tikz：交叉口坐标不正确

Question

尝试使用 tikz 库获取三角形中心的坐标intersections。这些线足够长，实际上可以相交，并且它们只相交一次。在图中，我预计黑点位于蓝线和红线的交点处。我做错了什么？感谢帮助

\documentclass[border=3pt,tikz]{standalone}
\usetikzlibrary{intersections,through,shapes,shapes.geometric}
\usetikzlibrary{calc}

% side lengths of triangle
\newcommand{\AB}{5cm}
\newcommand{\AC}{12cm}
\newcommand{\BC}{13cm}

\begin{document}

\begin{tikzpicture}[scale=0.6,thick]
  % draw points B and C horizontally (arbitrary choice)
  \coordinate (B) at (0, 0);
  \coordinate (C) at (\BC, 0);

  % get coordinates of A based on position of B and C
  \begin{pgfinterruptboundingbox}% prevent spacing from spilling out
      % draw circle with center B and radius AB
      \node (r1) at (B) [circle through=($ (B) + (0:\AB) $)] {};
      % draw circle with center C and radius AC
      \node (r2) at (C) [circle through=($ (C) + (0:\AC) $)] {};
  \end{pgfinterruptboundingbox}
  % A lies at the intersection of the two circles
  \coordinate (A) at (intersection 2 of r1 and r2);

  % draw triangle ABC
  \draw (B) node[below left] {$B$} 
     -- (C) node[below right] {$C$}
     -- (A) node[above] {$A$} 
     -- cycle; 
 
  % path of angle bisector at A
  \coordinate (A1) at ($(A)!10cm!(B)$);
  \coordinate (A2) at ($(A)!10cm!(C)$);
  \coordinate (A3) at ($(A1)!0.5!(A2)$); % midpoint
  \draw[name path=A4,blue] (A) -- (A3);

  % path of angle bisector at C
  \coordinate (C1) at ($(C)!15cm!(A)$);
  \coordinate (C2) at ($(C)!15cm!(B)$);
  \coordinate (C3) at ($(C1)!0.5!(C2)$); % midpoint
  \draw[name path=C4,red] (C) -- (C3);

  % center of the inscribed circle
  \coordinate[name intersections={of={C4} and {A4}, by={O}}];
  \draw[fill] (O) circle (2pt);

\end{tikzpicture}

\end{document}

Answer 1

问题似乎出在coordinate与 结合使用的命令上name-intersections。您可以改用或path，例如。drawfill\path[name intersections={of=C4 and A4, by={O}}];

\documentclass[border=3pt,tikz]{standalone}
\usetikzlibrary{intersections,through,shapes,shapes.geometric}
\usetikzlibrary{calc}

% side lengths of triangle
\newcommand{\AB}{5cm}
\newcommand{\AC}{12cm}
\newcommand{\BC}{13cm}

\begin{document}

\begin{tikzpicture}[scale=0.6,thick]
  % draw points B and C horizontally (arbitrary choice)
  \coordinate (B) at (0, 0);
  \coordinate (C) at (\BC, 0);

  % get coordinates of A based on position of B and C
  \begin{pgfinterruptboundingbox}% prevent spacing from spilling out
      % draw circle with center B and radius AB
      \node (r1) at (B) [circle through=($ (B) + (0:\AB) $)] {};
      % draw circle with center C and radius AC
      \node (r2) at (C) [circle through=($ (C) + (0:\AC) $)] {};
  \end{pgfinterruptboundingbox}
  % A lies at the intersection of the two circles
  \coordinate (A) at (intersection 2 of r1 and r2);

  % draw triangle ABC
  \draw (B) node[below left] {$B$} 
     -- (C) node[below right] {$C$}
     -- (A) node[above] {$A$} 
     -- cycle; 
 
  % path of angle bisector at A
  \coordinate (A1) at ($(A)!10cm!(B)$);
  \coordinate (A2) at ($(A)!10cm!(C)$);
  \coordinate (A3) at ($(A1)!0.5!(A2)$); % midpoint
  \draw[name path=A4,blue] (A) -- (A3);

  % path of angle bisector at C
  \coordinate (C1) at ($(C)!15cm!(A)$);
  \coordinate (C2) at ($(C)!15cm!(B)$);
  \coordinate (C3) at ($(C1)!0.5!(C2)$); % midpoint
  \draw[name path=C4,red] (C) -- (C3);

  % center of the inscribed circle
  \path[name intersections={of=C4 and A4, by={O}}];
  \draw[fill] (O) circle (2pt);

  % alternative
  % \fill[name intersections={of=C4 and A4, by={O}}] (O) circle (2pt);

\end{tikzpicture}

\end{document}