下面一個例子展示如何使用Tikz完成：

• 定義一個坐標點，以備后面畫線時直接使用窍奋；
• 定義一個極坐標點荐健，以備在圓上快速定點；
• 根據(jù)定義的點進行路徑的定義费变；
• 根據(jù)定義的路徑計算路徑的交點摧扇；
• 根據(jù)定義的坐標點進行封閉區(qū)域/形狀的旋轉(zhuǎn)！

注意：以上的所有操作不需要額外導(dǎo)入Tikz中的其他庫挚歧，直接導(dǎo)入\usepackages{tikz}就可以實現(xiàn)上面的各種功能。

% 極坐標定點示例：長度不帶單位吁峻，默認坐標單位一樣滑负！ —— 方便！
% 極坐標更方便的一點：代碼改動杏煤矮慕！只用調(diào)角度即可！
\begin{figure}[H]
\centering
\begin{tikzpicture}[scale = 3]
    %\draw [thick, <->] (-2,2.5) node [left] {$x_2$} -- (-2,-2) -- (2.5,-2) node [below right] {$x_1$};  
    \draw (0,0) circle [radius = 1];  % 注意：為了普通坐標和極坐標可以通用啄骇，把圓心定在原點痴鳄！
    % 第一個三角形：
    \coordinate (O) at (0:0);  % 原點
    \coordinate (A) at (90:1);  
    \coordinate (B) at (210:1);
    \coordinate (C) at (-30:1);
    \draw [red] (A) -- (B) -- (C) -- (A);
    % 第二個三角形：
    \coordinate (D) at (-90:1);  
    \coordinate (E) at (30:1);
    \coordinate (F) at (150:1);
    \draw [green] (D) -- (E) -- (F) -- (D);
    % 定義路徑：不畫出來
    \path [name path = AB] (A) -- (B); \path [name path = AC] (A) -- (C); \path [name path = BC] (B) -- (C);
    \path [name path = DE] (D) -- (E); \path [name path = DF] (D) -- (F); \path [name path = EF] (E) -- (F);
    % 算交點：不畫出來
    \path [ name intersections = {of = AB and EF, by = i1} ]; 
    \path [ name intersections = {of = AB and DF, by = i2} ];
    \path [ name intersections = {of = AC and EF, by = i3} ];
    \path [ name intersections = {of = AC and DE, by = i4} ];
    \path [ name intersections = {of = BC and DF, by = i5} ];
    \path [ name intersections = {of = BC and DE, by = i6} ];     
    % 填充：
    %\draw [very thin, fill = green, opacity = 0.5] (A) -- (i1) -- (i3) -- (A);
    \draw [very thin, fill = green, opacity = 0.5] (E) -- (i3) -- (i4) -- (E);
    %\draw [very thin, fill = green, opacity = 0.5] (C) -- (i4) -- (i6) -- (C);
    \draw [very thin, fill = green, opacity = 0.5] (D) -- (i5) -- (i6) -- (D);
    %\draw [very thin, fill = green, opacity = 0.5] (B) -- (i2) -- (i5) -- (B);
    \draw [very thin, fill = green, opacity = 0.5] (F) -- (i1) -- (i2) -- (F);
    
    % 旋轉(zhuǎn)一個圖形：在scope環(huán)境中
    \begin{scope}[rotate around={33:(O)}]
        % 坐標需要重定一遍
        \coordinate (A1) at (90:1);  
        \coordinate (B1) at (210:1);
        \coordinate (C1) at (-30:1);
        \draw[blue] (A1) -- (B1) -- (C1) -- cycle;  % cycle寫最后表示閉環(huán)
    \end{scope}
\end{tikzpicture}
\caption{定義點+極坐標點、路徑缸夹、交點痪寻、旋轉(zhuǎn)}
\end{figure}

效果如下：

效果圖