Nonlinear PGF Transformation Units Are Messed Up

Question

Adapted from my "answer" to this question: Why are the units messed up? I'm sure there's a quick fix. Many thanks!

\documentclass[tikz, border=1cm]{standalone}

\usepgfmodule{nonlineartransformations} 

\makeatletter
\def\customtransformation{
    \pgfmathsetmacro{\xnew}{
        (2.7^\pgf@x)*cos(\pgf@y) % u = e^x * cos(y)
    }
    \pgfmathsetmacro{\ynew}{
        (2.7^\pgf@x)*sin(\pgf@y) % v = e^x * sin(y)
    }
    \pgf@x=\xnew pt
    \pgf@y=\ynew pt
}
\makeatother

\begin{document}

\begin{tikzpicture}
    \begin{scope}[xshift=-6cm]
        \draw[xstep=.5pt,ystep=5pt,black!25,thin] (0,0) grid (4pt,250pt);
    \end{scope}
    \pgftransformnonlinear{\customtransformation}
    \draw[xstep=.5pt,ystep=5pt,black!25,thin] (0,0) grid (4pt,250pt);
\end{tikzpicture}

\end{document}

What do you mean by "units are messed up"? As far as I can see, you just did not take into account that the distances are measured in pt. — , Apr 19 '20 at 18:21
@Schrödinger'scat Okay, that might be very true, but what I mean is that, if I have (0,0) grid (1,1), I'd expect the transformed grid to reach (e*cos(1),e*sin(1)) and no more; where would I have to change the units (or multiply by a conversion factor) to achieve this? — steve, Apr 19 '20 at 19:05

score 1 · Accepted Answer · edited Apr 20 '20 at 12:19

1

You seem to be looking for the conversion to cm. This can be achieved by dividing the lengths \pgf@x and \pgf@y by 1cm. From your last comment I also take that you want to transform back to cm units at the end of the computation.

\documentclass[tikz, border=1cm]{standalone}

\usepgfmodule{nonlineartransformations} 
\usetikzlibrary{fpu}
\makeatletter
\newcommand{\PgfmathsetmacroFPU}[2]{\begingroup% https://tex.stackexchange.com/a/503835
\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
\pgfmathsetmacro{#1}{#2}%
\pgfmathsmuggle#1\endgroup}%

\def\customtransformation{%
\PgfmathsetmacroFPU{\xnew}{%
    (exp(\pgf@x/1cm))*cos(deg(\pgf@y/1cm))*1cm % u = e^x * cos(y)
}%
\PgfmathsetmacroFPU{\ynew}{%
    (exp(\pgf@x/1cm))*sin(deg(\pgf@y/1cm))*1cm % v = e^x * sin(y)
}%
\pgf@x=\xnew pt%
\pgf@y=\ynew pt%
}
\makeatother

\begin{document}

\begin{tikzpicture}
    \begin{scope}[xshift=-7cm]
        \draw[black!25,thin] (0,0) grid (4,4);
    \end{scope}
    \draw[red] ({exp(1)*cos(deg(1))},{exp(1)*sin(deg(1))}) circle[radius=.1];
    \pgfsettransformnonlinearflatness{3pt}
    \pgftransformnonlinear{\customtransformation}
    \draw[black!25,thin] (0,0) grid[step=0.25] (1,4);
    \draw[blue,dashed] (1,1) circle[radius=.1];
\end{tikzpicture}

\end{document}

Here I switched on the fpu library as here in case you go to more extensive applications. Note also that the density of sampling is controlled by a dimension \pgftransformnonlinearflatness, which can be set with \pgfsettransformnonlinearflatness, see the pgfmanual v3.1.5 on p. 1164:

So if you wish to decrease the grid steps, you may also want to decrease the flatness. Needless to say that decreasing the flatness increases the compilation time.

edited Apr 20 '20 at 12:19

steve

2,154

answered Apr 19 '20 at 19:14

That's exactly what I wanted, thank you! Just one more thing: now the resulting plot looks very "edged", and if I add some more steps to the grids (e.g. step=.25), some of the centrifugal lines escape the circle; how can I add more sampling points to this figure? (Seeing as it doesn't seem to be with the classic samples= option.) – steve Apr 19 '20 at 19:39
1

@ABlueChameleon You need to decrease the flatness. I added more explanations to the answer. – Apr 19 '20 at 19:49
Sorry, I should've checked the manual before asking. Thanks so much for the answer though, it looks fantastic! – steve Apr 19 '20 at 19:52
1

@ABlueChameleon I actually did not check the manual. I read pgfmodulenonlineartransformations.code.tex and then searched for the flatness in the manual. This is usually more efficient. – Apr 19 '20 at 19:56
Hmm... playing around some more with the answer, there's still one thing that confuses me; why is the scale of the transformed grid changed? I.e., if I write \fill (1.47,2.29) circle (.1); just before the transformation (approximate coordinates of (exp(1)*cos(1), exp(1)*sin(1))), and then write \fill (1,1) circle (.1); after the transformation, the circles are at different positions and of different sizes. – steve Apr 19 '20 at 20:25
1

@ABlueChameleon I think I finally understand what you wish to achieve. Then you need to multiply the result by 1cm. I completely rewrote the answer. – Apr 19 '20 at 20:41
This is just perfect, thank you! I updated my "answer" to the question from which mine originated with your code, hope that's cool. – steve Apr 19 '20 at 21:31
1

@ABlueChameleon Sure, why not? – Apr 19 '20 at 21:31

Nonlinear PGF Transformation Units Are Messed Up

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