我想绘制例如方程y^2 x + x^3-3y^2-2x^2+x=0。但同时我需要将平面的某些部分变灰（见阴影区域）。有办法吗？ 
答案1
我有一个tikz/pgfplot解决方案：
\documentclass[border=15pt]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}\pgfplotsset{compat=1.13}
\usetikzlibrary{arrows,positioning,calc,patterns}
\begin{document}
\begin{tikzpicture}[
thick]
\begin{axis}[
xmin=-3, xmax=6,
ymin=-5, ymax=5,
axis x line = center,
axis y line = center,
xtick = \empty,
ytick = \empty,
xlabel = {$x$},
ylabel = {$y$},
legend style = {nodes=right},
legend pos = north east,
clip mode = individual,
]
\addplot[red, samples=100, domain=0:2.6] {(x-1)*sqrt(x/(3-x))};
\addplot[red, samples=100, domain=0:2.6] {-(x-1)*sqrt(x/(3-x))};
\draw [dashed] (3,-5) -- (3,5);
\path [pattern=north west lines, pattern color = gray]
(3.1, -5+0.1) rectangle (5.5, 5-0.1);
\path [pattern=north west lines, pattern color = gray]
(-2.9, -5+0.1) rectangle (-0.1, 5-0.1);
\path (0,0) node [below left] {$O$};
\path (1,0) node [below] {$A$};
\filldraw [fill=white] (3,0) circle(1pt) node [below right]{3};
\path (2.6, 5-.5) node[fill=white, above] {$tg_{Y_\infty}$};
\end{axis}
\end{tikzpicture}
\end{document}
您可以根据需要调整颜色、标签等。请注意，如果您使用的是pgfplots1.11 之前的版本（我认为），则必须添加环境axis cs:中的所有绘图和路径坐标axis。
如果要使用方程的隐式形式，可以使用选项contour gnuplot（参见gnuplot 端和pgfplots 手册第 4.6 节)：
\documentclass[border=15pt]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}\pgfplotsset{compat=1.13}
\usetikzlibrary{arrows,positioning,calc,patterns}
\begin{document}
\begin{tikzpicture}[
thick]
\begin{axis}[
xmin=-3, xmax=6,
ymin=-5, ymax=5,
axis x line = center,
axis y line = center,
axis line style = {thick, gray},
xtick = \empty,
ytick = \empty,
xlabel = {$x$},
every axis x label/.append style = {below, gray},
ylabel = {$y$},
every axis y label/.append style = {above left, gray},
legend style = {nodes=right},
legend pos = north east,
clip mode = individual,
view = {0}{90},
]
\addplot3[contour gnuplot={
levels=0, labels=false,
},
samples=100,
]
{y*y*x + x*x*x -3*y*y-2*x*x+x};
\draw [dashed] (3,-5) -- (3,5);
\path [pattern=north west lines, pattern color = gray]
(3.1, -5+0.1) rectangle (5.5, 5-0.1);
\path [pattern=north west lines, pattern color = gray]
(-2.9, -5+0.1) rectangle (-0.1, 5-0.1);
\path (0,0) node [below left] {$O$};
\path (1,0) node [below] {$A$};
\filldraw [fill=white] (3,0) circle(1pt) node [below right]{3};
\path (2.6, 5-.5) node[fill=white, above] {$tg_{Y_\infty}$};
\end{axis}
\end{tikzpicture}
\end{document}
您必须使用-shell-escape（或 --enable-write18）标志来运行它pdflatex，并且要有耐心......（它真的很慢）：
答案2
由于 Tikz/pgf 目前还没有解决方案，我建议使用 来轻松解决pstricks。如果您使用开关（适用于 MiKTeX）或（TeX Live、MacTeX）pdflatex启动它，则可以编译它。或者，您可以使用 进行编译。--enable-write18-shell-escapeXeLaTeX
\documentclass[x11names, border=3pt]{standalone}
\usepackage{fourier}
\usepackage{pst-plot}
\usepackage{auto-pst-pdf}
\begin{document}
\psset{algebraic, unit=1.5, arrowinset=0.12, arrowsize=4pt, linejoin=1, plotstyle=curve, plotpoints=200}
\begin{pspicture*}(-3, -4)(6, 4.5)
\psaxes[linecolor=LightSteelBlue3, ticks=none, labels=none, arrows=-> ](0,0)(-3, -4)(6, 4)[$x$,-135] [$y$,120]
\psset{linewidth=1.2pt, linecolor=IndianRed3, plotpoints=100}
\begin{psclip}{\psframe[linestyle=none](0,-3.9)(3,3.9)}
\psplot{0}{2.6}{(x-1)*sqrt(x/(3-x))}
\psplot{0}{2.6}{(1-x)*sqrt(x/(3-x))}
\end{psclip}
\psdot(1,0)\uput[d](1,0){$ 1 $}
\psset{linestyle=dashed, dash=4pt 4pt, linecolor=LightSteelBlue3}
\psdot[dotstyle=o](3,0)
\psline[linewidth=0.4pt](3, -4)(3, 4) % asymptote
\uput[u](3,4){$tg_{Y_\infty}$}
\psset{linestyle=none, fillstyle=vlines, hatchwidth=0.4pt, framesep=1pt}
\psframe(-3,-3.9)(-0.1,3.9)
\psframe(3.1,-3.9)(5.7,3.9)
\uput[dr](3,0){\psframebox*{$ 3 $}}
\uput[dl](0,0){\psframebox*{$O$}}
\end{pspicture*}
\end{document}
