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填充由多条路径定义的区域的最简单方法

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填充由多条路径定义的区域的最简单方法

我有许多路径，在本例中是四圆，它们相交以定义图形中间的复杂区域。如何填充下图中的 A - B - C - D 区域？我更喜欢一种不对路径的公式做任何假设的解决方案，即：它们可以是具有随机控制点的贝塞尔曲线，而不是圆的象限。

\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{calc,intersections,through}

\begin{document}
\begin{tikzpicture}
    \path[draw,clip] (0,0) rectangle (6,6);
    \node(circle 1)[draw, circle through={(6,0)}] at (0,0) {}; 
    \node(circle 2)[draw, circle through={(0,0)}] at (6,0) {};
    \node(circle 3)[draw, circle through={(6,0)}] at (6,6) {};
    \node(circle 4)[draw, circle through={(0,0)}] at (0,6) {};

    \coordinate[label=A](A) at (intersection 2 of circle 1 and circle 2);
    \coordinate[label=B](B) at (intersection 1 of circle 1 and circle 4);
    \coordinate[label=C](C) at (intersection 2 of circle 3 and circle 4);
    \coordinate[label=D](D) at (intersection 2 of circle 2 and circle 3);
\end{tikzpicture}
\end{document}

enter image description here

答案1

enter image description here

此解决方案使用环境中定义的Asymptote函数来绘制由四条连续相交路径界定的区域。但是，假设相交的顺序是一定的。如果路径是绝对随机的（例如，可能不相交），则需要进行更多检查。ABCDasydef

%
% xsect.tex :
%
\documentclass[10pt,a4paper]{article}
\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
\usepackage{lmodern}
\usepackage{subcaption}
\usepackage[inline]{asymptote}
\begin{asydef}
void ABCD(guide AB, guide BC, guide CD, guide DA
     ,pen linepen=deepblue+1.2bp
     ,pen areapen=red+1.4bp
     ,pen fillpen=palegreen){

  real tA[], tB[], tC[], tD[];
  pair A,B,C,D;

  tA=intersect(AB,DA); // tA[0] - AB time of intersection, t[1] - DA time of intersection
  tB=intersect(BC,AB); // tB[0] - BC time of intersection, t[1] - AB time of intersection
  tC=intersect(CD,BC); // tC[0] - CD time of intersection, t[1] - BC time of intersection
  tD=intersect(DA,CD); // tD[0] - DA time of intersection, t[1] - CD time of intersection

  A=point(AB,tA[0]);
  B=point(BC,tB[0]);
  C=point(CD,tC[0]);
  D=point(DA,tD[0]);

  guide area=buildcycle(AB,BC,CD,DA);

  draw(AB^^BC^^CD^^DA,linepen);
  filldraw(area,fillpen,areapen);

  label("$A$",A,2N);  
  label("$B$",B,2W);  
  label("$C$",C,2S);  
  label("$D$",D,2E);  

  dot(new pair[]{A,B,C,D},UnFill);
}
\end{asydef}
%
\begin{document}
%
\begin{figure}
\captionsetup[subfigure]{justification=centering}
\centering
\begin{subfigure}{0.49\textwidth}
\begin{asy}
size(200);
ABCD(
   arc(( 1,-1),2, 90,180)
  ,arc(( 1, 1),2,180,270)
  ,arc((-1, 1),2,-90,  0)
  ,arc((-1,-1),2,  0, 90)
);
\end{asy}
%
\caption{}
\label{fig:1a}
\end{subfigure}
%
\begin{subfigure}{0.49\textwidth}
\begin{asy}
size(200);
ABCD(
   (1,2)..(-1.2,0.1)..(-1.7,-1.8)
  ,(-2,1)..(-1,1)..(-0.5,0)..(0.5,-0.8)
  ,arc((-1, 1),2,-90,  0)
  ,(2,-1)..(2,0)..(0.5,1)..(0,1.7)
  ,olive+0.4bp
  ,orange+1.3bp
  ,lightyellow
);
\end{asy}
%
\caption{}
\label{fig:1b}
\end{subfigure}
\caption{}
\label{fig:1}
\end{figure}
%
\end{document}
%
% Process :
%
% pdflatex xsect.tex
% asy xsect-*.asy
% pdflatex xsect.tex

答案2

使用 PSTricks。在这种情况下，交叉不是必需的，因为简单的逻辑可以帮助您找到弧线开始和结束的角度。请参阅以下说明如何计算角度。

enter image description here

\documentclass[pstricks,border=12pt]{standalone}

\degrees[12]
\psset{dimen=monkey}

\begin{document}
\begin{pspicture}(-3,-3)(3,3)
    \psframe(-3,-3)(3,3)
    \pscustom*[linecolor=yellow]
    {
        \foreach \x/\y/\a in {-3/-3/1, 3/-3/4, 3/3/7, -3/3/10}
            {\psarc(\x,\y){6}{\a}{!\a\space 1 add}}
    }
    \foreach \x/\y/\a in {-3/-3/0, 3/-3/3, 3/3/6, -3/3/9}
        {\psarc(\x,\y){6}{\a}{!\a\space 3 add}}
\end{pspicture}
\end{document}

enter image description here

各种各样的

通过改为{!\a\space 3 add}，{!\a\space 2 add}我们得到了一个镜头光圈。

\documentclass[pstricks,border=12pt]{standalone}

\degrees[12]
\psset{dimen=monkey}

\begin{document}
\begin{pspicture}(-3,-3)(3,3)
    \psframe(-3,-3)(3,3)
    \pscustom*[linecolor=yellow]
    {
        \foreach \x/\y/\a in {-3/-3/1, 3/-3/4, 3/3/7, -3/3/10}
            {\psarc(\x,\y){6}{\a}{!\a\space 1 add}}
    }
    \foreach \x/\y/\a in {-3/-3/0, 3/-3/3, 3/3/6, -3/3/9}
        {\psarc(\x,\y){6}{\a}{!\a\space 2 add}}
\end{pspicture}
\end{document}

enter image description here

答案3

TikZ 的另一种方法，应用了 Marienplatz 建议的简单逻辑。谢谢

这里，圆 1 的原点是我的参考点，并绘制了第一个圆弧。接下来是重复 90 度差异的图案，因为这是绘制其余圆的方式。

enter image description here

代码

\documentclass{minimal}
\usepackage{tikz}
\usetikzlibrary{calc,intersections,through}

\begin{document}
\begin{tikzpicture}
\path[draw,clip] (0,0) rectangle (6,6);
\node(circle 1)[draw, very thick,circle through={(6,0)}] at (0,0) {}; 
\node(circle 2)[draw, very thick,circle through={(0,0)}] at (6,0) {};
\node(circle 3)[draw, very thick,circle through={(6,0)}] at (6,6) {};
\node(circle 4)[draw, very thick,circle through={(0,0)}] at (0,6) {};
\coordinate[label=A](A) at (intersection 2 of circle 1 and circle 2);
\coordinate[label=B](B) at (intersection 1 of circle 1 and circle 4);
\coordinate[label=C](C) at (intersection 2 of circle 3 and circle 4);
\coordinate[label=D](D) at (intersection 2 of circle 2 and circle 3);
\fill[red] (30:6) arc (30:60:6) arc (120:150:6) arc(210:240:6) arc(300:330:6);
%\draw [black,thick] (30:6) arc (30:60:6) arc (120:150:6) arc(210:240:6) arc(300:330:6);
\end{tikzpicture}
\end{document}

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