[Tex/LaTex] Angle specified in “bend left=<...>” in TikZ interpreted incorrectly

tikz-arrowstikz-pgf

I have a strange problem with the "bend left=…" option for arrows in TikZ which I can't seem to find an existing solution for.

EDITED:

Basically I want to create this kind of diagram. That is, both red and blue arrows bend upward (90 deg) relative to the two points connecting each arc.

I have created my own command, \myarrows, for this since I'll be wanting to make lots of this with variable length (number of arcs) and offsettings.
My idea was that if the requested number of loops is negative (first argument), then the loops are drawn in the opposite direction (to the left). In that case I should simply multiply the bend angle with the sign of the first argument (number of loops). This, however, does not seem to work. What am I doing wrong here? Note that if I specify the angles directly in the code (commented out), it works fine.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{calc} 
\pgfplotsset{compat=newest}

\pgfplotsset{ /pgf/declare function={
    logkn(\n)   = log10(1.3^\n);
    N           = 120;
    dN          = 12;
    sgn(\x)     = \x/abs(\x);
    y(\n)       = 1.07^\n * 5e-2;
}}

\pgfplotsset{xlabel=$\log x$, ylabel=$\log y$,ytick=\empty,xtick=\empty,axis lines=left,xmin=logkn(1),xmax=logkn(N), domain=1:N,samples=1e2}

\newcommand{\myarrows}[3]{  % \myarrows{NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}

    \pgfplotsinvokeforeach{0,...,#1}{ 

        % CORRECTLY BENDS IN ONE DIRECTION
%       \draw[mystyle,#3] (axis cs:{logkn( #2+dN*##1 )}, {y( #2+dN*##1 )}) to [bend left=+90.0, distance=0.5cm] ( axis cs: {logkn( #2+dN*(##1+sgn(#1)) )}, {y( #2+dN*(##1+sgn(#1)) )});
        % CORRECTLY BENDS IN OTHER DIRECTION
%       \draw[mystyle,#3] (axis cs:{logkn( #2+dN*##1 )}, {y( #2+dN*##1 )}) to [bend left=-90.0, distance=0.5cm] ( axis cs: {logkn( #2+dN*(##1+sgn(#1)) )}, {y( #2+dN*(##1+sgn(#1)) )});
        % MY ATTEMPT TO GENERALIZE USING THE SIGN OF #1 -- DOES NOT WORK
        \draw[mystyle,#3] (axis cs:{logkn( #2+dN*##1 )}, {y( #2+dN*##1 )}) to [bend left={90*sgn(#1)}, distance=0.5cm] ( axis cs: {logkn( #2+dN*(##1+sgn(#1)) )}, {y( #2+dN*(##1+sgn(#1)) )});
    }       
    \node[] at ({logkn(#2+dN*#1)},1e-1) {\scriptsize bend left$=\pgfmathparse{90*sgn(#1)}\pgfmathresult$};
}

\begin{document}
\begin{tikzpicture}[scale=2, mystyle/.style={thick,->,black}]
\begin{semilogyaxis}[ymin=1e-2,ymax=1e2]
        \myarrows{2}{60}{blue}  % {NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}
        \myarrows{-2}{60}{red}  % {NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}
\end{semilogyaxis}
\end{tikzpicture}
\end{document}

which produces

Thank you!

Best Answer

(This bug has been fixed since version 3.1 of pgf/TikZ.)

The bug

It's a bug in bend left (ticket):

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
  \draw [red,->] (0,0) to[bend left=90*-1] (1,0);
\end{tikzpicture}
\end{document}

Edited answer

Use in, out, and relative:

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{calc} 
\pgfplotsset{compat=newest}

\pgfplotsset{ /pgf/declare function={
    logkn(\n)   = log10(1.3^\n);
    N           = 120;
    dN          = 12;
    sgn(\x)     = \x/abs(\x);
    y(\n)       = 1.07^\n * 5e-2;
}}

\pgfplotsset{xlabel=$\log x$, ylabel=$\log y$,ytick=\empty,xtick=\empty,axis lines=left,xmin=logkn(1),xmax=logkn(N), domain=1:N,samples=1e2}

\newcommand{\myarrows}[3]{  % \myarrows{NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}

  \pgfplotsinvokeforeach{0,...,#1}{ 
    \draw[mystyle,#3] (axis cs:{logkn( #2+dN*##1 )}, {y( #2+dN*##1 )}) to [out=90*sgn(#1),in=90*sgn(#1),relative, distance=0.5cm] ( axis cs: {logkn( #2+dN*(##1+sgn(#1)) )}, {y( #2+dN*(##1+sgn(#1)) )});
  }       
  \node[] at ({logkn(#2+dN*#1)},1e-1) {\scriptsize bend left$=\pgfmathparse{90*sgn(#1)}\pgfmathresult$};
}

  \begin{document}
\begin{tikzpicture}[scale=2, mystyle/.style={thick,->,black}]
\begin{semilogyaxis}[ymin=1e-2,ymax=1e2]
        \myarrows{2}{60}{blue}  % {NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}
        \myarrows{-2}{60}{red}  % {NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}
\end{semilogyaxis}
\end{tikzpicture}
\end{document}

First answer

Don't use bend left as you want only out=90,in=90:

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{calc} 
\pgfplotsset{compat=newest}

\pgfplotsset{ /pgf/declare function={
    logkn(\n)   = log10(1.3^\n);
    N           = 120;
    dN          = 12;
    sgn(\x)     = (\x/abs(\x));
  }}

\pgfplotsset{xlabel=$\log x$, ylabel=$\log y$,ytick=\empty,xtick=\empty,axis lines=left,xmin=logkn(1),xmax=logkn(N), domain=1:N,samples=1e2}

\newcommand{\myarrows}[3]{  % \myarrows{NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}
  \pgfplotsinvokeforeach{0,...,#1}{ 
    \draw[mystyle,#3]
    (axis cs:{logkn(#2+dN*##1},1e0)
    to [out=90, in=90, distance=0.5cm]
    ( axis cs:{logkn(#2+dN*(##1+sgn(#1)))}, 1e0);
  }

  \node[] at ({logkn(#2+dN*#1)},1e-1) {\scriptsize bend left$=\pgfmathparse{90*sgn(#1)}\pgfmathresult$};
}

\begin{document}
\begin{tikzpicture}[scale=2, mystyle/.style={thick,->,black}]
  \begin{semilogyaxis}[ymin=1e-2,ymax=1e2]
    \myarrows{2}{60}{blue}  % {NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}
    \myarrows{-2}{60}{red}  % {NUMBER OF LOOPS -1}{XAXIS OFFSET}{COLOR}
  \end{semilogyaxis}
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] Drawing rectilinear curves in Tikz, aka an Etch-a-Sketch drawing

\draw (20,12) -- ++(2,0) -- ++(0,2) -- ++(-3,0) -- ++(45:3);

Use ++ before each new incremental coordinate to make it relative to the last one and put the pencil there.

Here's a complete example:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\tikz\draw (20,12) -- ++(2,0) -- ++(0,2) -- ++(-3,0) -- ++(30:3) {[rounded corners=10pt]-- ++(5,0) -- ++(0,-6)} -- ++(-7,0) -- cycle;
\end{document}

Of course, combining this with the -| or |- path operators can simplify the code even further; the following two pieces of code produce the same result:

\tikz\draw (20,12) -- ++(2,0) -- ++(0,2) -- ++(3,0) -- ++(0,1) -- ++(1,0) -- ++(0,-3) -- ++(2,0);\par\bigskip

and

\tikz\draw (20,12) -| ++(2,2) -| ++(3,1) -- ++(1,0) |- ++(2,-3);

I don't think that defining commands in this case adds anything; in fact, I think it reduces the functionality of the existing syntax (which is already simple). The example demonstrates that you can use, for example, polar coordinates and modify (up to TikZ limitations) the path attributes midways; even if the current question doesn't require this, it's a good thing to have the possibility to do those kind of modification if they are required.

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\definecolor{lightblue}{RGB}{124,184,201}

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            inner sep=1pt]
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