TikZ：与双线路径的交点

Question 1

您可以使用calcTikZ 包来完成这项工作：

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections,calc}
\begin{document}

\begin{tikzpicture}
\def \borderSep {3pt} % Define the border separation as a constant
\node (rect) [name path=rect,draw,double,ultra thick,double distance=\borderSep, rounded   corners,minimum size=1cm]{};
\draw[name path=line,draw] (rect.center)--(.7,.7);
\path[name intersections = {of=rect and line, by={a}}];
% Offset the nodes by sqrt(2) * separation
\node at ($(a) + 1/1.41*(\borderSep,\borderSep)$) [circle,fill=blue,inner sep=.5pt]{};
\node at ($(a) - 1/1.41*(\borderSep,\borderSep)$) [circle,fill=blue,inner sep=.5pt]{};
\end{tikzpicture}

\end{document}

您将获得以下内容：在此处输入图片描述

编辑：更通用的解决方案：

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections,calc}
\begin{document}

\begin{tikzpicture}
% If the rect has single border, set borderSep and borderThickness to 0pt
\def \borderSep {3pt}
\def \borderThickness {1.5pt}
\node (rect) [name path=rect,draw,double,ultra thick,double distance=\borderSep,rounded corners,minimum size=1cm]{};
\draw[name path=line,draw] (rect.center)--(.7,.1);

% Construct invisible rectangles at the positions of the borders
\node (rect) [name path=rectIn, rounded corners=6pt, minimum size=1cm+\borderSep+\borderThickness]{};
\node (rect) [name path=rectOut, rounded corners=2pt, minimum size=1cm-\borderSep-\borderThickness]{};

\path[name intersections = {of=rectIn and line, by={intIn}}];
\path[name intersections = {of=rectOut and line, by={intOut}}];
\node at (intIn) [circle,fill=blue,inner sep=.5pt]{};
\node at (intOut) [circle,fill=blue,inner sep=.5pt]{};
\end{tikzpicture}

\end{document}

现在，这在一般情况下也有效。请注意，如果您想要更精细的控制，则需要编辑（例如使用全局变量）rectIn 和 rectOut 圆角的半径。在此处输入图片描述

Answer

您可以使用calcTikZ 包来完成这项工作：

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections,calc}
\begin{document}

\begin{tikzpicture}
\def \borderSep {3pt} % Define the border separation as a constant
\node (rect) [name path=rect,draw,double,ultra thick,double distance=\borderSep, rounded   corners,minimum size=1cm]{};
\draw[name path=line,draw] (rect.center)--(.7,.7);
\path[name intersections = {of=rect and line, by={a}}];
% Offset the nodes by sqrt(2) * separation
\node at ($(a) + 1/1.41*(\borderSep,\borderSep)$) [circle,fill=blue,inner sep=.5pt]{};
\node at ($(a) - 1/1.41*(\borderSep,\borderSep)$) [circle,fill=blue,inner sep=.5pt]{};
\end{tikzpicture}

\end{document}

您将获得以下内容：在此处输入图片描述

编辑：更通用的解决方案：

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections,calc}
\begin{document}

\begin{tikzpicture}
% If the rect has single border, set borderSep and borderThickness to 0pt
\def \borderSep {3pt}
\def \borderThickness {1.5pt}
\node (rect) [name path=rect,draw,double,ultra thick,double distance=\borderSep,rounded corners,minimum size=1cm]{};
\draw[name path=line,draw] (rect.center)--(.7,.1);

% Construct invisible rectangles at the positions of the borders
\node (rect) [name path=rectIn, rounded corners=6pt, minimum size=1cm+\borderSep+\borderThickness]{};
\node (rect) [name path=rectOut, rounded corners=2pt, minimum size=1cm-\borderSep-\borderThickness]{};

\path[name intersections = {of=rectIn and line, by={intIn}}];
\path[name intersections = {of=rectOut and line, by={intOut}}];
\node at (intIn) [circle,fill=blue,inner sep=.5pt]{};
\node at (intOut) [circle,fill=blue,inner sep=.5pt]{};
\end{tikzpicture}

\end{document}

现在，这在一般情况下也有效。请注意，如果您想要更精细的控制，则需要编辑（例如使用全局变量）rectIn 和 rectOut 圆角的半径。在此处输入图片描述

Question 2

这是一种数学方法，\dimexpr在需要与单位无关的地方使用（适用于 pt、cm 或其他单位）。

它仅适用于线（使用\myline命令添加，但它可以像真正的 tikz 线一样接受参数）。线可以从任何点开始并终止于任何其他点，但必须与双路径相交。

双路径部分的距离也必须定义为\DoubleDist变量中定义。我认为代码可以更通用，并适用于超厚（但尚未包含此类参数，我不知道是否可以在不定义新参数的情况下添加）。

最后，交叉点的形状（圆形）最好由用户选择，但我也厌倦了这样做。（我想任何能理解代码的人都可以自己做）。

代码：

\documentclass[tikz,border=1mm]{standalone}
\usetikzlibrary{intersections}
\usetikzlibrary{calc}
\begin{document}

\def\DoubleDist{4.1 pt}


%\Usage \myline(x1,y1)(x2,y2)[parameters]=\draw[parameters] (x1,y1)--(x2,y2); +keep needed numbers
\makeatletter
\def\myline{\@ifnextchar({\readFirstOPoint}{\node at (0,0){Error in line 1};}}
\def\readFirstOPoint(#1,#2){
\gdef\lineXStart{#1}
\gdef\lineYStart{#2}
\@ifnextchar(
{\readSecondPoint}
{\node at (0,0){Error in line 2};}
}
\def\readSecondPoint(#1,#2){
\gdef\lineXStop{#1}
\gdef\lineYStop{#2}
\readParametersAndDraw
}
\def\readParametersAndDraw
{\@ifnextchar[{\Storeparam}{\gdef\LineParam{\empty}\ExecuteLine}}
\def\Storeparam[#1]
{
\gdef\LineParam{[#1]}
\ExecuteLine
}
\def\ExecuteLine
{
\draw\LineParam (\lineXStart,\lineYStart)--(\lineXStop,\lineYStop);
}
\makeatother


% Will be used to shift the point
\newlength{\xsh}
\newlength{\ysh}

% Finding double path intersections. Usage \FindIndersections(path)
\makeatletter
\def\FindIndersections{
\@ifnextchar({\ReadIndersection}{\node at (0,0){Error in readind indersection}}
}
\def\ReadIndersection(#1){
\pgfmathsetmacro\XShiftFactor{(\lineXStop-\lineXStart)/sqrt((\lineXStart-\lineXStop)^2+(\lineYStart-\lineYStop)^2)}
\pgfmathsetmacro\YShiftFactor{(\lineYStop-\lineYStart)/sqrt((\lineXStart-\lineXStop)^2+(\lineYStart-\lineYStop)^2)}
\setlength{\xsh}{\dimexpr\XShiftFactor\dimexpr\dimexpr\DoubleDist/2\relax+\pgflinewidth\relax\relax}
\setlength{\ysh}{\dimexpr\YShiftFactor\dimexpr\dimexpr\DoubleDist/2\relax+\pgflinewidth\relax\relax}
\draw[fill=blue] ($(#1)-(\the\xsh ,\the\ysh)$) circle (1pt);
\draw[fill=blue] ($(#1)+(\the\xsh, \the\ysh)$) circle (1pt);
}
\makeatother

\begin{tikzpicture}
\node (rect) [name path=rect,draw,double,double distance=\DoubleDist, rounded corners,minimum size=30 pt]{};
\myline(0.2,0)(0.8,0.3)[brown,name path=line]
\path[name intersections={of= rect and line}];
\FindIndersections(intersection-1)
\end{tikzpicture}

\end{document}

输出：

对于像云一样的一些复杂形状，交点无法找到真正的中间，所以我的方法也失败了：

代码：

\begin{tikzpicture}
\node (rect) [name path=rect,draw,draw, cloud,,double,double distance=\DoubleDist,minimum size=1.3 cm]{};
\myline(0.2,0)(-0.7,-0.4)[brown,name path=line]
\path[name intersections={of= rect and line}];
\draw[fill=red] (intersection-1) circle (1pt);
\FindIndersections(intersection-1)
\end{tikzpicture}

（使用 tikzlibrary 形状）。

结果：

Answer