"Dimension too large" in this picture, why?

Question

When I run the following code, there is a "dimension too large" error:

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{hobby}
\definecolor{col1}{RGB}{24,127,127}
\definecolor{col2}{RGB}{240,240,240}
\begin{document}
\begin{tikzpicture}[use Hobby shortcut]
    \clip (0,0) rectangle (1,1);
    \path[yshift=10,
    postaction={
        decorate,
        decoration={
            markings,
            mark=between positions 0 and \pgfdecoratedpathlength step .01cm with {
                \pgfmathsetmacro\myval{multiply(divide(
                    \pgfkeysvalueof{/pgf/decoration/mark info/distance from start}, \pgfdecoratedpathlength),100)};
                \pgfsetfillcolor{col2!\myval!col1};
                \pgfpathcircle{\pgfpointorigin}{1.5};
                \pgfusepath{fill};}
    }}] 
    ([closed].075,.2)..(.2,.4)..(.8,0)..(.925,.2)..(.8,.4)..(.2,0);
\end{tikzpicture}
\end{document}

I did a little search on this problem, and it turns out it is neither caused by length>16384pt nor incorrect shift. The error sometimes disappear when the order of the points at last line changes, but I don't remember the exact order, and I think it is not very relevant to this problem.

How should I fix this problem?

Answer 1

This is a known problem. Somewhere on this site it has already been pointed out that a large fraction of these errors can be avoided by using a reciprocal from the fpu library. This fixes the problem also in your case. Per request by Henri Menke here is a version that works with the newest pgf version, v3.1.6. You can read about this in section 50.2 Handling “Dimension too large” errors of pgfmanual v3.1.6.

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{hobby}
\usetikzlibrary{fpu}
\definecolor{col1}{RGB}{24,127,127}
\definecolor{col2}{RGB}{240,240,240}
\begin{document}
\begin{tikzpicture}[use Hobby shortcut,/pgf/fpu/install only={reciprocal}]
    \clip (0,0) rectangle (1,1);
    \path[yshift=10,
    postaction={
        decorate,
        decoration={
            markings,
            mark=between positions 0 and \pgfdecoratedpathlength step .01cm with {
                \pgfmathsetmacro\myval{multiply(divide(
                    \pgfkeysvalueof{/pgf/decoration/mark info/distance from start}, \pgfdecoratedpathlength),100)};
                \pgfsetfillcolor{col2!\myval!col1};
                \pgfpathcircle{\pgfpointorigin}{1.5};
                \pgfusepath{fill};}
    }}] 
    ([closed].075,.2)..(.2,.4)..(.8,0)..(.925,.2)..(.8,.4)..(.2,0);
\end{tikzpicture}
\end{document}

If you have an older TeX installation use the original code that appeared here before this was added to pgf.

\documentclass[tikz]{standalone}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{hobby}
\usetikzlibrary{fpu}
\makeatletter
\tikzset{use fpu reciprocal/.code={%
\def\pgfmathreciprocal@##1{%
    \begingroup
    \pgfkeys{/pgf/fpu=true,/pgf/fpu/output format=fixed}%
    \pgfmathparse{1/##1}%
    \pgfmath@smuggleone\pgfmathresult
    \endgroup
}}}%
\makeatother
\definecolor{col1}{RGB}{24,127,127}
\definecolor{col2}{RGB}{240,240,240}
\begin{document}
\begin{tikzpicture}[use Hobby shortcut,use fpu reciprocal]
    \clip (0,0) rectangle (1,1);
    \path[yshift=10,
    postaction={
        decorate,
        decoration={
            markings,
            mark=between positions 0 and \pgfdecoratedpathlength step .01cm with {
                \pgfmathsetmacro\myval{multiply(divide(
                    \pgfkeysvalueof{/pgf/decoration/mark info/distance from start}, \pgfdecoratedpathlength),100)};
                \pgfsetfillcolor{col2!\myval!col1};
                \pgfpathcircle{\pgfpointorigin}{1.5};
                \pgfusepath{fill};}
    }}] 
    ([closed].075,.2)..(.2,.4)..(.8,0)..(.925,.2)..(.8,.4)..(.2,0);
\end{tikzpicture}
\end{document}