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quick-references/LaTeX/TikZ

一些有趣的实例

复杂的箭头

\draw[-Implies, double, double distance = 0.5ex, red, out=30] (2em,1em) to [pos=0.5] node {\color{red} \huge $\times$} (12em, 0em);

可以直接在TikZ中使用三角函数

\documentclass[tikz,border=3.14mm]{standalone}
\begin{document}
\begin{tikzpicture}
	\draw (-2, 0) -- (2, 0)node[right] {$\infty$};
	\draw (0, -2) -- (0, 2)node[above] {$0$};

	\def\angle{45}
	\draw ({-2*cos(\angle)}, {-2*sin(\angle)}) -- ({2*cos(\angle)}, {2*sin(\angle)}) node[right] {1};
	\def\angle{135}
	\draw ({-2*cos(\angle)}, {-2*sin(\angle)}) -- ({2*cos(\angle)}, {2*sin(\angle)}) node[left] {-1};
	\def\angle{30}
	\draw ({-2*cos(\angle)}, {-2*sin(\angle)}) -- ({2*cos(\angle)}, {2*sin(\angle)}) node[right] {2};
	\def\angle{150}
	\draw ({-2*cos(\angle)}, {-2*sin(\angle)}) -- ({2*cos(\angle)}, {2*sin(\angle)}) node[left] {-2};
	\def\angle{20}
	\draw ({-2*cos(\angle)}, {-2*sin(\angle)}) -- ({2*cos(\angle)}, {2*sin(\angle)}) node[right] {3};
	\def\angle{160}
	\draw ({-2*cos(\angle)}, {-2*sin(\angle)}) -- ({2*cos(\angle)}, {2*sin(\angle)}) node[left] {-3};
\end{tikzpicture}

\end{document}

非常丑陋的逻辑链

\documentclass[tikz]{standalone}
\usetikzlibrary{arrows.meta}

\begin{document}
\begin{tikzpicture}[
    every node/.style={align=center} % 启用自动换行
]
\node at (0,0) {Countable additivity};
\draw[-Implies, double, double distance = 0.5ex] (0,-1ex) -- (0,-1cm+1ex); % => 
\node at (0,-1cm) {Continuity of measure};
\draw[-Implies, double, double distance = 0.5ex] (0,-1cm-1ex) -- (0,-2cm+1ex); % => 
\node at (0,-2cm) {Egoroff's Theorem};
\draw[-Implies, double, double distance = 0.5ex] (0,-2cm-1ex) -- (0,-3cm+1ex); % => 
\node at (0,-3.2cm) {Bounded Convergence\\Theorem};
\draw[-Implies, double, double distance = 0.5ex] (0,-3.6cm) -- (0,-4.4cm); % => 
\node at (0,-4.6cm) {Fatou's Lemma};

\draw[-Implies, double, double distance = 0.5ex] (1.5em,-4.8cm) -- (2cm,-6cm); % => 
\draw[-Implies, double, double distance = 0.5ex] (-1.5em,-4.8cm) -- (-2cm,-6cm); % => 

\node at (-2cm,-6.8cm) {Monotone\\Convergence\\Theorem}; 
\node at (2cm,-6.8cm) {Lebesgue\\Dominated\\Convergence\\Theorem}; 

\draw[-Implies, double, double distance = 0.5ex] (2,-7.6) -- (2,-8.6); % => 
\node at (2cm,-9.4) {General Lebesgue\\Dominated\\Convergence\\Theorem}; 
\end{tikzpicture}
\end{document}

两个圆相交

\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{patterns, intersections}

\begin{document}
\begin{tikzpicture}[scale=1]
    % 坐标轴
    \draw[->] (-1, 0) -- (2.5, 0) node[right] {$x$};
    \draw[->] (0, -1) -- (0, 2.5) node[above] {$y$};
    \node[below left] at (0,0) {$O$};

    % 定义圆心和半径
    \coordinate (D1) at (1,0);
    \coordinate (D2) at (0,1);
    \def\radius{1}

    % 绘制圆形路径
    \path[name path=D1] (D1) circle (\radius);
    \path[name path=D2] (D2) circle (\radius);

    % 计算交集区域并填充
    \begin{scope}
        \clip (D1) circle (\radius); % 剪切第一个圆
        \fill[pattern=north east lines] (D2) circle (\radius); % 填充交集区域
    \end{scope}

    % 绘制圆形边界
    \draw[thick] (D1) circle (\radius) node[below right=0.5em] {$D_1$};
    \draw[thick] (D2) circle (\radius) node[below left=0.5em] {$D_2$};
    \node at (D1) {$\bullet$};
    \node at (D2) {$\bullet$};
    \node[below] at (D1) {$1$};
    \node[left] at (D2) {$\mathrm{i}$};

    % 标注交集区域
    \node[fill=white, inner sep=1pt] at (0.5,0.5) {$d_{12}$};
\end{tikzpicture}
\end{document}

映射

\begin{tikzpicture}[line width=1pt]
	\begin{scope}[xshift=-4cm]
		\draw[->] (-2, 0) -- (2,0) node[right] {$x$};
		\draw[->] (0, -2) -- (0,2) node[above] {$y$};
		\draw[blue] (0,0) circle ({exp(1/2)});
		\draw[blue] (0,0) circle ({exp(-1/2)});
		\node[above left, blue] at ({-exp(-1/2)/sqrt(2)},{exp(-1/2)/sqrt(2)}) {$m_3$};
		\node[above left, blue] at ({-exp(1/2)/sqrt(2)},{exp(1/2)/sqrt(2)}) {$m_4$};
		\draw[red] (0,0) -- (2,2) node[right] {$m_2$};
		\draw[red] (0,0) -- (2,-2) node[right] {$m_1$};
		\node[white] at (0,0) {$\bullet$};
		\node[red] at (0,0) {$\circ$};
	\end{scope}
	\draw[<-] (-1,0.5) to [pos=0.5] node[above] {$e^z$} (1,0.5);
	\draw[->, red] (-1,-0.5) to [pos=0.5] node[above] {$\operatorname{Ln} z$} (1,-0.5);
	\begin{scope}[xshift=4cm]
		\draw[->] (-2, 0) -- (2,0) node[right] {$x$};
		\draw[->] (0, -2) -- (0,2) node[above] {$y$};

		\draw[red] (-2,1) -- (2,1) node[above] {$l_2$};
		\draw[red] (-2,-1) -- (2,-1) node[below] {$l_1$};
		\draw[blue] (-1/2, -2) -- (-1/2, 2) node[left] {$m_3$};
		\draw[blue] (1/2, -2) -- (1/2, 2) node[right] {$m_4$};
	\end{scope}
\end{tikzpicture}


% 需要 \usepackage{pgfplots}
\begin{tikzpicture}[scale=0.6]
	\begin{scope}[xshift=-5cm]
		\begin{axis}[
				at={(0,0)},
				anchor=center,
				axis lines=center, % 显示普通坐标轴
				axis equal,
				enlargelimits=true,
			]
			\addplot[
				variable=\t,   % 参数变量为t
				red,
				samples=201,
				smooth,
				domain=0:4,
			] ({t * cos(180/pi*5*t)}, {t * sin(180/pi*5*t)});
		\end{axis}
	\end{scope}
	\draw[->] (-1,0) to [pos=0.5] node[above] {$\operatorname{Ln} z$} (1,0);
	\begin{scope}[xshift=5cm]
		\begin{axis}[
				at={(0,0)},
				anchor=center,
				axis lines=center,
				%axis lines=none, 
				%axis equal,
				% xlabel=$x$,
				% ylabel=$y$,
				enlargelimits=true,
				ytick={0, 2*pi, 4*pi, 6*pi}, % 设置y轴刻度位置
				yticklabels={         % 设置y轴刻度标签
						$0$, $2\pi$, $4\pi$, $6\pi$
					},
				yticklabel style={above left}
			]
			\addplot[
				variable=\t,   % 参数变量为t
				red,
				samples=201,
				smooth,
				domain=0.01:4,
			] ({ln(t)}, {5*t});
			\foreach \i in {1,2,3} {
					\addplot[samples=2, red, domain=-5:2] {\i*2*pi};
				}
		\end{axis}
	\end{scope}
\end{tikzpicture}


\begin{tikzpicture}
	\pgfmathsetmacro{\radius}{0.07}
	\begin{scope}[xshift=-4cm]
		\draw[->] (-2, 0) -- (2,0) node[right] {$x$};
		\draw[->] (0, -2) -- (0,2) node[above] {$y$};
		\draw[red, fill=white] (0,0) circle (\radius);
		\draw[red, dashed] (0, \radius) -- (-2, \radius);
		\draw[red, dashed] (0, -\radius) -- (-2, -\radius);
		\fill[red] (1,0) circle (\radius) node[below, red] {$1$};
	\end{scope}
	\draw[->] (-1,0) to (1,0);
	\begin{scope}[xshift=4cm]
		\draw[->] (-2, 0) -- (2,0) node[right] {$x$};
		\draw[->] (0, -2) -- (0,2) node[above] {$y$};
		\fill[red]  (0,0) circle (\radius) node[below right, red] {$f_0(1)$};
		\fill[red]  (0,1) circle (\radius) node[right, red] {$f_0(2)$};
		\fill[red]  (0,-1) circle (\radius) node[right, red] {$f_{-1}(1)$};
	\end{scope}
\end{tikzpicture}


\documentclass[a4paper,zihao=5,UTF8]{ctexart}
\usepackage{tikz}
\usetikzlibrary{positioning, shapes.geometric}

\begin{document}
這個是風鈴：
\begin{center}
    \begin{tikzpicture}[node distance=30pt]
        \node[draw, diamond, aspect=2]     (choice)  {風有在吹嗎？};
        \node[draw, below=of choice, minimum width=5g0pt, minimum height=140pt]       (step 1)  {};

        \node at (step 1) [yshift=15pt] {叮};
        \node at (step 1) [yshift=0pt] {鈴};
        \node at (step 1) [yshift=-15pt] {|};

        \draw[-] (choice) -- node[right]  {Yes} (step 1);
    \end{tikzpicture}
\end{center}
\end{document}