使用 tikzpicture 环境按部分查找函数的良好视图

Question

我想绘制sqrt(-xy)如果xy<=0，以及-x^2+y如果的图表xy>0。

请考虑这个MWE：

\documentclass{article}
\usepackage[utf8]{inputenc}

\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\pgfplotsset{soldot/.style={color=black,only marks,mark=*}}
\pgfplotsset{holdot/.style={color=red,fill=white,very thick,only marks,mark=*}}

\begin{document}

\begin{center}                                                      
\begin{tikzpicture}[scale=2]
    \begin{axis}[
        legend pos=outer north east,
        axis lines = center,
        view={-35}{15},
        xticklabel style = {font=\tiny},
        yticklabel style = {font=\tiny},
        zticklabel style = {font=\tiny},
        xlabel = $x$,
        ylabel = $y$,
        zlabel = $z$,
        legend style={cells={align=left}}
    ]
    \addplot3[surf,mesh/ordering=y varies,shader=interp,domain=-3:0,domain y=0:3,samples=40, samples y=20] {sqrt(-x*y)};
    \addplot3[surf,mesh/ordering=y varies,shader=interp,domain=0:3,domain y=0:-3,samples=40, samples y=20] {sqrt(-x*y)};
    \addplot3[surf,mesh/ordering=y varies,shader=interp,domain=0:3,domain y=0:3,samples=40, samples y=20] {-x*x+y};
    \addplot3[surf,mesh/ordering=y varies,shader=interp,domain=-3:0,domain y=0:-3,samples=40, samples y=20] {-x*x+y};
    \end{axis}
\end{tikzpicture}
\end{center}

\end{document}

我找不到好的视图来显示该功能x<0。我觉得我喜欢从那里看到的景色y<0，但图像很丑。你有什么推荐吗没有使用 gnuplot？

谢谢！

编辑。我还想绘制 7 个范数为 的向量1：-平面上有 4 个xy，和 方向上有 3 个x>0。y>0即：

在 中3D。如果看起来复杂，您可以2D像图片一样在 中进行操作。

Answer 1

这是个建议。手工绘制轴并隐藏必须隐藏的内容。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\begin{document}
\begin{tikzpicture}[scale=2,
declare function={f(\x,\y)=ifthenelse(\x*\y<0,sqrt(-\x*\y),-\x*\x+\y);}]
    \begin{axis}[hide axis,
        legend pos=outer north east,
        view={75}{45},clip=false
    ]
     \draw[thick,-stealth] (0,0,0) -- (0,4,0) node[right]{$y$};
     \addplot3[opacity=0.8,surf,mesh/ordering=y varies,shader=interp,domain=-3:3,domain
     y=-3:3,samples=61, samples y=61,on layer=axis background] {f(x,y)};
     \addlegendentry{$f(x,y)$}
     \draw[thick,-stealth] (0,0,0) -- (0,0,4) node[right]{$z$};
     \draw[thick,-stealth] (0,0,0) -- (4,0,0) node[right]{$x$};
    \end{axis}
\end{tikzpicture}
\end{document}

我认为，在正 xy 平面上绘制这些单位向量的任何尝试看起来都不太好。在负 xy 平面上绘制它们怎么样？

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\begin{document}
\begin{tikzpicture}[scale=2,
declare function={f(\x,\y)=ifthenelse(\x*\y<0,sqrt(-\x*\y),-\x*\x+\y);}]
    \begin{axis}[hide axis,
        legend pos=outer north east,
        view={-145}{45},clip=false
    ]
     \addplot3[opacity=0.8,surf,mesh/ordering=y varies,shader=interp,domain=-3:3,domain
     y=-3:3,samples=61, samples y=61,on layer=axis background] {f(x,y)};
     \addlegendentry{$f(x,y)$}
     \draw[thick,-stealth] (0,0,0) -- (0,4,0) node[below]{$y$};
     \draw[thick,-stealth] (0,0,0) -- (0,0,4) node[right]{$z$};
     \draw[thick,-stealth] (0,0,0) -- (4,0,0) node[above]{$x$};
     \pgfplotsinvokeforeach{0,22.5,...,90}{%
     \draw[thick,-stealth] (0,0,0) -- ({-cos(#1)},{-sin(#1)},0);}
    \end{axis}
\end{tikzpicture}
\end{document}

这是带有勾号的第三个版本。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}

\begin{document}
\begin{tikzpicture}[scale=2,
declare function={f(\x,\y)=ifthenelse(\x*\y<0,sqrt(-\x*\y),-\x*\x+\y);}]
    \begin{axis}[axis on top,xlabel={$x$},ylabel={$y$},
        axis lines=middle,xtick={-1,0,1},ytick={-1,0,1},
        legend pos=outer north east,
          z axis line style={opacity=0},
        view={-145}{45},clip=false
    ]
     \addplot3[opacity=0.8,surf,mesh/ordering=y varies,shader=interp,domain=-3:3,domain
     y=-3:3,samples=61, samples y=61,on layer=axis background] {f(x,y)};
     \addlegendentry{$f(x,y)$}
     \draw[-stealth] (0,0,0) -- (0,0,4) node[right]{$z$};
     \pgfplotsinvokeforeach{0,22.5,...,90}{%
     \draw[-stealth] (0,0,0) -- ({-cos(#1)},{-sin(#1)},0);}
    \end{axis}
\end{tikzpicture}
\end{document}