绘制并阴影化 $\mathbb{R}^2$ 中由函数参数化的区域

Question

我正在尝试绘制平面的这个区域

德= {（x,y) ∈ ℝ ² :X∈[a,b], −x ² +X≤ y ≤ −X³ +2X； 0 ≤X≤1}

这就是我目前的情况

\documentclass[preview, convert={size=598x414,outext=.png}]{standalone}
\usepackage{pgfplots,tikz}
\pgfplotsset{compat=1.12}
\begin{document}
            \begin{tikzpicture}
            \begin{axis} [xlabel = x, ylabel = y, axis lines=center]
                \addplot [domain=0:1, smooth] {2*x-x^3};
                \addplot [domain=0:1, smooth] {x-x^2};
        \draw [thick] (1,0) -- (1,1);
            \end{axis}
        \end{tikzpicture}
\end{document}

我需要一种方法来为区域 D 着色，同时我想将标签放在xx 轴下方。

Answer 1

您只需要对您的代码进行一些细微的调整。

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.18}
\begin{document}
        \begin{tikzpicture}
            \begin{axis}[ 
                xmax=1.1,
                axis lines=center,
                xlabel=$x$,
                xlabel style={at={(axis description cs:1.01,0.0)},anchor=north},
                ymax=1.1,
                ylabel = $y$
                ]
                \addplot [name path=A,domain=0:1, smooth] {2*x-x^3};
                \addplot [name path=B,domain=0:1, smooth] {x-x^2};
                \addplot [gray!20] fill between[of=A and B];
                \addplot [black] coordinates {(1,0) (1,1)};
            \end{axis}
        \end{tikzpicture}
\end{document}

Answer 2

这是@kabenyuk 变体的改进版本，其中我们不需要额外的线来关闭填充区域。

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usepgfplotslibrary{fillbetween}

\begin{document}
        \begin{tikzpicture}
            \begin{axis}[ 
                xmax=1.1,
                axis lines=center,
                xlabel=$x$,
                xlabel style={at={(axis description cs:1.01,0.0)},anchor=north},
                ymax=1.1,
                ylabel = $y$
                ]
                \addplot [name path=A,domain=0:1, smooth] {2*x-x^3};
                \addplot [name path=B,domain=0:1, smooth] {x-x^2};
                \addplot [fill=gray!20,draw=black] fill between[of=A and B];% <-- added draw=black
            \end{axis}
        \end{tikzpicture}
\end{document}

Answer 3

使用 MetaPost 来实现这一目的的方法，包含在 LuaLaTeX 程序中，对于可能感兴趣的人，可以使用buildcyclePlain MetaPost 的宏。

\documentclass[border=2mm]{standalone}
\usepackage{luamplib}
    \mplibsetformat{metafun}
    \mplibnumbersystem{decimal}
    \mplibtextextlabel{enable}

\begin{document}
\begin{mplibcode}
    vardef function(expr xmin, xmax, xstep)(text f_x) =
        save x; x := xmin;
        (x, f_x)
        forever: hide(x := x + xstep) exitif x > xmax;
            .. (x, f_x)
        endfor
        if x - xstep < xmax: hide(x := xmax) .. (x, f_x) fi
    enddef;
        
    vardef f(expr x) = x - x**2 enddef;
    vardef g(expr x) = 2x - x**3 enddef;
    
    u = v = 8cm; path area; len := 2bp;
    area = buildcycle(
        function(0, 1, .05)(f(x)), 
        (1, f(1)) -- (1, g(1)), 
        function(0, 1, .05)(g(x))
    ) xyscaled (u,v);
    
    beginfig(1);
        fill area withcolor .8white; draw area; 
        drawarrow origin -- (1.1u, 0); drawarrow origin -- (0,1.1v);
        for i = 0.2 step .2 until 1: 
            draw (i*u, -len) -- (i*u, len); 
            label.bot("$" & decimal i & "$", (i*u, 0));
            draw (-len , i*v) -- (len, i*v); 
            label.lft("$" & decimal i & "$", (0, i*v));
        endfor;
    endfig;
\end{mplibcode}
\end{document}