Rounded corners do not transform well in Tikz under a nonlinear transformation

Question

I want to apply a nonlinear transformation to the following image

Whose code is

\begin{tikzpicture}
\draw (-4,-2) grid [step=1] (4,2);
\draw[
fill=green!30, draw=blue, very thick, rounded corners=5ex, opacity=.5, dashed] (-2.,-1.) rectangle (2.,1.);
\end{tikzpicture}

With the nonlinear transformation I found there I get

The code is

\documentclass[tikz,border=3mm]{standalone}
\usepgfmodule{nonlineartransformations}
\makeatletter
\def\mytransformation{%
\pgfmathsetmacro{\myX}{\pgf@x + 4sin(4\pgf@y) }
\pgfmathsetmacro{\myY}{\pgf@y}
\setlength{\pgf@x}{\myX pt}
\setlength{\pgf@y}{\myY pt}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\begin{scope}%Inside the scope transformation is active
\pgftransformnonlinear{\mytransformation}
\draw (-4,-2) grid [step=1] (4,2);
\draw[
fill=green!30, draw=blue, very thick, rounded corners=5ex, opacity=.5, dashed] (-2.,-1.) rectangle (2.,1.);
\end{scope}
\end{tikzpicture}
\end{document}

How is it possible to let the edges transform well ?

score 2 · Accepted Answer · answered Jul 27 '22 at 12:37

The rounded cornerscommand does not seem to work in this case (see here about it Nonlinear transformation applied on decorations along path with a custom pic). I propose this way to solve this problem.

\documentclass[tikz,border=3mm]{standalone}
\usepgfmodule{nonlineartransformations}
\makeatletter
\def\mytransformation{%
\pgfmathsetmacro{\myX}{\pgf@x + 4sin(4\pgf@y) }
\pgfmathsetmacro{\myY}{\pgf@y}
\setlength{\pgf@x}{\myX pt}
\setlength{\pgf@y}{\myY pt}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\newcommand\xx{1}
\pgftransformnonlinear{\mytransformation}
\draw (-5,-5) grid [step=1] (5,5);
\draw[fill=green!30, draw=blue, very thick,opacity=.5, dashed]
(-2,-1+\xx) -- (-2,1-\xx).. controls (-2,1) ..
(-2+\xx,1) -- (2-\xx,1).. controls (2,1) ..
(2,1-\xx) -- (2,-1+\xx).. controls (2,-1) ..
(2-\xx,-1) -- (-2+\xx,-1).. controls (-2,-1) ..
(-2,-1+\xx);
\end{tikzpicture}
\end{document}

Of course, you can play with the \xx parameter within certain limits.

Apart from the fact that the object is to be defined manually, very nice solution!. It seems you've been working with my old code on this post. Thanks — Physor, Jul 27 '22 at 13:53
So do you mean with \xx a number one must choose or is it a part of the code, a variable for example ? — Physor, Jul 27 '22 at 14:08
@Physor Thank you. If the rectangle has dimensions a x b and a<b, then parameter xx can be chosen in the range 0<=xx<= a/2, either as described in my code \newcommand\xx{1} or like this \def\xx{0.8} In addition you can change control points or add new ones if needed. — kabenyuk, Jul 27 '22 at 14:50

score 1 · Answer 2 · answered Jul 27 '22 at 12:39

The option rounded corners is quite stubborn sometimes: it has several pitfalls. For instance it does not work well with scale, see pgfmanual.pdf, Section 14.5 Rounding Corners.

To avoid using this option, one simple way is define your own round rectangle path

\def\myround{.4}        % radius of the rounding corners    
\def\myrectangle{(0,2)
    --(3-\myround,2)   arc(90:0:\myround)
    --(3,-2+\myround)  arc(0:-90:\myround)
    --(-3+\myround,-2) arc(-90:-180:\myround)
    --(-3,2-\myround)  arc(180:90:\myround)--cycle;
}

Hence, with your \pgftransformnonlinear{\mytransformation}

and without \pgftransformnonlinear{\mytransformation}

Complete code:

\documentclass[tikz,border=3mm]{standalone}
\usepgfmodule{nonlineartransformations}
\makeatletter
\def\mytransformation{%
    \pgfmathsetmacro{\myX}{\pgf@x + 4*sin(4*\pgf@y) }
    \pgfmathsetmacro{\myY}{\pgf@y}
    \setlength{\pgf@x}{\myX pt}
    \setlength{\pgf@y}{\myY pt}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\def\myround{.4}        % radius of the rounding corners    
\def\myrectangle{(0,2)
    --(3-\myround,2)   arc(90:0:\myround)
    --(3,-2+\myround)  arc(0:-90:\myround)
    --(-3+\myround,-2) arc(-90:-180:\myround)
    --(-3,2-\myround)  arc(180:90:\myround)--cycle;
}   
\begin{scope} % Inside the scope, the transformation is active
\pgftransformnonlinear{\mytransformation}
\draw[gray!30] (-5,-3) grid (5,3);
\draw[blue,fill=green!30,very thick,fill opacity=.5,dashed] \myrectangle;
\end{scope}
\end{tikzpicture}
\end{document}

The other solution is also similar, but it seems better to use controls than acrs. Because the edges didn't stick to the grid as in the other answer. — Physor, Jul 27 '22 at 13:57

Rounded corners do not transform well in Tikz under a nonlinear transformation

2 Answers2