如何画圆的切线束？

Question

为了绘制圆的一些切线，我使用了 (1,0) 处与圆相切的单个垂直线段，然后按如下循环旋转

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\foreach \t in {0,...,30}
{
\pgfmathsetmacro{\s}{360/30*\t}
\draw[rotate=\s](1,-2)--(1,2);
}
\end{tikzpicture}
\end{document}

我应该如何绘制第二个图？太晚了，我没法弄清楚。

Answer 1

我可以修改你之前的例子。这只是三角函数的一小部分：每个切线空间都在一个点的上方和下方几厘米处（cosX，罪X)，因此您多使用几个\pgfmathsetmacro电话。

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[very thick, blue] (0,0) circle [y radius=0.67cm, x radius=1cm];
\foreach \t in {0,...,30}
{
  \pgfmathsetmacro{\s}{360/30*\t}
  \pgfmathsetmacro{\x}{cos(\s+10)}
  \pgfmathsetmacro{\y}{0.67*sin(\s+10)-3}
  \pgfmathsetmacro{\yy}{\y+6}
  \draw[thick, red] (\x, \y) -- (\x,\yy);
}
\end{tikzpicture}
\end{document}

Answer 2

对 Arun Debray 的回答只有一点小小的修改：

\documentclass{article}
\usepackage{tikz}
    \usetikzlibrary{backgrounds}

\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
    \setlength\PreviewBorder{1em}

    \begin{document}
\begin{tikzpicture}
\draw[ultra thick, blue] (0,0) circle [y radius=0.67cm, x radius=1cm];
\foreach \t in {0,...,30}
{
  \pgfmathsetmacro{\s}{360/30*\t}
  \pgfmathsetmacro{\x}{cos(\s+10)}
  \pgfmathsetmacro{\y}{0.67*sin(\s+10)-2}
  \pgfmathsetmacro{\yy}{\y+4}
  \ifnum\t<15
  \scoped[on background layer]
  \draw[thick,red!50] (\x, \y) -- (\x,\yy)
  \else
  \draw[thick,red] (\x, \y) -- (\x,\yy)
  \fi;
}
\end{tikzpicture}
    \end{document}

Answer 3

我稍微修改了你的答案并认为有人可能会觉得它有用。

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{tikz}
    \usetikzlibrary{backgrounds}

\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
    \setlength\PreviewBorder{1em}

\begin{document}
\begin{tikzpicture}
    %\draw (-2,-2.5) grid (3,3);
    \draw[ultra thick, blue] (0,0) circle [y radius=0.5cm, x radius=1cm];
\foreach \t in {0,...,30}
{
    \pgfmathsetmacro{\s}{360/30*\t}
    \pgfmathsetmacro{\x}{cos(\s+10)}
    \pgfmathsetmacro{\y}{0.5*sin(\s+10)-2}
    \pgfmathsetmacro{\yy}{\y+4}
    \ifnum\t<15
        \scoped[on background layer]
        \draw[thick,red!50] (\x, \y) -- (\x,\yy);
    \else
        \ifnum\t=20
            \draw[thick, black] (\x, \y) -- (\x,\yy);
        \else
            \draw[thick,red] (\x, \y) -- (\x,\yy);
        \fi;
    \fi;
}
    \node[blue] at (1.3,0) {$\mathcal{M}$};
    \node[red] at (1.8,1.5) {$\mathcal{E} = T\mathcal{M}$};


    \pgfmathsetmacro{\s}{360/30*20}
    \pgfmathsetmacro{\x}{cos(\s+10)}
    \pgfmathsetmacro{\y}{0.5*sin(\s+10)-2}
    \pgfmathsetmacro{\yy}{\y+4}
    \draw (\x, \yy/2+\y/2) node[circle, fill, inner sep=1pt, label=below:$p$] (p) {};
    \node at (\x, \yy+0.2) {$T_p\mathcal{M}$};
\end{tikzpicture}
\end{document}