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When scaling tikzpicture using option scale, some points that had equal coordinates appear to be shifted a little bit. So the precise comparision \ifdim \y1 = \y2 will not do anymore.

I'm aware of \pgfmathapproxequalto, but the problem is that dimensions are not plain numbers.

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I was not aware of \pgfmathapproxequalto, but know that using dimensions instead of plain numbers is not a problem with the \pgfmath... macros. You can simply use it with dimensions: \pgfmathapproxequalto{1pt}{1pt} or even mixed: \pgfmathapproxequalto{1pt}{1}. Did you tried that and got an error? It works OK in my little tests. –  Martin Scharrer Apr 18 '11 at 6:55
    
@Martin: Yes, you are right, it seems to work. I messed up with \the macro (\the\y1), which led me to errors. This problem is the consequence of this topic (tex.stackexchange.com/questions/15107/…). When scaling, I get the same artifacts, even when I check the points to be on horizontal or vertical line. –  Dmitrii F. Volosnykh Apr 18 '11 at 7:29
    
@Dmitry: You should put your edit into an answer instead and then accept it so that this question won't appear unanswered. –  TH. Apr 18 '11 at 9:42
    
@TH: Yeah, you are right, and I will do that shortly. There's restriction for me (being quite a new user) to self-answer only after 24 hours. Thanks, anyway. –  Dmitrii F. Volosnykh Apr 18 '11 at 15:37
    
The 24 hours accept-your-own-answer is active for all users, not just the new ones. And with 120rep you should be free of all new-user restrictions relevant for posting. –  Martin Scharrer Apr 18 '11 at 15:44
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The problem was that \pgfmathapproxequalto uses fixed precision of 0.0001, but in my case scaling was so distorting that finally I had to set precision to 0.01. So, the solution was to use \pgfmathparse{abs(\y1 - \y2) <= 0.01}.

By the way, I have to call this macro from inside of pgfextra, because this condition is used to alter path construction on the fly.

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