如何将（爱好）路径一分为二

Question

几乎所有的碎片都在 TikZ 和业余爱好代码的某个地方，只需要稍微组装一下拼图碎片并修复业余爱好代码中的两个错误。错误修复将（最终）进入业余爱好代码。其余的也可能在某些地方非常有用（我对结库有一些想法）。

简而言之，新节点可以放置在交叉点仿佛已指定键pos。这意味着节点可以旋转以位于该点处的曲线上（使用交点库提供的坐标不允许最后一点）。然后其东/西锚点位于该点处与曲线相切的线上，可用于定义新曲线的控制点。

交叉点库提供了所有必要的信息，关键在于提取这些信息。请参阅下面的代码以了解如何做到这一点。

业余爱好错误与将节点放置在业余爱好生成的曲线的部分有关。这些问题现在已在业余爱好版本中得到修复github（运行tex hobby.dtx以生成文件）所以我从下面的代码中删除了它们。

\documentclass[a4paper]{article}
%\url{https://tex.stackexchange.com/q/372089/86}
\usepackage{tikz}
\usetikzlibrary{hobby,intersections,calc}

\makeatletter
\tikzset{
  place at intersection with code/.code={%
    % Test to see if the named path exists, if not display a message
    \pgfutil@ifundefined{tikz@intersect@path@name@#1}{\message{Path `#1' not found.}}{\find@intersection@point{#1}}
  },
  place at intersection with/.style={
    % This option defines the intersection point
    place at intersection with code=#1,
    node contents={},
    % The next two mean that the placed node will align itself with the curve
    sloped,
    allow upside down=true
  }
}

\def\find@intersection@point#1{%
  % Do everything inside a group so as not to upset things
  \begingroup
  % First step is to reconstruct the last path segment, using the \tikz@timer stuff
  \def\intersection@pathsegment{}%
  % Save the current path
  \pgfsyssoftpath@getcurrentpath\intersection@temppath
  % And initialise with an empty path
  \pgfsyssoftpath@setcurrentpath\intersection@pathsegment%
  % Move to the starting point
  \pgfpathmoveto{\tikz@timer@start}%
  % The rest depends on the type of segment we just had
  \ifx\tikz@timer\tikz@timer@curve
  % Bezier curve
  \pgfpathcurveto{\tikz@timer@cont@one}{\tikz@timer@cont@two}{\tikz@timer@end}%
  \else
  \ifx\tikz@timer@line
  % Straight line
  \pgfpathlineto{\tikz@timer@end}%
  \else
  \ifx\tikz@timer\tikz@timer@hvline
  % Horizontal-Vertical line
  \tikz@timer@start
  \pgf@ya=\pgf@y
  \tikz@timer@end
  \pgf@xa=\pgf@x
  \pgfpathlineto{\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
  \pgfpathlineto{\tikz@timer@end}%
  \else
  \ifx\tikz@timer\tikz@timer@vhline
  % Vertical-horizontal line
  \tikz@timer@start
  \pgf@xa=\pgf@x
  \tikz@timer@end
  \pgf@ya=\pgf@y
  \pgfpathlineto{\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
  \pgfpathlineto{\tikz@timer@end}%
  \else
  \ifx\tikz@timer\tikz@timer@arc
  % Need to find out how to reconstruct an arc ...
  \fi
  \fi
  \fi
  \fi
  \fi
  % Get the newly created path segment
  \pgfsyssoftpath@getcurrentpath\intersection@pathsegment
  % Restore the original path
  \pgfsyssoftpath@setcurrentpath\intersection@temppath%
  % Sorting the intersections is the trigger for remembering the intersection point as a parameter along the path
  \pgfintersectionsortbyfirstpath
  % Call the intersection algorithm
  \pgfintersectionofpaths{\pgfsetpath\intersection@pathsegment}{\expandafter\pgfsetpath\csname tikz@intersect@path@name@#1\endcsname}%
  %
  \ifnum\pgfintersectionsolutions>0\relax
  % If we got an intersection, store the parameter corresponding to the first one
  \xdef\intersection@time{\csname pgf@g@intersect@solution@1@time@a\endcsname}%
  \else
  % If not, say so and default to the start of the segment
  \message{No intersection found}%
  \gdef\intersection@time{0}%
  \fi
  \endgroup
  % Set the position of the current node to the found parameter
  \tikzset{pos=\intersection@time}%
}
\makeatother

\begin{document}

\begin{tikzpicture}[scale=2,use Hobby shortcut]
% This is the path we'll use to define our cutting points.  The 'overlay' option means that it doesn't affect the bounding box
\path[name path=c,overlay] (-.3,0) -- +(0,1) -- +(0,-1);
% Define our hobby curve
\draw[line width=3,white,double=black,double distance=1,closed]
(180:1) .. (240:0.9)
% The 'place at intersection with=c' key puts this node at the intersection of this segment with path 'c'
% Even though we've specified `node contents={}` in the style, we still need the trailing {} due to how nodes are collected on paths
.. node[place at intersection with=c,name=dpt] {}  ([blank=soft]300:0.3) .. (120:0.3) 
.. ([blank=soft]60:0.9) .. (0:1) .. (300:0.9)   .. (240:0.3)
.. ([blank=soft,]60:0.3) .. node[place at intersection with=c,name=upt] {}  (120:0.9) [save Hobby path={trefoil}];
\draw[line width=3,white,double=black,double distance=1,restore and use Hobby path={trefoil}{invert soft blanks,disjoint}];
% Once we have our nodes placed, we can use the anchors to define the 'exit' paths.  The centre node is at the intersection point and the east-west line goes along the tangent line.
\draw[dashed] (upt.center) .. controls ($(upt.center)!2cm!(upt.east)$) and +(0,2) .. (1.5,0) .. controls +(0,-2) and  ($(dpt.center)!2cm!(dpt.west)$) .. (dpt.center);
\end{tikzpicture}
\end{document}

我希望这就是你所追求的。

Answer 1