如何在任意点绘制参数定义曲线的切线（使用原始 gnuplot 选项绘制）？
答案来自这里适用于单调递增或递减函数。
对于曲线的任意点的解均不起作用。
\documentclass{standalone}
\usepackage{tikz,pgfplots}
% from https://tex.stackexchange.com/a/198046/121799
\usetikzlibrary{intersections}
\makeatletter
\def\parsenode[#1]#2\pgf@nil{%
\tikzset{label node/.style={#1}}
\def\nodetext{#2}
}
\tikzset{
add node at x/.style 2 args={
name path global=plot line,
/pgfplots/execute at end plot visualization/.append={
\begingroup
\@ifnextchar[{\parsenode}{\parsenode[]}#2\pgf@nil
\path [name path global = position line #1-1]
({axis cs:#1,0}|-{rel axis cs:0,0}) --
({axis cs:#1,0}|-{rel axis cs:0,1});
\path [xshift=1pt, name path global = position line #1-2]
({axis cs:#1,0}|-{rel axis cs:0,0}) --
({axis cs:#1,0}|-{rel axis cs:0,1});
\path [
name intersections={
of={plot line and position line #1-1},
name=left intersection
},
name intersections={
of={plot line and position line #1-2},
name=right intersection
},
label node/.append style={pos=1}
] (left intersection-1) -- (right intersection-1)
node [label node]{\nodetext};
\endgroup
}
}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis lines = middle,
axis line style={-stealth},
width = 10cm,
height = 10cm,
clip=false,
xmin = -5, xmax = 5,
ymin = -5, ymax = 5,
tangent/.style args={at #1 with style #2 and length #3}{
add node at x={#1}{
[
sloped,
append after command={(\tikzlastnode.west) edge [#2] (\tikzlastnode.east)},
minimum width=#3
]
}
}
]
\addplot [red,thick,domain=0:5, samples=100, raw gnuplot,
tangent=at 0 with style {blue,thick} and length 1.5cm,
tangent=at 2 with style {green,thick} and length 1.5cm,
tangent=at 4 with style {black,thick} and length 1.5cm
] gnuplot {
set parametric;
set samples 1000;
set size square;
plot [0:10] 5*exp(-0.1*t)*cos(2*t), 5*exp(-0.1*t)*sin(2*t);
};
\end{axis}
\end{tikzpicture}
\end{document}
答案1
我修改了样式以考虑所有交叉点。这是通过添加“级别”来实现的，该级别表示交叉点编号（从最低的交叉点向上计数）。例如，要添加示例中的交叉点，您需要级别 5、6 和 2，但级别取决于设置。
\documentclass{standalone}
\usepackage{tikz,pgfplots}
% from https://tex.stackexchange.com/a/198046/121799
\usetikzlibrary{intersections}
\makeatletter
\def\parsenode[#1]#2\pgf@nil{%
\tikzset{label node/.style={#1}}
\def\nodetext{#2}
}
\tikzset{
add node at x/.style n args={3}{
name path global=plot line,
/pgfplots/execute at end plot visualization/.append={
\begingroup
\@ifnextchar[{\parsenode}{\parsenode[]}#2\pgf@nil
\path [name path global = position line #1-1]
({axis cs:#1,0}|-{rel axis cs:0,0}) to[bend left=0]
({axis cs:#1,0}|-{rel axis cs:0,1});
\path [xshift=1pt, name path global = position line #1-2]
({axis cs:#1,0}|-{rel axis cs:0,0}) to[bend left=0]
({axis cs:#1,0}|-{rel axis cs:0,1});
\path [
name intersections={
of={plot line and position line #1-1},
name=left intersection,sort by=position line #1-1
},
name intersections={
of={plot line and position line #1-2},
name=right intersection,sort by=position line #1-2
},
label node/.append style={pos=1}
] (left intersection-#3) -- (right intersection-#3)
node [label node]{\nodetext};
\endgroup
}
}
}
\makeatother
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis lines = middle,
axis line style={-stealth},
width = 10cm,
height = 10cm,
clip=false,
xmin = -5, xmax = 5,
ymin = -5, ymax = 5,
tangent/.style args={at #1 with style #2 and length #3 at level #4}{
add node at x={#1}{
[
sloped,
append after command={(\tikzlastnode.west) edge [#2] (\tikzlastnode.east)},
minimum width=#3
]
}{#4}
}
]
\addplot [red,thick,domain=0:5, samples=100, raw gnuplot,
tangent=at 0 with style {blue,thick} and length 1.5cm at level 5,
tangent=at 1.5 with style {green,thick} and length 1.5cm at level 6,
tangent=at 3 with style {black,thick} and length 1.5cm at level 2
] gnuplot {
set parametric;
set samples 1000;
set size square;
plot [0:10] 5*exp(-0.1*t)*cos(2*t), 5*exp(-0.1*t)*sin(2*t);
};
\end{axis}
\end{tikzpicture}
\end{document}
顺便说一句，如果你想知道为什么我添加了一条直线bend left=0：这里是原因。否则 Ti钾Z 无法让人们可靠地对直线路径上的交叉路口进行排序。