Tikz：3D分段函数

Question

我有以下分段函数

其图形由

问题 1。如何绘制与中间部分未正确绘制相对应的表面？

问题2. 我们如何才能将 $z$ 轴的刻度和标签移动到另一侧？

我按照以下方式绘制该函数。

\documentclass[a4paper,12pt]{article}

%\usepackage{graphicx}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}

\begin{document}

\begin{figure}[ht]
  \centering
    \begin{tikzpicture}[
      baseline=(origin),
      declare function={
        f(\t,\y)=(y<=0)*2*\t+(\t>0)*(\y>\t)*(\y<=\t^2)*2*(1-\y/\t)*\t+(\y>=\t^2)*(-2)*\t;
      }
    ]
      \begin{axis}[
        width=100mm,
        height=60mm,
        view={135}{45},
        xmin=0,
        xmax=1,
        xlabel={$t$},
        ymin=-1,
        ymax=1,
        ylabel={$y$},
        zmin=-2,
        zmax=2,
        zlabel={$z$},
        zlabel style={rotate=-90},
      ]
        \coordinate (origin) at (axis cs:0,0,0);
        \addplot3[surf,color=blue,opacity=0.5,domain=0:1,y domain=-1:1,faceted color=blue]{f(\x,\y)};
        \draw[variable=\t,domain=0:1,color=red,thick] plot (axis cs:\t,0,{2*\t});
        \draw[variable=\t,domain=0:1,color=red,thick] plot (axis cs:\t,{\t^2},{(-2)*\t});
      \end{axis}
    \end{tikzpicture}
    \caption{Graphic of $f:[0,1]\times[-1,1]\to[-2,2]$.}
\end{figure}

\end{document} 

Answer 1

我得到了以下近似解。

\documentclass[a4paper,12pt]{article}

\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}

\begin{figure}[ht]
  \centering
    \begin{tikzpicture}[baseline=(origin)]
      \begin{axis}[
        width=100mm,
        height=60mm,
        view={135}{45},
        xmin=0,
        xmax=1,
        xlabel={$t$},
        ymin=-1,
        ymax=1,
        ylabel={$y$},
        zmin=-2,
        zmax=2,
        zlabel={$z$},
        zlabel style={rotate=-90},
      ]
        \coordinate (origin) at (axis cs:0,0,0);
        \fill[color=blue] (axis cs:0,0,0)
              -- (axis cs:0,-1,0)
              -- (axis cs:1,-1,2)
              -- (axis cs:1,0,2)
              -- cycle;
        \fill[color=blue] (axis cs:0,0,0)
          \foreach \pt in {0.1,0.2,...,1}{ -- (axis cs:\pt,0,{2*\pt})}
          \foreach \pt in {1,0.9,...,0}{ -- (axis cs:\pt,{\pt^2},{(-2)*\pt})};
        \fill[color=blue] (axis cs:0,0,0) -- (axis cs:0,1,0) -- (axis cs:1,1,-2)
          \foreach \pt in {1,0.9,...,0}{ -- (axis cs:\pt,{\pt^2},{(-2)*\pt})};
        \draw[variable=\t,domain=0:1,color=red,thick] plot (axis cs:\t,0,{2*\t});
        \draw[variable=\t,domain=0:1,color=red,thick] plot (axis cs:\t,{\t^2},{(-2)*\t});
      \end{axis}
    \end{tikzpicture}
    \caption{Graphic of $f:[0,1]\times[-1,1]\to[-2,2]$.}
\end{figure}

\end{document}