在 tikz 绘制的一个图中，如何让所有的两两相交的曲线在交点处不重合

虽然已经有最佳答案了，我也来补充一个治标的方法，需要保证连续的线可以使用双线 double 绘制，选项 [draw = white, double=black,double distance =0.4pt]（当然如果图线颜色和底色并非黑白的时候，以及线宽非默认时要自己调整），例：

\begin{tikzpicture}
        \draw(0,0)--(1,1);
        \draw[draw=white,double=black,double distance =0.4pt](0,1)--(1,0);
    \end{tikzpicture}

参考 knots 包

虽然已经有最佳答案了，我也来补充一个治标的方法，需要保证连续的线可以使用双线 double 绘制，选项 [draw = white, double=black,double distance =0.4pt]

也许比较治本的方法。

\documentclass[tikz,border=5pt]{standalone}
% https://tex.stackexchange.com/a/762955/322482
% https://github.com/loopspace/spath3/issues/37
\ExplSyntaxOn
\msg_redirect_name:nnn { kernel } { variant-same-as-base } { info }
\ExplSyntaxOff

\usetikzlibrary{knots}

\ExplSyntaxOn
\msg_redirect_name:nnn { kernel } { variant-same-as-base } { error }
\ExplSyntaxOff

\begin{document}
\begin{tikzpicture}
    \begin{knot}[clip width=5, flip crossing=1]
    \strand[red, ultra thick] (0,0) .. controls +(1,0) and +(-1,0) .. (2,1) .. controls +(1,0) and +(-1,0) .. (4,0);
    \strand[blue, ultra thick] (0,1) .. controls +(1,0) and +(-1,0) .. (2,0) .. controls +(1,0) and +(-1,0) .. (4,1);
    \end{knot}
\end{tikzpicture}
\end{document}

\documentclass[tikz,border=5pt]{standalone}
% https://tex.stackexchange.com/a/762955/322482
% https://github.com/loopspace/spath3/issues/37
\ExplSyntaxOn
\msg_redirect_name:nnn { kernel } { variant-same-as-base } { info }
\ExplSyntaxOff

\usetikzlibrary{intersections,spath3}

\ExplSyntaxOn
\msg_redirect_name:nnn { kernel } { variant-same-as-base } { error }
\ExplSyntaxOff

\begin{document}
\begin{tikzpicture}
\path[spath/save=pathA] (0,0) .. controls +(1,0) and +(-1,0) .. (2,1) .. controls +(1,0) and +(-1,0) .. (4,0);
\path[spath/save=pathB] (0,1) .. controls +(1,0) and +(-1,0) .. (2,0) .. controls +(1,0) and +(-1,0) .. (4,1);
\tikzset{
  spath/split at intersections={pathA}{pathB},
  spath/insert gaps after components={pathA}{5pt}{1},
  spath/insert gaps after components={pathB}{5pt}{2},
}

\draw[red, ultra thick, spath/use=pathA];
\draw[blue, ultra thick, spath/use=pathB];
\end{tikzpicture}
\end{document}

那个最佳答案里的 knot 宏包实际上也有问题，不能满足我的要求

...? 或许补充更多原始需求的信息...?

类似花老师的这个需求：

• https://tex.stackexchange.com/q/759978/322482
• https://tex.stackexchange.com/q/760012/322482
• https://code.mathforge.org/KnightsTour/