如何在线（线性不等式线）的边缘自动获取箭头？

Question

我想得到如图所示的箭头，表示线性不等式对应的解空间方向。请帮帮我。

 \documentclass[12pt,border=10pt]{standalone}
 \usepackage{tikz,pgfplots}
 \begin{document}
 \begin{tikzpicture}
 \begin{axis}[title={},ylabel={$x_2$},ymin=0,ymax=100,ytick={10, 20,...,100}, unbounded coords=jump, xmin=0,xmax=100,xtick={0,10,20,...,100},xlabel={$ x_1$},width=15.0cm,height=11.0cm,enlargelimits =false, grid,legend cell align=left, legend style={at={(0.8,0.96)},anchor=north}]
 \addplot+[smooth,ultra thick,color=red,mark=none]
 coordinates{
 (0,72)
 (54,0)
 };
 \addplot+[smooth,ultra thick,dashed,color=blue,mark=none]
 coordinates{
 (0,64)
 (98,0)
 };
 \addplot+[only marks,color=black,fill=black,mark=*]
 coordinates{
 (12,56)
 };
 \addplot+[thin,color=yellow!40,fill=yellow!40,mark=none]
 coordinates{
 (0.1,0.1)
 (53.5,0.1)
 (12,55.5)
 (0.1,63.5)
 (0.1,0.1)
 };
 \end{axis} 
 \node[text width=3.5cm] at (2.29,2.6) {Feasible Region};
 \node[text width=3.5cm] at (2.1,2.05) {(or) Solution Space};
 \end{tikzpicture}
 \end{document}

Answer 1

你可以使用这个calc库。首先将线的端点存储在符号坐标中(r0)，(r1)对于红色图，

 \addplot+[smooth,ultra thick,color=red,mark=none]
 coordinates{
 (0,72)
 (54,0)
 } coordinate[pos=0] (r0) coordinate[pos=1](r1);

蓝色图也一样。然后使用部分的计算语法13.5.4 距离修饰符的语法pgfmanual v3.1.5 绘制正交线后 \end{axis}（避免被剪掉）

 \path[thick,-stealth] (r0) edge ($(r0)!1cm!-90:(r1)$)
 (r1) edge ($(r1)!1cm!90:(r0)$);

完整代码和结果：

\documentclass[tikz,12pt,border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\usetikzlibrary{calc}
\begin{document}
 \begin{tikzpicture}
 \begin{axis}[title={},ylabel={$x_2$},ymin=0,ymax=100,ytick={10, 20,...,100}, unbounded coords=jump, xmin=0,xmax=100,xtick={0,10,20,...,100},xlabel={$ x_1$},width=15.0cm,height=11.0cm,enlargelimits =false, grid,legend cell align=left, legend style={at={(0.8,0.96)},anchor=north}]
 \addplot+[smooth,ultra thick,color=red,mark=none]
 coordinates{
 (0,72)
 (54,0)
 } coordinate[pos=0] (r0) coordinate[pos=1](r1);
 \addplot+[smooth,ultra thick,dashed,color=blue,mark=none]
 coordinates{
 (0,64)
 (98,0)
 } coordinate[pos=0] (b0) coordinate[pos=1](b1); 
 \addplot+[only marks,color=black,fill=black,mark=*]
 coordinates{
 (12,56)
 };
 \addplot+[thin,color=yellow!40,fill=yellow!40,mark=none]
 coordinates{
 (0.1,0.1)
 (53.5,0.1)
 (12,55.5)
 (0.1,63.5)
 (0.1,0.1)
 };
 \end{axis} 
 \node[text width=3.5cm] at (2.29,2.6) {Feasible Region};
 \node[text width=3.5cm] at (2.1,2.05) {(or) Solution Space};
 \path[thick,-stealth] (r0) edge ($(r0)!1cm!-90:(r1)$)
 (r1) edge ($(r1)!1cm!90:(r0)$)
 (b0) edge ($(b0)!1cm!-90:(b1)$)
 (b1) edge ($(b1)!1cm!90:(b0)$);
\end{tikzpicture}
\end{document}

另一种方法是使用decorations.markings。然后您可以引入一种样式，这样您只需将键添加end arrows到相应的图中。长度和样式分别存储在 pgf 键vert arrow length和中varrow。

\documentclass[tikz,12pt,border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\usetikzlibrary{decorations.markings}
\begin{document}
 \begin{tikzpicture}[vert arrow/.style={postaction={decorate,
    decoration={markings,
    mark=at position #1 with {%
     \draw[varrow] (0,0) -- (0,\pgfkeysvalueof{/tikz/vert arrow length});}}}},
    end arrows/.style={vert arrow/.list={0,1}},
    varrow/.style={-stealth,thick,black,solid},
    vert arrow length/.initial=-1cm
    ]
 \begin{axis}[title={},ylabel={$x_2$},ymin=0,ymax=100,ytick={10, 20,...,100},
 unbounded coords=jump, xmin=0,xmax=100,xtick={0,10,20,...,100},xlabel={$
 x_1$},width=15.0cm,height=11.0cm,enlargelimits =false, grid,legend cell
 align=left, legend style={at={(0.8,0.96)},anchor=north},clip=false]
 \addplot+[ultra thick,color=red,mark=none,end arrows]
 coordinates{
 (0,72)
 (54,0)
 };
 \addplot+[ultra thick,dashed,color=blue,mark=none,end arrows]
 coordinates{
 (0,64)
 (98,0)
 }; 
 \addplot+[only marks,color=black,fill=black,mark=*]
 coordinates{
 (12,56)
 };
 \addplot+[thin,color=yellow!40,fill=yellow!40,mark=none]
 coordinates{
 (0.1,0.1)
 (53.5,0.1)
 (12,55.5)
 (0.1,63.5)
 (0.1,0.1)
 };
 \end{axis} 
 \node[text width=3.5cm] at (2.29,2.6) {Feasible Region};
 \node[text width=3.5cm] at (2.1,2.05) {(or) Solution Space};
\end{tikzpicture}
\end{document}