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计算交叉点

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计算交叉点

在此处输入图片描述

我想绘制这个图形，这是我迄今为止编写的代码，但形状看起来很不一样......我无法解决如何用点填充区域......请帮帮我。

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\begin{document}
\begin{figure}
\begin{tikzpicture}[scale=1]

% Axis

\draw (0,7) -- (0,0) node[below]{0} -- (7,0) node[below] {1};
\draw (0,7) -- (7,7)  -- (7,0);


% curve

\draw (0,0) to (7,7);
\draw [very thick] (0,0) to [out=90, in=180] (2,2);
\draw [very thick] (2,2) to [out=0, in=270] (4,4);
\draw [very thick] (4,4) to [out=90, in=180] (7,6);

\draw (0.3,0.3) to [out=0, in=-270] (0.5,0) ;
\node[right] at (0.6,0.25) {$45^{o}$};

\draw [dashed] (2,0) -- (2,2);
\draw [dashed] (4,0) -- (4,4);
\draw [dashed] (5.9,0) -- (5.9,5.9);


\node[below] at (2,0) {\large $\lambda_1$};
\node[below] at (4,0) {\large $\lambda_2$};
\node[below] at (5.9,0) {\large $\lambda_3$};


\draw[<-,>=latex] (2,6) node[above] {\LARGE \begin{tabular}{c}$D(e(\lambda)$)\end{tabular}} to[out=-90,in=-100] (4.05,4.4);
\node[above] at (1.9,6.5) {-};

\end{tikzpicture}

\end{figure}

\end{document}

答案1

正如 Henri 所说，您可以定义自己的图案。下面的代码显示了一个这样的定义。您可以使用 键更改点的大小dots size，例如\fill [pattern=mydots, dots size=3pt]，并使用 更改间距dots spread，例如\fill [pattern=mydots, dots spread=15pt]。

与 Jasper 一样，我使用\bar{e}而不是手动绘制该条，而是使用arc来绘制角度标记。我还使用循环来绘制带有 lambda 的三条虚线。

在此处输入图片描述

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{patterns}

\tikzset{
    dots size/.store in=\dotssize,
    dots size=1pt,
    dots spread/.store in=\dotsspread,
    dots spread=10pt
    }

\makeatletter
\pgfdeclarepatternformonly[\dotssize,\dotsspread]{mydots}
{\pgfpointorigin}
{\pgfpoint{\dotsspread}{\dotsspread}}
{\pgfpoint{\dotsspread}{\dotsspread}}
{
    \pgfsetcolor{\tikz@pattern@color}
    \pgfpathcircle{\pgfpoint{\dotsspread/2}{\dotsspread/2}}{\dotssize}
    \pgfusepath{fill}
}
\makeatother

\begin{document}
\begin{tikzpicture}

% Axis
\draw (7,7) -| (0,0) node[below]{0} -| node[below] {1} cycle;

% curve    
\draw (0,0) to (7,7);

\fill [pattern=mydots, opacity=0.7] (0,0) to [out=80,in=200] (2,2)
                           to [out=20, in=250] (4,4) 
                           to [out=70, in=200] (7,6.4)
                           |- cycle;
\draw [very thick] (0,0) to [out=80,in=200] (2,2)
                         to [out=20, in=250] (4,4) 
                         to [out=70, in=200] coordinate[pos=0.2] (m) (7,6.4);


\draw (0.5,0) arc[start angle=0,end angle=45,radius=0.5] node[midway,right] {$45^{\circ}$} ;

\foreach \i in {1,2,3}
   \draw [dashed,thick] (2*\i,2*\i) -- (2*\i, 0) node[below,font=\large] {$\lambda_{\i}$};

\draw[<-,>=latex] (2,6) node[above] {\LARGE $D(\bar{e}(\lambda)$)} to[out=270,in=200] (m);

\end{tikzpicture}
\end{document}

计算交叉点

不确定这种情况是否有意义，但可以使用库来计算 D 曲线和直线之间的交点intersections。不过这需要几秒钟。

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{patterns, intersections}

\tikzset{
    dots size/.store in=\dotssize,
    dots size=1pt,
    dots spread/.store in=\dotsspread,
    dots spread=10pt
    }

\makeatletter
\pgfdeclarepatternformonly[\dotssize,\dotsspread]{mydots}
{\pgfpointorigin}
{\pgfpoint{\dotsspread}{\dotsspread}}
{\pgfpoint{\dotsspread}{\dotsspread}}
{
    \pgfsetcolor{\tikz@pattern@color}
    \pgfpathcircle{\pgfpoint{\dotsspread/2}{\dotsspread/2}}{\dotssize}
    \pgfusepath{fill}
}
\makeatother

\begin{document}
\begin{tikzpicture}

% Axis
\draw (7,7) -| (0,0) node[below]{0} -| node[below] {1} cycle;

% curve
% add name path=x
\draw [name path=x] (0,0) to (7,7);

\fill [pattern=mydots, opacity=0.7] (0,0) to [out=80,in=200] (2,2)
                           to [out=20, in=250] (4,4) 
                           to [out=70, in=200] (7,6.4)
                           |- cycle;

% add name path=D
\draw [very thick, name path=D] (0,0) to [out=80,in=200] (2,2)
                         to [out=20, in=250] (4,4) 
                         to [out=70, in=200] coordinate[pos=0.2] (m) (7,6.4);


\draw (0.5,0) arc[start angle=0,end angle=45,radius=0.5] node[midway,right] {$45^{\circ}$} ;

% find intersections
\path [name intersections={of=x and D, name=lambda}];
%first intersection is at x=0, so use intersections 2-4
\foreach [count=\i] \j in {2,3,4}
   \draw [dashed,thick] (lambda-\j) -- (lambda-\j |- 0,0) node[below,font=\large] {$\lambda_{\i}$};

\draw[<-,>=latex] (2,6) node[above] {\LARGE $D(\bar{e}(\lambda)$)} to[out=270,in=200] (m);

\end{tikzpicture}
\end{document}

答案2

与亨利的答案非常相似，但有几个小的改进：

  • 点状图案的阴影较浅
  • 45°标记使用arc
  • 使用标签\bar{}
  • 轴和标签后面的曲线和图案

-

\documentclass[tikz]{standalone}
\usetikzlibrary{patterns}

\begin{document}
\begin{tikzpicture}

% curve

\fill[pattern=dots,pattern color=black!25] (0,0) to[out=80, in=200] (2,2) 
       to[out=20, in=260] (4,4)
       to[out=80, in=180, distance=45] (7,6)
       -- (7,0) -- cycle;

\draw[very thick] (0,0) to[out=80, in=200] (2,2) 
       to[out=20, in=260] (4,4)
       to[out=80, in=180, distance=45] (7,6);

\draw[<-,>=latex] (2,6) node[above] {\LARGE $D(\bar{e}(\lambda))$} to[out=-90,in=180] (4.05,4.4);

% axis

\draw (0,7) -- (0,0) node[below]{0} -- (7,0) node[below] {1} 
            -- (7,7)  -- cycle;

\draw (0,0) to (7,7);
\draw (0:.5) arc (0:45:.5) node[above right,midway] {$45^{\circ}$};

\draw[dashed] (2,0) node[below] {\large $\lambda_1$} -- (2,2);
\draw[dashed] (4,0) node[below] {\large $\lambda_2$} -- (4,4);
\draw[dashed] (5.9,0) node[below] {\large $\lambda_3$} -- (5.9,5.9);

\end{tikzpicture}
\end{document}

在此处输入图片描述

答案3

您快完成了。我本来可以使用一些不同的角度。为了获得点画效果，我使用了图书馆dots中的图案patterns。

不幸的是 Ti 中的图案钾Z 没有任何参数，因此您必须忍受非常密集的填充。否则，您必须定义自己的点图案。

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}
\begin{figure}
\begin{tikzpicture}[scale=1]

% Axis

\draw (0,7) -- (0,0) node[below]{0} -- (7,0) node[below] {1};
\draw (0,7) -- (7,7)  -- (7,0);


% curve

\draw (0,0) to (7,7);
\draw [very thick] (0,0) to [out=90, in=200] (2,2)
to [out=20, in=250] (4,4)
to [out=70, in=180] (7,6);

\fill [pattern=dots] (0,0) to [out=90, in=200] (2,2)
to [out=20, in=250] (4,4)
to [out=70, in=180] (7,6)
-- (7,0) -- cycle;


\draw (0.3,0.3) to [out=0, in=-270] (0.5,0) ;
\node[right] at (0.6,0.25) {$45^{o}$};

\draw [dashed] (2,0) -- (2,2);
\draw [dashed] (4,0) -- (4,4);
\draw [dashed] (5.9,0) -- (5.9,5.9);


\node[below] at (2,0) {\large $\lambda_1$};
\node[below] at (4,0) {\large $\lambda_2$};
\node[below] at (5.9,0) {\large $\lambda_3$};


\draw[<-,>=latex] (2,6) node[above] {\LARGE \begin{tabular}{c}$D(e(\lambda)$)\end{tabular}} to[out=-90,in=-100] (4.05,4.4);
\node[above] at (1.9,6.5) {-};

\end{tikzpicture}

\end{figure}

\end{document}

在此处输入图片描述

答案4

只是为了和 MetaFun 一起玩（双关语）。

\startMPpage
  input hatching ;

  numeric u, t, l[] ;
  u := 6cm ;
  l1 := .22u ;
  l2 := .55u ;
  l3 := .9u ;
  t := .8 ;

  draw unitsquare scaled (1u) ;
  for i = 0, 1:
      label.bot("$" & decimal i & "$", (i*u,0)) ;
  endfor ;
  draw (0,0) -- (1u,1u) ;

  path p ; p := (0,0){up}
      .. tension t .. (l1,l1)
      .. tension t .. (l2,l2)
      .. tension t .. (l3,l3)
      .. tension t .. (1u,.92u);
  draw image (
      interim linecap := butt ;
      draw p withpen pencircle scaled (2pt) ;
  ) ;

  hatchoptions (dashed withdots);
  hatchfill (p -- (1u,0) -- cycle) withcolor (
      -45, % hatching angle
      5pt, % distance between lines
      -1pt % thickness of lines
  );

  for i = 1 upto 3:
      draw (l[i],0) -- (l[i],l[i]) dashed evenly ;
      label.bot("$\lambda_{" & decimal i & "}$", (l[i],0)) ;
  endfor;

  draw anglebetween(origin -- (1u,0),origin -- (l1,l1),"$45^\circ$") ;

  label.top("$D(\bar{e}(\lambda))$", (.3u,.85u));
  drawarrow (point 2.1 of p){left} .. {up}(.3u,.85u) ;
\stopMPpage

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