如果距离低于阈值，则绘制路径

Question

我想绘制一个交叉图，为此我有一个带坐标的数组。

现在我循环遍历它们并计算坐标之间的距离，如果它低于圆的半径，就应该画一条线。

我可以用某种\path let \p1 ... \n1 = veclen()东西来计算距离，但是我不能用这个距离进行比较，而只能在一条路径中使用它。

我该怎么办？

这是我现在的 tikzpicture：

\begin{tikzpicture}[scale=0.5]
\newcommand{\centers}{(0,1),(0,0),(5,3),(2,1),(0.5,1),(4,3),(0,5),(1.6,3.5),(6,0.5)}

\foreach [count=\i] \coord in \centers{\draw \coord circle(1) node{\i};} 
\foreach \coord in \centers{\fill \coord circle(0.15);}        


 \foreach [count=\i]\a in \centers{
    \foreach [count=\j]\b in \centers{
    \ifthenelse{\i < \j}{
   % calculating distance between \a and \b 
   % and drawing lines here
    }{};
  }
 }

\end{tikzpicture}

以下是我想要实现的目标的图画：

Answer 1

你可以像\ifnum这样使用\ifdim：

\documentclass[tikz,border=7mm]{standalone}
\usetikzlibrary{calc}

\begin{document}
  \newcommand{\centers}{(0,1),(0,0),(5,3),(2,1),(0.5,1),(4,3),(0,5),(1.6,3.5),(6,0.5)}
  \begin{tikzpicture}
    % link centers if circles intersect
    \foreach[count=\i] \a in \centers {
      \foreach[count=\j] \b in \centers {
        \ifnum \j < \i
          \draw[red] let \p1=\a, \p2=\b, \n1={veclen(\x1-\x2,\y1-\y2)} in
            {\ifdim \n1 < 2 cm \a -- \b \fi};
        \fi
      }
    }
    % draw circles
    \foreach [count=\i] \coord in \centers{\draw \coord circle(1);}
    \foreach \coord in \centers{\fill \coord circle(2pt);}
  \end{tikzpicture}
\end{document}

Answer 2

我通过一些额外的宏解决了这个问题veclen。

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

\makeatletter
\def\veclen#1=#2->#3;{%
  \edef\x{\noexpand\@veclen\noexpand#1#2#3}%
  \x
}
\def\@veclen#1(#2,#3)(#4,#5){%
  \pgfmathsetmacro#1{veclen(#2-#4,#3-#5)}%
}
\makeatother

\begin{document}
\begin{tikzpicture}[scale=0.5]
  \def\thresh{2.0}
  \def\centers{(0,1),(0,0),(5,3),(2,1),(0.5,1),(4,3),(0,5),(1.6,3.5),(6,0.5)}

  \foreach \coord [count=\i] in \centers {
    \node[draw,fill,circle,inner sep=1pt] (n-\i) at \coord {};
    \draw (n-\i) circle (1);
  }

  \foreach \a [count=\i] in \centers{
    \foreach \b [count=\j] in \centers{
      \ifnum\i<\j
        \veclen\dist=\a->\b;
        \ifdim\dist pt<\thresh pt
          \draw[red] (n-\i) -- (n-\j);
        \fi
      \fi
    }
  }
\end{tikzpicture}
\end{document}