Reverse arrow disturbs smooth paths (draw plot)

[tcpaiva]

Brief outline of the bug

The curve of the line for
\draw[]plot[smooth]coordinates{(0,1)(1,0)(2,1)}
is the same for
\draw[->]plot[smooth]coordinates{(0,1)(1,0)(2,1)}
but it is not the same for
\draw[<-]plot[smooth]coordinates{(0,1)(1,0)(2,1)}

Minimal working example (MWE)

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \draw[->]plot[smooth]coordinates{(0,1)(1,0)(2,1)};
  \draw[<-, blue, opacity=0.3]plot[smooth]coordinates{(0,1)(1,0)(2,1)}; %% unexpected
\end{tikzpicture}
\end{document}

[muzimuzhi]

diff --git a/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex b/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex
index 5a9c5fc2..a29609f9 100644
--- a/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex
+++ b/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex
@@ -622,7 +626,7 @@
 % Line shortening for straight lines:
 %
 \def\pgf@do@shorten@straightstart{%
-  \edef\pgfprocessresultpathsuffix{\pgfsubpathfirsttoken{\the\pgf@xa}{\the\pgf@ya}\pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}}%
+  \edef\pgfprocessresultpathsuffix{\pgfsubpathfirsttoken{\the\pgf@xa}{\the\pgf@ya}\pgfsubpathsecondtoken{\the\pgf@xa}{\the\pgf@ya}}%
   \expandafter\expandafter\expandafter\def%
   \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix%
   \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathsuffix\pgfsubpath
end}%

Full example

\documentclass{article}
\usepackage{tikz}
\usepackage{xpatch}

\makeatletter
\xpatchcmd\pgf@do@shorten@straightstart
  {\pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}}
  {\pgfsubpathsecondtoken{\the\pgf@xa}{\the\pgf@ya}}
  {}{\PatchFailed}
\makeatother

\begin{document}
\begin{pgfpicture}
  % all control points
  \foreach \i/\j in { 0pt/20pt, 14.45pt/0pt, 20pt/0pt, 25.55pt/0pt, 40pt/20pt }
    {
      \pgfpathcircle{\pgfqpoint{\i}{\j}}{1pt}
    }
  % new path start after shortening
  \pgfpathcircle{\pgfqpoint{0.26936pt}{19.62717pt}}{1pt}
  \pgfusepath{stroke}
  
  \pgfpathmoveto{\pgfqpoint{0pt}{20pt}}
  \pgfpathcurveto
    {\pgfqpoint{0.0pt}{20.0pt}}{\pgfqpoint{14.45007pt}{0.0pt}}{\pgfqpoint{20.0pt}{0.0pt}}
  \pgfpathcurveto 
    {\pgfqpoint{25.54993pt}{0.0pt}}{\pgfqpoint{40.0pt}{20.0pt}}{\pgfqpoint{40.0pt}{20.0pt}}
  \pgfgetpath{\mypath}
  \pgfusepath{stroke}

  \pgfsetstrokecolor{red}
  \pgfsetarrows{->}
  \pgfsetpath{\mypath}
  \pgfusepath{stroke}

  \pgfsetstrokecolor{blue}
  \pgfsetarrows{<-}
  \pgfsetpath{\mypath}
  \pgfusepath{stroke}
\end{pgfpicture}

% based on original example
\begin{tikzpicture}[every plot/.append style={smooth}]
  \draw
    plot coordinates {(0,1) (1,0) (2,1)};
  \draw[->, yshift=2pt, red, opacity=.3]
    plot coordinates {(0,1) (1,0) (2,1)};
  \draw[<-, yshift=-2pt, blue, opacity=.3]
    plot coordinates {(0,1) (1,0) (2,1)}; %% unexpected
\end{tikzpicture}
\end{document}

Before	after

[muzimuzhi]

Ah, my patch was wrong (or too simple), when the starting and first support points of curve-to is not identical.

What really helpful is to load bending library, which will turn on precise path shortening (needed when path has arrow tips). Without bending a curve-to is treated like a straight line, which is bound to give unsatisfied shortening results in certain cases.

Full example 2

\documentclass{article}
\usepackage{tikz}

\usepackage{xpatch}

\begin{document}
\def\tests{
\begin{tikzpicture}[scale=3]
\def\pathP{ (0, 1) .. controls (0,1) and (.7, 0) .. (1,0) }
\def\pathQ{[xshift=1cm] (0,1) .. controls (0,.5) and (.7, 0) .. (1,0) }
\def\pathR{[xshift=2cm] (0,1) .. controls (0.5,1) .. (1,0) }
\def\pathS{[xshift=3cm] (0,1) .. controls (0,.5) and (.7, 0) .. (.7,0) }

\foreach \i in {\pathP, \pathQ, \pathR, \pathS}
  {
    \draw \i;
    \draw[->, shift={(1pt, 1pt)}, red,  opacity=.3] \i;
    \draw[<-, shift={(-1pt, -1pt)}, blue, opacity=.3] \i;
  }

\end{tikzpicture}}

\subsection*{Before (pgf-tikz v3.1.10)}
\tests

\subsection*{+ wront patch}
{
\makeatletter
\xpatchcmd\pgf@do@shorten@straightstart
{\pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}}
{\pgfsubpathsecondtoken{\the\pgf@xa}{\the\pgf@ya}}
{}{\PatchFailed}
\makeatother
\tests
}

\subsection*{+ bending library}
\usetikzlibrary{bending}
\tests
\end{document}

[muzimuzhi]

Ah, my patch was wrong (or too simple), when the starting and first support points of curve-to is not identical.

An improved patch. More knowledge about Bezier curve than what I got is needed to make up more test cases.

diff --git a/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex b/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex
index 5a9c5fc2..a9d7d4f1 100644
--- a/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex
+++ b/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex
@@ -622,7 +622,13 @@
 % Line shortening for straight lines:
 %
 \def\pgf@do@shorten@straightstart{%
-  \edef\pgfprocessresultpathsuffix{\pgfsubpathfirsttoken{\the\pgf@xa}{\the\pgf@ya}\pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}}%
+  \edef\pgfprocessresultpathsuffix{%
+    \pgfsubpathfirsttoken{\the\pgf@xa}{\the\pgf@ya}%
+    \ifx\pgfpointfirstonpath\pgfpointsecondonpath
+      \pgfsubpathsecondtoken{\the\pgf@xa}{\the\pgf@ya}%
+    \else
+      \pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}%
+    \fi}%
   \expandafter\expandafter\expandafter\def%
   \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix%
   \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathsuffix\pgfsubpath
end}%

Full example 3 (containing patch v2)

\documentclass{article}
\usepackage{tikz}

\usepackage{xpatch}

\begin{document}
\def\tests{
  \begin{tikzpicture}[scale=2]
    \def\pathP{ (0, 1) .. controls (0,1) and (.7, 0) .. (1,0) }
    \def\pathQ{[xshift=1cm] (0,1) .. controls (0,.5) and (.7, 0) .. (1,0) } 
    \def\pathR{[xshift=2cm] (0,1) .. controls (0.7,.5) .. (1,0) }
    \def\pathS{[xshift=2.2cm] (1,0) .. controls (1.3,0) and (2,1) .. (2,1) }
  
    \foreach \i in {\pathP, \pathQ, \pathR, \pathS}
      {
        \draw \i;
        \draw[->, shift={(1pt, 1pt)}, red,  opacity=.3] \i;
        \draw[<-, shift={(-1pt, -1pt)}, blue, opacity=.3] \i;
      }
  \end{tikzpicture}}

\subsection*{Before (pgf-tikz v3.1.10)}
\tests

\subsection*{+ wront patch (v1)}
{
  \makeatletter
  \xpatchcmd\pgf@do@shorten@straightstart
    {\pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}}
    {\pgfsubpathsecondtoken{\the\pgf@xa}{\the\pgf@ya}}
    {}{\PatchFailed}
  \makeatother
  \tests
}

\subsection*{+ revised patch (v2)}
{
  \makeatletter
  % perhaps a symmetric patch can be applied in \pgf@do@shorten@straightend
  \xpatchcmd\pgf@do@shorten@straightstart
    {\pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}}
    {%
     % use the same condition in \pgf@prep@straightstart
     \ifx\pgfpointfirstonpath\pgfpointsecondonpath
       \pgfsubpathsecondtoken{\the\pgf@xa}{\the\pgf@ya}%
     \else
       \pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}%
     \fi
    }
    {}{\PatchFailed}
  \makeatother
  \tests
}

\subsection*{+ bending library}
\usetikzlibrary{bending}
\tests
\end{document}