Intersections are incorrect under transformations

[AndreC75]

The problem is explained here: How to make so that the calculation of an intersection is correct during a change of scale?

\documentclass{article}
\usepackage{tikz}   
\usetikzlibrary{calc,intersections}
\usepackage{esvect}
   
\begin{document}

Faux 

 \begin{tikzpicture}[x={(-1,0)},scale=0.9]
\coordinate (O) at (0,0);
\coordinate (Od) at ($(O)+(0.4,0)$);
\coordinate (Og) at ($(O)-(0.4,0)$);

\draw[dashed] ($(O)-(0,3.5)$) -- ($(O) +(0,1.5)$);
\draw[blue,thick,fill=green!40] (Og) --++(-4,0)coordinate(bout) coordinate[pos=0.8](Of)--++(0,-0.2) --++(3.7,-0.3) --++(0,-1.5)coordinate(Ob)-|(Og);
\draw[blue,thick,fill=green!40] (Od) --++(0.3,0)coordinate(Oa) -- (Ob-|Oa) -| (Od);
\draw[fill] (Od) coordinate(A) circle (0.05) node[above left]{$A$};
\draw[fill] (Og|-Ob) coordinate(B) circle (0.05) node[below right]{$B$};
\draw[latex-,ultra thick] (Of)node[above left]{$\vv{F}$}node[below]{$C$} -- ++(0,1.5);

\draw[thin, red,opacity=0.3,fill] ($(A) +(2,0.6)$) -- (A) --($(A) +(2,-0.6)$);
\draw[name path =aa, dashed,red] (A) --++(-5,-1.5);
\draw[ultra thick, red, -latex] (A) -- ++(3,0.9)node[above]{$\vv{R_A}$};
\draw[thin, red,opacity=0.3,fill] ($(B) +(-2,0.6)$) -- (B) --($(B) +(-2,-0.6)$);
\draw[ultra thick, red, -latex] (B) -- ++(-3,0.9)node[above]{$\vv{R_B}$};
\draw[name path =bb, dashed,red] (B) --++(-5,1.5);

\coordinate [name intersections={of=aa and bb, by=I}];
\draw [dashed, blue] (I)node[below]{$I$} --++(0,3);

\draw[thin,-latex] ($(O)+(0,1)$)coordinate(oo) -- node[above]{$x_{lim}$} (oo-|I);
\draw[-latex] (O) -- (-5,0) node[below]{$\vv{x}$};
\draw[-latex] (O) -- (0,2) node[right]{$\vv{y}$};
\end{tikzpicture}

Correct

 \begin{tikzpicture}[x={(-1,0)}]
\coordinate (O) at (0,0);
\coordinate (Od) at ($(O)+(0.4,0)$);
\coordinate (Og) at ($(O)-(0.4,0)$);

\draw[dashed] ($(O)-(0,3.5)$) -- ($(O) +(0,1.5)$);
\draw[blue,thick,fill=green!40] (Og) --++(-4,0)coordinate(bout) coordinate[pos=0.8](Of)--++(0,-0.2) --++(3.7,-0.3) --++(0,-1.5)coordinate(Ob)-|(Og);
\draw[blue,thick,fill=green!40] (Od) --++(0.3,0)coordinate(Oa) -- (Ob-|Oa) -| (Od);
\draw[fill] (Od) coordinate(A) circle (0.05) node[above left]{$A$};
\draw[fill] (Og|-Ob) coordinate(B) circle (0.05) node[below right]{$B$};
\draw[latex-,ultra thick] (Of)node[above left]{$\vv{F}$}node[below]{$C$} -- ++(0,1.5);

\draw[thin, red,opacity=0.3,fill] ($(A) +(2,0.6)$) -- (A) --($(A) +(2,-0.6)$);
\draw[name path =aa, dashed,red] (A) --++(-5,-1.5);
\draw[ultra thick, red, -latex] (A) -- ++(3,0.9)node[above]{$\vv{R_A}$};
\draw[thin, red,opacity=0.3,fill] ($(B) +(-2,0.6)$) -- (B) --($(B) +(-2,-0.6)$);
\draw[ultra thick, red, -latex] (B) -- ++(-3,0.9)node[above]{$\vv{R_B}$};
\draw[name path =bb, dashed,red] (B) --++(-5,1.5);

\coordinate [name intersections={of=aa and bb, by=I}];
\draw [dashed, blue] (I)node[below]{$I$} --++(0,3);

\draw[thin,-latex] ($(O)+(0,1)$)coordinate(oo) -- node[above]{$x_{lim}$} (oo-|I);
\draw[-latex] (O) -- (-5,0) node[below]{$\vv{x}$};
\draw[-latex] (O) -- (0,2) node[right]{$\vv{y}$};
\end{tikzpicture}
\end{document}

[hmenke]

Please use the issue template and provide a minimal example.

[muzimuzhi]

Considering the following mwe:

Brief outline of the bug

In a scaled scope, name intersections={of=...} used as coordinate/node option creates intersections with wrong coordinates.

Similar question: https://tex.stackexchange.com/questions/218210/rotating-tikzpicture-messes-up-intersections.

Minimal working example (MWE)

\documentclass{article}
\usepackage{tikz}   
\usetikzlibrary{intersections}

\begin{document}
Faux 

\begin{tikzpicture}[scale=0.9]
  \draw[name path=aa] (0, 0) -- ++(3, 3);
  \draw[name path=bb] (0, 3) -- ++(3, -3);
  
  \coordinate[name intersections={of=aa and bb}] (x);
  % or one of 
  % \path coordinate[name intersections={of=aa and bb}] (x);
  % \path node[name intersections={of=aa and bb}] (x) {};
  % \node[name intersections={of=aa and bb}] (x) {};
  \fill (intersection-1) circle (2pt);
\end{tikzpicture}

Correct

\begin{tikzpicture}[scale=0.9]
  \draw[name path=aa] (0, 0) -- ++(3, 3);
  \draw[name path=bb] (0, 3) -- ++(3, -3);
  
  \path[name intersections={of=aa and bb}] coordinate (x);
  \fill (intersection-1) circle (2pt);
\end{tikzpicture}

\end{document}

[hmenke]

Looks like the intersection are calculated in the untransformed system (which makes a lot of sense) but then the transformation is not applied to the result again.

[muzimuzhi]

I don't know why but it seems the transformation is applied to intersection coordinates twice.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{intersections, scopes}

\begin{document}
\makeatletter

Faux\par
\begin{tikzpicture}[scale=0.9]
  \draw[name path=aa] (0, 0) -- ++(3, 3);
  \draw[name path=bb] (0, 3) -- ++(3, -3);
  
  \path { coordinate[name intersections={of=aa and bb}] (x)};
  % print "macro:->{1.0}{0.0}{0.0}{1.0}{34.5696.pt}{34.5696.pt}"
  \node {\expandafter\meaning\csname pgf@sh@nt@intersection-1\endcsname};
  \fill (intersection-1) circle (2pt);
\end{tikzpicture}

Attempt\par
\begin{tikzpicture}[scale=0.9]
  \draw[name path=aa] (0, 0) -- ++(3, 3);
  \draw[name path=bb] (0, 3) -- ++(3, -3);
  
  % added {[reset cm] ...}
  \path {[reset cm] coordinate[name intersections={of=aa and bb}] (x)};
  % print "macro:->{1.0}{0.0}{0.0}{1.0}{38.41093pt}{38.41093pt}"
  \node {\expandafter\meaning\csname pgf@sh@nt@intersection-1\endcsname};
  \fill (intersection-1) circle (2pt);
\end{tikzpicture}

Correct\par
\begin{tikzpicture}[scale=0.9]
  \draw[name path =aa] (0, 0) -- ++(3, 3);
  \draw[name path =bb] (0, 3) -- ++(3, -3);
  
  \path[name intersections={of=aa and bb}] coordinate (x);
  % print "macro:->{1.0}{0.0}{0.0}{1.0}{38.41093pt}{38.41093pt}"
  \node {\expandafter\meaning\csname pgf@sh@nt@intersection-1\endcsname};
  \fill (intersection-1) circle (2pt);
\end{tikzpicture}

\end{document}

[hmenke]

Not sure if this is really a fix:

diff --git a/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex b/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex
index cf94f923..ca0e7a1c 100644
--- a/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex
+++ b/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex
@@ -104,7 +104,7 @@
         \pgfmathloop%
         \ifnum\pgfmathcounter>\pgfintersectionsolutions\relax%
         \else%
-          \path[reset cm]\pgfextra{\pgftransformshift{\pgfpointintersectionsolution{\pgfmathcounter}}}%
+          \path\pgfextra{\pgftransformshift{\pgfpointintersectionsolution{\pgfmathcounter}}}%
             coordinate (\tikz@intersect@@name-\pgfmathcounter);
         \repeatpgfmathloop%
         \ifx\tikz@intersect@by\pgfutil@empty%
diff --git a/tex/generic/pgf/libraries/pgflibraryintersections.code.tex b/tex/generic/pgf/libraries/pgflibraryintersections.code.tex
index 24571576..c920dbae 100644
--- a/tex/generic/pgf/libraries/pgflibraryintersections.code.tex
+++ b/tex/generic/pgf/libraries/pgflibraryintersections.code.tex
@@ -352,7 +352,9 @@
     \pgf@iflinesintersect{#1}{#2}{#3}{#4}%
     {%
         \pgfextract@process\pgf@intersect@solution@candidate{%
+            \pgftransforminvert
             % pgf@x and pgf@y are already assigned by \pgf@iflinesintersect
+            \pgfpointtransformed{\pgfqpoint{\pgf@x}{\pgf@y}}%
         }%
         \pgf@ifsolution@duplicate{\pgf@intersect@solution@candidate}{%
             % ah - we a duplicate. Apparently, we have a hit on an

However, this also fixes the following example:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}
\begin{document}

\def\pathA{%
    \pgfpathmoveto{\pgfpointorigin}%
    \pgfpathlineto{\pgfqpoint{30pt}{30pt}}%
}

\def\pathB{%
    \pgfpathmoveto{\pgfqpoint{0pt}{30pt}}%
    \pgfpathlineto{\pgfqpoint{30pt}{0pt}}%
}

\begin{pgfpicture}
    \pgftransformscale{0.9}
    \pgftransformrotate{30}
    \pathA\pgfusepath{stroke}%
    \pathB\pgfusepath{stroke}%
    \pgfintersectionofpaths\pathA\pathB
    \pgfpathcircle{\pgfpointintersectionsolution{1}}{2pt}
    \pgfusepath{stroke}%
\end{pgfpicture}

\end{document}

[hmenke]

Definitely a candidate for regression. Let's see.