以下是代码：
\begin{figure}[H]\centering
\begin{tikzpicture}
\begin{axis}[
xmin=-4,xmax=4,
ymin=-15,ymax=15,
height = 5in,
axis lines=center,
axis line style=->, xlabel = {$x_1$}, ylabel={$x_2$},
%axis equal,
legend cell align = {left},
every axis x label/.style={ at={(ticklabel* cs:1.05)}, anchor=west,},
every axis y label/.style={at={(ticklabel* cs:1.05)}, anchor=south,},
title= {Extremal Curves Problem 1}, title style={xshift=0, yshift=1.75em},
domain=0:15,samples=300,legend pos=outer north east]
\addplot[latex-][color = blue, thick, domain = 2:3] {-1 + (x + 1)^2};
\addplot[latex-][color = blue, thick, domain = 1:2] {-1 + (x + 1)^2} node[below right, pos = 0.5, font = \small] {\(u^* = 1\)};
\addplot[color = blue, thick, domain = 0:1] {-1 + (x + 1)^2};
\addplot[-latex][color = red, thick, domain = -3:-2] {1 - (-x + 1)^2};
\addplot[-latex][color = red, thick, domain = -2:-1] {1 - (-x + 1)^2} node[above left, pos = 0.5, font = \small] {\(u^* = -1\)};
\addplot[color = red, thick, domain = -1:0] {1 - (-x + 1)^2};
\addplot [color = red, thick, dashed, domain = 0:3, -latex] ({-1 + (4 + 1)*exp(-x)}, {-1 + (-15 + 1)*exp(-2*x)});
\addplot [color = blue, thick, dashed, domain = 0:3, -latex] ({1 + (-4 - 1)*exp(-x)}, {1 + (15 - 1)*exp(-2*x)});
\end{axis}
\end{tikzpicture}
\caption{Extremal curves for problem 1. Note that the red curve is the fastest curve.}
\end{figure}
相应的输出如下：
编辑：我想制作一些类似虚线图的图，使得蓝色虚线图停止在蓝色实线图上，红色虚线图停止在红色实线图上，并且每个图中都有几个间距均匀的箭头。标准是，出现在实线上方的虚线图将为蓝色（例如，从 (-4, -2) 开始的图将为蓝色并转到蓝色实线），而出现在实线下方的虚线图将为红色（例如，从 (4, 2) 开始的图将为红色并转到红色实线）。有没有办法这样做pgfplots？我尝试了该\clip命令，但它只剪掉其中的一部分而不是全部。有没有办法解决这个问题？
答案1
您可以使用decorations.markings库添加箭头，并使用 pgfplots 库将一条路径停在另一条路径上fillbetween。这允许您访问相交路径的相交段。不幸的是，似乎无法轻松找到装饰路径的相交段，这就是为什么我单独添加用于相交段的路径。好处是用于相交的路径结合了蓝色和红色曲线。
\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{decorations.markings}
\tikzset{arrow marks/.style={postaction=decorate,decoration={markings,
mark=between positions #1 and 1 step #1 with {\arrow{>}}}},
arrow marks/.default=10pt}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}
\begin{axis}[
xmin=-4,xmax=4,
ymin=-15,ymax=15,
height = 5in,width=0.9\textwidth,
axis lines=center,
axis line style=->, xlabel = {$x_1$}, ylabel={$x_2$},
%axis equal,
legend cell align = {left},
every axis x label/.style={ at={(ticklabel* cs:1.05)}, anchor=west,},
every axis y label/.style={at={(ticklabel* cs:1.05)}, anchor=south,},
title= {Extremal Curves Problem 1}, title style={xshift=0, yshift=1.75em},
domain=0:15,samples=300,legend pos=outer north east]
\addplot[->,>=latex,arrow marks=1cm,color = blue, thick, domain = 3:0,
tips=proper]
{-1 + (x + 1)^2};
\addplot[->,>=latex,arrow marks=1cm,tips=proper,
color=red,thick, domain = -3:0] {1 - (-x + 1)^2};
\addplot[draw=none,name path=second, domain = -3:3]
{-sign(x)*(1 - (abs(x) + 1)^2)};
\addplot[draw=none,name path=first,domain=0:3]
({-1 + (2 + 1)*exp(-x)}, {-1 + (2 + 1)*exp(-2*x)});
\draw [->,>=latex,orange,thick,arrow marks=1cm,
intersection segments={of=first and second, sequence={A0},}];
\end{axis}
\end{tikzpicture}
\caption{Extremal curves for problem 1. Note that the red curve is the fastest
curve.}
\end{figure}
\end{document}
也可以使用它\clip来完善路径。
\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usetikzlibrary{decorations.markings}
\tikzset{arrow marks/.style={postaction=decorate,decoration={markings,
mark=between positions #1 and 1 step #1 with {\arrow{>}}}},
arrow marks/.default=10pt}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}
\begin{axis}[
xmin=-4,xmax=4,
ymin=-15,ymax=15,
height = 5in,width=0.9\textwidth,
axis lines=center,
axis line style=->, xlabel = {$x_1$}, ylabel={$x_2$},
%axis equal,
legend cell align = {left},
every axis x label/.style={ at={(ticklabel* cs:1.05)}, anchor=west,},
every axis y label/.style={at={(ticklabel* cs:1.05)}, anchor=south,},
title= {Extremal Curves Problem 1}, title style={xshift=0, yshift=1.75em},
domain=0:15,samples=300,legend pos=outer north east]
\addplot[->,>=latex,arrow marks=1cm,color = blue, thick, domain = 3:0,
tips=proper]
{-1 + (x + 1)^2};
\addplot[->,>=latex,arrow marks=1cm,tips=proper,
color=red,thick, domain = -3:0] {1 - (-x + 1)^2};
\clip plot[variable=\x,domain=-3:3]
(\x,{-sign(\x)*(1 - pow(abs(\x) + 1,2))}) |-cycle;
\addplot[->,>=latex,arrow marks=1cm,tips=proper,
color=orange,thick,domain=0:3]
({-1 + (2 + 1)*exp(-x)}, {-1 + (2 + 1)*exp(-2*x)});
\end{axis}
\end{tikzpicture}
\caption{Extremal curves for problem 1. Note that the red curve is the fastest
curve.}
\end{figure}
\end{document}
您还可以将箭头设置在图长度的某些部分。
\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\usetikzlibrary{decorations.markings}
\tikzset{arrow marks/.style={postaction=decorate,decoration={markings,
mark=between positions 1/#1 and 1-1/#1 step 1/#1 with {\arrow{>}}}},
arrow marks/.default=5}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}[tips=proper]
\begin{axis}[
xmin=-4,xmax=4,
ymin=-15,ymax=15,
height = 5in,width=0.9\textwidth,
axis lines=center,
axis line style=->, xlabel = {$x_1$}, ylabel={$x_2$},
%axis equal,
legend cell align = {left},
every axis x label/.style={ at={(ticklabel* cs:1.05)}, anchor=west,},
every axis y label/.style={at={(ticklabel* cs:1.05)}, anchor=south,},
title= {Extremal Curves Problem 1}, title style={xshift=0, yshift=1.75em},
domain=0:15,samples=300,legend pos=outer north east]
\addplot[->,>=latex,arrow marks,color = blue, thick, domain = 3:0]
{-1 + (x + 1)^2};
\addplot[->,>=latex,arrow marks,
color=red,thick, domain = -3:0] {1 - (-x + 1)^2};
\clip plot[variable=\x,domain=-3:3]
(\x,{-sign(\x)*(1 - pow(abs(\x) + 1,2))}) |-cycle;
\addplot[->,>=latex,arrow marks,
color=orange,thick,domain=0:3]
({-1 + (2 + 1)*exp(-x)}, {-1 + (2 + 1)*exp(-2*x)});
\end{axis}
\end{tikzpicture}
\caption{Extremal curves for problem 1. Note that the red curve is the fastest
curve.}
\end{figure}
\end{document}
