我正在尝试在 tikz 中绘制以下图形。
我迄今为止的尝试已经让我到达这里。
\documentclass[border=3mm]{standalone}
\usepackage[dvipsnames]{xcolor}
\usepackage{pgfplots}
\pgfplotsset{width=8cm,compat=newest}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xtick = \empty, ytick = \empty,
xlabel = {$t$},
x label style = {at={(1,0)},anchor=west},
ylabel = {$q$},
y label style = {at={(0,1)},rotate=-90,anchor=south},
axis lines=left,
enlargelimits=0.2,
]
\addplot[mark=none, blue] coordinates {(1.85,1.1)(0.0,3)};
\addplot[color=red,smooth,thick,-] coordinates {
(0.3,2.7) (1.3,1) (2.5,2) (4,0.65) (6,0.8)};
\end{axis}
\end{tikzpicture}
\end{document}
输出是；
我花了大半天时间才画好。我不明白如何写出坐标来得到我想要的切线曲线的形状。我想知道这有什么诀窍，有人能给我一些关于如何正确塑造事物的建议吗？一定有比我现在的做法更好的方法！
答案1
绘制数学表达式，然后“手动”添加切线......
\documentclass[border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=8cm,compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xtick = \empty, ytick = \empty,
xlabel = {$t$},
x label style = {at={(1,0)},anchor=west},
ylabel = {$q$},
y label style = {at={(0,1)},rotate=-90,anchor=south},
axis lines=left,
enlargelimits=0.2,
]
\addplot[color=red,smooth,thick,-] {(x)^2};
\addplot[mark=none, blue] coordinates {(-6,20) (0,-4)};
\end{axis}
\end{tikzpicture}
\end{document}
（如果有人想知道我是如何计算出切线坐标的：我知道的斜率x^2为2x，因此在x=-2处它将为-4，其余的如下...）
如果您想对不同的位置执行此操作，那么您可能会发现重新打开 xticks 和 yticks 并添加网格会很有帮助，同时您还能获得正确的定位。您可以通过注释掉轴选项的第一行来做到这一点：
\begin{axis}[
%xtick = \empty, ytick = \empty,
grid=both,
...
得出的结果为：
答案2
根据杰克给出的代码进行改编这里对于类似的问题，你可以在任意 x 坐标处添加一条切线”自动地“。这也应该适用于\addplot您陈述的每个命令，以及\addplot coordinates问题中给出的命令。
% used PGFPlots v1.13 and TikZ v3.0.1a
\documentclass[border=2mm]{standalone}
\usepackage{xcolor}
\colorlet{Curve}{red!75!black}
\colorlet{Tangent}{blue!75!black}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}
\usetikzlibrary{
calc,
intersections,
math,
}
\makeatletter
\def\parsenode[#1]#2\pgf@nil{%
\tikzset{label node/.style={#1}}
\def\nodetext{#2}
}
\tikzset{
% define style for the points
Point/.style={
shape=circle,
inner sep=0pt,
minimum size=3pt,
},
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};
% ---------------------------------------------------------
% draw the tangent line from a bit right of the point on
% the curve to the intersection with the ordinate
% and draw the corresponding points
\draw [Tangent] let
\p1=($ (left intersection-1) - (right intersection-1) $),
\p2=($ (left intersection-1)!sign(#1)*5mm!(right intersection-1) $),
\p3=($ ({axis cs:0,0}) - (\p2) $),
\n1={\x3/\x1}
in
(\p2) -- +($ {\n1}*(\x1,\y1) $)
% node [Point,fill=Tangent] (origin intersection) {}
% node [Point,fill=Curve] at (left intersection-1) {}
;
% % ----------
% % draw the horizontal line at the curve intersection point
% % plus the label above/below the line
% \tikzmath{
% coordinate \c1;
% \c1=(left intersection-1) - (right intersection-1);
% \slope=\cy1/\cx1*sign(#1);
% }
% \pgfmathsetmacro{\AboveBelow}{ \slope>0 ? "above" : "below" }
% \draw [dotted]
% ([xshift=sign(#1)*2.5mm] left intersection-1) --
% (left intersection-1) --
% node [\AboveBelow,node font=\scriptsize] {$f(x)$}
% (left intersection-1 -| origin intersection) --
% +($ sign(#1)*(-2.5mm,0) $)
% coordinate [pos=0.5] (a)
% ;
% % draw the horizontal line at the ordinate intersection point
% \draw [dotted] (origin intersection)
% +($ sign(#1)*(-2.5mm,0) $) --
% (origin intersection);
% % draw vertical line left/right of the ordinate
% \pgfmathsetmacro{\LeftRight}{ #1<0 ? "right" : "left" }
% \draw [stealth-stealth] (origin intersection)
% +($ sign(#1)*(-1.25mm,0) $) -- (a)
% node [midway,\LeftRight,node font=\scriptsize] {$p$}
% ;
% % ---------------------------------------------------------
\endgroup
},
},
}
\makeatother
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
enlargelimits=0.1,
xmin=-0.5,
xmax=3.25,
ymin=0,
ymax=5.5,
xtick=\empty,
ytick=\empty,
xlabel=$x$,
ylabel=$y$,
domain=\pgfkeysvalueof{/pgfplots/xmin}:(\pgfkeysvalueof{/pgfplots/xmax},
samples=50,
tangent/.style={
add node at x={#1}{},
},
]
\addplot [thick,draw=Curve,
tangent=-0.5,
tangent=0.8,
tangent=2.3,
] {0.5*x^2 - 2*x + 4};
\end{axis}
\end{tikzpicture}
\end{document}
上述代码的结果是
当你取消注释注释行时，你会得到
