0, 255) = (80, 10, 0, 255).

• Now when you have a white background you always end up mixing with white for the initial pixel. So if you plot any pixel for the first time with an alpha channel it will get blended with white and become washed out. (255, 255, 255, 255) blended with (255, 0, 0, 50) = (255, 205, 205, 255)

• This is the default behavior of tikz and most graphics packages that plot with alpha channel(you just mix pixels)

• I would like, instead, to plot where the first color does not mix. Basically if it is the first pixel to be plotted then it's alpha channel will always be set to 255. This prevents colors from being washed out and allows for complex geometrical conditions that break others.

• Anyone know if TiKz can do this or be modified to do it? Basically one has to keep a bit buffer where each bit represents if a pixel has been plotted for the first time or not(sort of a like a z-buffer). Blending mode - This mode is basically "Set Alpha channel to 255 for new pixels"

• One can do the test on the primitive level in tikz BUT this does not get partial overlapped objects. Think of two circles that overlap but not totally. One circle is "new"(in the sense that all pixels are new) and the other is partially new(some pixels, the overlapped ones) are not new while the others are. Using tikz's fill opacity cannot handle this case(although you could do some clipping and stuff that becomes very complex quickly).

One way to see this at http://www.texample.net/tikz/examples/venn-diagram/

notice the last diagram and how washed out all the colors are. In my mode they will not be washed out because none of the circles pixels will be blended with white but all blend with themselves.

Again, one can achieve my effect in a very complex manner by using clipping and changing alpha values but it can be achieved much easier given the method I have described = if new pixel then force alpha channel = 255.

Answer 1

As far as I know, this is not possible because the output formats do not implement it. The most common output formats for TikZ/PGF are vector formats. This means that they do not specify graphic elements by pixels but by paths, with instructions on what to do with those paths. This has definite advantages in that they are typically smaller (admittedly, for types of drawing particularly suited to this format) and they scale perfectly. It is the job of the renderer or viewer to interpret these commands into something on the screen or paper and it is only at that stage where pixels come into play. By this point, TeX is out of play and it is not possible to feed back information from the renderer to the original tex process.

For more on what a vector format is, take a look at the Wikipedia page on PDF.

However, that's not to say that what you ask for is impossible. It is certainly possible to simulate the effect that you want. The most straightforward way that I can think of is the following: you want the "base" colour at each point to be the colour that is first drawn there. So we start by creating a copy of the picture where each colour is its initial colour. Then we draw the real picture on top of this with the alphas as desired. This should have the correct effect since when each element gets rendered then if it is "first" it will get blended with an opaque copy of itself, whence be the opaque version of itself, but if it is not first then it blends with what's already there as it ought to.

To create the copy where each colour is its initial colour then we draw the image in reverse with each colour set to fully opaque. This might take a little planning for a particular picture, of course.

Here's the example of the Venn diagram that you linked to.

\documentclass{article}
%\url{http://tex.stackexchange.com/q/48905/86}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\def\firstcircle{(0,0) circle (1.5cm)}
\def\secondcircle{(45:2cm) circle (1.5cm)}
\def\thirdcircle{(0:2cm) circle (1.5cm)}
\begin{document}
\begin{tikzpicture}
\begin{scope}[fill opacity=0.5,text opacity=1]
        \fill[red] \firstcircle;
        \fill[green] \secondcircle;
        \fill[blue] \thirdcircle;
        \draw \firstcircle node[below] {$A$};
        \draw \secondcircle node [above] {$B$};
        \draw \thirdcircle node [below] {$C$};
    \end{scope}
\begin{scope}[yshift=-5cm]
        \fill[blue] \thirdcircle;
        \fill[green] \secondcircle;
        \fill[red] \firstcircle;
\begin{scope}[fill opacity=0.5,text opacity=1,every node/.style={ellipse,fill=white}]
        \fill[red] \firstcircle;
        \fill[green] \secondcircle;
        \fill[blue] \thirdcircle;
        \draw \firstcircle node[below] {$A$};
        \draw \secondcircle node [above] {$B$};
        \draw \thirdcircle node [below] {$C$};
    \end{scope}
\end{scope}
\end{tikzpicture}
\end{document}

Result (original on top):

Answer 2

I don't quite understand the precise details of what you're looking for, but I suspect that you would find these links informative:

• Ghostcript's Transparency operators

• Adobe Technical Note #5407, "Transparency in PDF"