向 3D 参数曲线添加支撑线

Question

我已经成功使用 绘制了一条 3D 参数曲线pgfplots，但我想在我的图中添加支撑线以增加深度，即从图到xy-平面的垂直线。有人知道如何做到这一点，而无需手动添加曲线上各个点的线条吗？

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[ 
height=15cm,
width=15cm,
clip=false, 
axis lines = middle,
ticks=none,
xmin=-2,xmax=6,
ymin=-6,ymax=6,
zmin=-1,zmax=6,
] 

\addplot3 [only marks,mark=*] coordinates {(5,5,1) (1,5,2)};
\addplot3 [only marks,mark=x,mark size=3pt] coordinates {(-1,-5,5) (5,-2,2)};

\node[anchor=north] at (axis cs:5,5,1) {$(5,5,1)$};
\node[anchor=south] at (axis cs:-1,-5,5) {$(-1,-5,5)$};
\node[anchor=west] at (axis cs:5,-2,2) {$(5,-2,2)$};
\node[anchor=south] at (axis cs:1,5,2) {$(1,5,2)$};

\draw[dashed] (axis cs:5,5,1) -- (axis cs:-1,-5,5) -- (axis cs:5,-2,2) -- (axis cs:1,5,2);

\addplot3 [y domain=0:0,
domain=0:1,
samples=50,
variable=\t]({-22*t^3+36*t^2-18*t+5},{-9*t^3+39*t^2-30*t+5},{10*t^3-21*t^2+12*t+1});

\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

您可以使用该功能添加“虚拟”图来实现此目的ycomb。有关更多详细信息，请查看代码中的注释。

% used PGFPlots v1.14
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            height=15cm,
            width=15cm,
            clip=false,
            axis lines=middle,
            ticks=none,
            xmin=-2,xmax=6,
            ymin=-6,ymax=6,
            zmin=-1,zmax=6,
        ]

            % before plotting the "real" plot add the `ycomb' plot with a
            % reduced number of sample ploints
            \addplot3 [
                draw=black!25,
                y domain=0:0,
                domain=0:1,
                samples=11,
                variable=\t,
                ycomb,
            ] (
                {-22*t^3+36*t^2-18*t+5},
                {-9*t^3+39*t^2-30*t+5},
                {10*t^3-21*t^2+12*t+1}
            );
            % now plot the real line
            \addplot3 [
                y domain=0:0,
                domain=0:1,
                samples=50,
                variable=\t,
            ] (
                {-22*t^3+36*t^2-18*t+5},
                {-9*t^3+39*t^2-30*t+5},
                {10*t^3-21*t^2+12*t+1}
            );

            \addplot3 [only marks,mark=*] coordinates {(5,5,1) (1,5,2)};
            \addplot3 [only marks,mark=x,mark size=3pt] coordinates {(-1,-5,5) (5,-2,2)};

            \node [anchor=north] at (axis cs:5,5,1)   {$(5,5,1)$};
            \node [anchor=south] at (axis cs:-1,-5,5) {$(-1,-5,5)$};
            \node [anchor=west]  at (axis cs:5,-2,2)  {$(5,-2,2)$};
            \node [anchor=south] at (axis cs:1,5,2)   {$(1,5,2)$};

            \draw [dashed] (axis cs:5,5,1) -- (axis cs:-1,-5,5)
                -- (axis cs:5,-2,2) -- (axis cs:1,5,2);

        \end{axis}
    \end{tikzpicture}
\end{document}