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填充曲线之间的区域

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填充曲线之间的区域

我需要重现以下情节： CAP 曲线

我尝试使用以下代码pgfplots：

\documentclass[8pt]{beamer}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}
\begin{document}
  \begin{frame}
  \begin{tikzpicture}
  \begin{axis}[domain=0:1,
   width=10cm,
  minor tick num=3,
   height=8cm,
  ymin=0,
  ymax=1,
  xmin=0,
  xmax=1,
  xticklabel=\empty,
  yticklabel=\empty,
  samples=50,
  smooth,
  xlabel=$r_{k}$,
  ylabel=$s_{k}$,
  extra x ticks={0,1},
  extra y ticks={1},
  extra x tick style={grid=major,thick},
  extra y tick style={grid=major,thick},
  extra x tick labels={$0$,$1$},
  extra y tick labels={$1$},
  legend pos=north east]


\addplot[fill=green,draw=none,domain=0:1,pattern=north east lines,pattern      color=yellow,stack plots=y]{x^0.25-x} \closedcycle;
\addplot[fill=green,draw=none,domain=0:1,stack plots=y]{1-x}\closedcycle;

\addplot[id=naive,color=black,domain=0:1,samples=50] {x};
\addplot[id=mod,color=black,domain=0:1,samples=50]{x^0.25};
\addplot[id=perf,color=black,domain=0:1,samples=50]{1};


\node (a) at (axis cs:0.4,0.6)  {$a_{R}$};
\node (b) at (axis cs:0.1,0.8)  {$a_{P}$};
\end{axis}
\end{tikzpicture}
\end{frame}
\end{document}

我的形状不正确。填充区域颠倒，不适用于指定区域。我回答过许多类似的问题，尝试过不同的方法，但到目前为止，没有一种方法对我有用。

答案1

问题不包含生成图像中显示的图形所需的函数或坐标，因此我使用了一些虚拟坐标，但想法是一样的。还定义了两个可自定义的填充模式：

\documentclass[8pt]{beamer}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}

% New customizable pattern
\tikzset{
  hatch distance/.store in=\hatchdistance,
  hatch distance=8pt,
  hatch thickness/.store in=\hatchthickness,
  hatch thickness=5pt,
  hatch color/.store in=\hatchcolor,
  hatch color=gray!20
}

\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{thick vlines}
  {\pgfpointorigin}{\pgfqpoint{\hatchthickness}{100pt}}{\pgfqpoint{\hatchdistance}{100pt}}%
  {
  \pgfsetlinewidth{\hatchthickness}
  \pgfpathmoveto{\pgfqpoint{0.5pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{0.5pt}{100pt}}
  \pgfusepath{stroke}
  }
\pgfdeclarepatterninherentlycolored[\hatchcolor]{crosshatch dots color}
{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
{\pgfpoint{8pt}{8pt}}
{
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
  \pgfusepath{fill}
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathcircle{\pgfpoint{2pt}{1.75pt}}{20pt}
  \pgfpathcircle{\pgfpoint{6pt}{5.75pt}}{20pt}
  \pgfusepath{fill}
  \pgfsetfillcolor{pgf@darklightsteelblue!70}
  \pgfpathcircle{\pgfpoint{2pt}{2.25pt}}{0.4pt}
  \pgfpathcircle{\pgfpoint{6pt}{6.25pt}}{0.4pt}
  \pgfusepath{fill}
}

\begin{document}

\begin{frame}
  \begin{tikzpicture}
  \begin{axis}[domain=0:1,
   width=10cm,
  minor tick num=3,
   height=8cm,
  ymin=0,
  ymax=1.2,
  xmin=0,
  xmax=1,
  xticklabel=\empty,
  yticklabel=\empty,
  samples=50,
  smooth,
  xlabel=$r_{k}$,
  ylabel=$s_{k}$,
  extra x ticks={0,1},
  extra y ticks={1},
  extra x tick style={grid=major,thick},
  extra y tick style={grid=major,thick},
  extra x tick labels={$0$,$1$},
  extra y tick labels={$1$},
  legend pos=north east]

\draw[pattern=crosshatch dots color]
  (axis cs:0,0) -- (axis cs:0.12,1) -- (axis cs:1,1) -- (axis cs:0,0);
\addplot+[
  id=mod,
  color=black,
  domain=0:1,
  samples=50,
  pattern=thick vlines,
  hatch thickness=3pt
] coordinates {(0,0) (0.2,0.45) (0.5,0.8) (0.75,0.92) (1,1)};
\addplot[id=naive,color=black,domain=0:1,samples=50] {x} ;

\node (a) at (axis cs:0.2,0.8)  {$a_{P}$};
\node[draw,fill=gray!30] (b) at (axis cs:0.45,0.6)  {$a_{R}$};

\begin{scope}[
  every pin edge/.style={<-,>=latex},
  pin distance=1.5cm
]
\node[pin=-30:{Rating model},] at (axis cs:0.5,0.8) {};
\node[pin=-30:{Random model},] at (axis cs:0.3,0.3) {};
\node[pin=15:{Perfect model},] at (axis cs:0.4,1.01) {};
\end{scope}
\end{axis}
\end{tikzpicture}
\end{frame}

\end{document}

在此处输入图片描述

并使用x^0.45生成曲线路径：

\documentclass[8pt]{beamer}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

% New customizable pattern
\tikzset{
  hatch distance/.store in=\hatchdistance,
  hatch distance=8pt,
  hatch thickness/.store in=\hatchthickness,
  hatch thickness=5pt,
  hatch color/.store in=\hatchcolor,
  hatch color=gray!20
}

\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{thick vlines}
  {\pgfpointorigin}{\pgfqpoint{\hatchthickness}{100pt}}{\pgfqpoint{\hatchdistance}{100pt}}%
  {
  \pgfsetlinewidth{\hatchthickness}
  \pgfpathmoveto{\pgfqpoint{0.5pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{0.5pt}{100pt}}
  \pgfusepath{stroke}
  }
\pgfdeclarepatterninherentlycolored[\hatchcolor]{crosshatch dots color}
{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
{\pgfpoint{8pt}{8pt}}
{
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
  \pgfusepath{fill}
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathcircle{\pgfpoint{2pt}{1.75pt}}{20pt}
  \pgfpathcircle{\pgfpoint{6pt}{5.75pt}}{20pt}
  \pgfusepath{fill}
  \pgfsetfillcolor{pgf@darklightsteelblue!70}
  \pgfpathcircle{\pgfpoint{2pt}{2.25pt}}{0.4pt}
  \pgfpathcircle{\pgfpoint{6pt}{6.25pt}}{0.4pt}
  \pgfusepath{fill}
}

\begin{document}

\begin{frame}
  \begin{tikzpicture}
  \begin{axis}[domain=0:1,
   width=10cm,
  minor tick num=3,
   height=8cm,
  ymin=0,
  ymax=1.2,
  xmin=0,
  xmax=1,
  xticklabel=\empty,
  yticklabel=\empty,
  samples=50,
  smooth,
  xlabel=$r_{k}$,
  ylabel=$s_{k}$,
  extra x ticks={0,1},
  extra y ticks={1},
  extra x tick style={grid=major,thick},
  extra y tick style={grid=major,thick},
  extra x tick labels={$0$,$1$},
  extra y tick labels={$1$},
  legend pos=north east]

\draw[pattern=crosshatch dots color]
  (axis cs:0,0) -- (axis cs:0.05,1) -- (axis cs:1,1) -- (axis cs:0,0);
\addplot[
  id=mod,
  color=black,
  domain=0:1,
  samples=100,
  pattern=thick vlines,
  hatch thickness=3pt
] {(x^(0.45))};
\addplot[id=naive,color=black,domain=0:1,samples=50] {x} ;

\node (a) at (axis cs:0.2,0.8)  {$a_{P}$};
\node[draw,fill=gray!30] (b) at (axis cs:0.45,0.6)  {$a_{R}$};

\begin{scope}[
  every pin edge/.style={<-,>=latex},
  pin distance=1.5cm
]
\node[pin=-30:{Rating model},] at (axis cs:0.5,0.8) {};
\node[pin=-30:{Random model},] at (axis cs:0.3,0.3) {};
\node[pin=15:{Perfect model},] at (axis cs:0.4,1.01) {};
\end{scope}
\end{axis}
\end{tikzpicture}
\end{frame}

\end{document}

在此处输入图片描述

一般来说，可以使用以下代码来填充两个函数 f 和 g 的图形之间的区域：

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
  domain=-2:9,
  samples=60,
  stack plots=y
]
% draw graph for the first function f
\addplot+[mark=none] {(x-3)^2};
% draw graph of max(g-f, 0) and stack
\addplot+[mark=none,fill=green!40,draw=red] {max(x+2-((x-3)^2),0)} \closedcycle;
% draw graph of min(g-f, 0) and stack
\addplot+[mark=none,fill=none,draw=red] {min(x+2-((x-3)^2),0)};
\end{axis}
\end{tikzpicture}

\end{document}

在此处输入图片描述

答案2

只是为了和 PSTricks 一起玩。

\documentclass[pstricks]{standalone}
\usepackage{pst-plot,pst-eucl}
\psset{xunit=7,yunit=5,runit=\psxunit,linejoin=1,PointName=none,fillstyle=solid,fillcolor=lightgray}
\begin{document}
\begin{pspicture}(-.3,-.3)(1.3,1.3)
    \psline[fillstyle=none]{<->}(0,1.2)(0,0)(1.2,0)
    \psxTick(1){1}\psyTick(1){1}
    \rput[tr](1.2,-20pt){\scriptsize proportion of all debtors}
    \rput[br]{90}(-20pt,1.2){\scriptsize proportion of defaulted debtors}
    \pstGeonode[PointSymbol={none,default}](.1,1){C}(0,0){A}(1,1){B}
    \pspolygon(A)(B)(C) 
    \pstGeonode(.1,.4){D}(.3,.7){E}(.5,.8){F}(.7,.9){G}
    \pspolygon[fillstyle=vlines,hatchangle=0,hatchwidth=2pt](A)(D)(E)(F)(G)(B)
    \rput(.2,.8){$a_P$}
    \psTextFrame(.375,.55)(.475,.65){$a_R$}
    \rput[bl](.5,1.1){\rnode[l]{permodelA}{perfect model}}
    \rput[tl](.4,.2){\rnode[l]{ranmodelA}{random model}}
    \rput[tl](.8,.6){\rnode[l]{ratmodelA}{rating model}}
    \pnodes(.3,1){permodelB}([nodesep=.3]{B}A){ranmodelB}
    \psset{arrows=->,nodesep=3pt}
    \ncline{permodelA}{permodelB}
    \ncline{ranmodelA}{ranmodelB}
    \ncline{ratmodelA}{F}
\end{pspicture}
\end{document}

在此处输入图片描述

在此处输入图片描述

答案3

只是为了完成。下一个代码（借用自 Gonzalo 的答案）展示了如何使用fillbetween pgfplots' 库（需要 v1.10）来填充曲线之间的区域。不需要绘制closed路径，只需绘制name它们和pgfplots计算交叉点并填充其间的区域。

\documentclass[8pt]{beamer}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=newest}

% New customizable pattern
\tikzset{
  hatch distance/.store in=\hatchdistance,
  hatch distance=8pt,
  hatch thickness/.store in=\hatchthickness,
  hatch thickness=5pt,
  hatch color/.store in=\hatchcolor,
  hatch color=gray!20
}

\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{thick vlines}
  {\pgfpointorigin}{\pgfqpoint{\hatchthickness}{100pt}}{\pgfqpoint{\hatchdistance}{100pt}}%
  {
  \pgfsetlinewidth{\hatchthickness}
  \pgfpathmoveto{\pgfqpoint{0.5pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{0.5pt}{100pt}}
  \pgfusepath{stroke}
  }
\pgfdeclarepatterninherentlycolored[\hatchcolor]{crosshatch dots color}
{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
{\pgfpoint{8pt}{8pt}}
{
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
  \pgfusepath{fill}
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathcircle{\pgfpoint{2pt}{1.75pt}}{20pt}
  \pgfpathcircle{\pgfpoint{6pt}{5.75pt}}{20pt}
  \pgfusepath{fill}
  \pgfsetfillcolor{pgf@darklightsteelblue!70}
  \pgfpathcircle{\pgfpoint{2pt}{2.25pt}}{0.4pt}
  \pgfpathcircle{\pgfpoint{6pt}{6.25pt}}{0.4pt}
  \pgfusepath{fill}
}

\begin{document}

\begin{frame}
  \begin{tikzpicture}
  \begin{axis}[domain=0:1,
   width=10cm,
   minor tick num=3,
   height=8cm,
   ymin=0,
   ymax=1.2,
   xmin=0,
   xmax=1,
   xticklabel=\empty,
   yticklabel=\empty,
   samples=50,
%  smooth,
   xlabel=$r_{k}$,
   ylabel=$s_{k}$,
   extra x ticks={0,1},
   extra y ticks={1},
   extra x tick style={grid=major,thick},
   extra y tick style={grid=major,thick},
   extra x tick labels={$0$,$1$},
   extra y tick labels={$1$},
   legend pos=north east]

% Add a name to any path, even not closed
\addplot [name path=perfect]  coordinates {(0,0) (0.05,1) (1,1)};
\addplot [name path=naive] {x};

% and use both names to set filled area
% pattern option is added to `addplot` options not to `fill between`.
\addplot [pattern=crosshatch dots color] fill between[of=perfect and naive];

\addplot [name path=random,smooth] {(x^(0.45))};
\addplot [pattern=thick vlines, hatch thickness=3pt] fill between[of=random and naive];

\node (a) at (axis cs:0.2,0.8)  {$a_{P}$};
\node[draw,fill=gray!30] (b) at (axis cs:0.45,0.6)  {$a_{R}$};

\begin{scope}[
  every pin edge/.style={<-,>=latex},
  pin distance=1.5cm
]
\node[pin=-30:{Rating model},] at (axis cs:0.5,0.75) {};
\node[pin=-30:{Random model},] at (axis cs:0.3,0.3) {};
\node[pin=15:{Perfect model},] at (axis cs:0.4,1.01) {};
\end{scope}
\end{axis}
\end{tikzpicture}
\end{frame}
\end{document}

在此处输入图片描述

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