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TikZ：修改复杂分析的轮廓

tag-icon • tag-icon tikz-pgf arc contour
TikZ：修改复杂分析的轮廓

我想修改黑色曲线，以便包含现在留在外面的红色虚线。围绕原点的圆弧应该围绕复平面下半部分的红点。

\documentclass[8pt,usenames,dvipsnames]{beamer}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.markings}

\begin{document}        
\begin{figure}
\centering
\begin{tikzpicture}[scale=0.7, every node/.style={scale=0.85}]
% Configurable parameters
\def\gap{0.2}
\def\bigradius{3}
\def\littleradius{0.25}
% Axes
\draw [help lines,->] (-1.25*\bigradius, 0) -- (1.25*\bigradius,0);
\draw [help lines,->] (0, -1.25*\bigradius) -- (0, 1.25*\bigradius);
% Path
\draw[line width=1pt,   decoration={ markings,
  mark=at position 0.2455 with {\arrow[line width=0.9pt]{>}},
  mark=at position 0.765 with {\arrow[line width=0.9pt]{>}},
  mark=at position 0.87 with {\arrow[line width=0.9pt]{>}},
  mark=at position 0.97 with {\arrow[line width=0.9pt]{>}}},
  postaction={decorate}]
  let
     \n1 = {asin(\gap/2/\bigradius)},
     \n2 = {asin(\gap/2/\littleradius)}
  in (\n1:\bigradius) arc (\n1:360-\n1:\bigradius)
  -- (-\n2:\littleradius) arc (-\n2:-360+\n2:\littleradius)
  -- cycle;
 \filldraw [red] (1,0) circle (2pt);
 \filldraw [red] (0.5,-1) circle (2pt);
\draw[red, dashed] (1,0) -- (1.25*\bigradius,0);
\draw[red, dashed] (1,0) -- (0.5,-1);
%Labels
\node at (3.6,-0.4){$\Re(z)$};
\node at (-0.6,3.53) {$\Im(z)$};
\end{tikzpicture}
\end{figure}

\end{document}

答案1

欢迎！calc您正在加载的库允许人们构造与线相距给定距离的点。因此，以下代码中的步骤如下：

  1. 命名红点。
  2. 构造与红色虚线段平行但向左或向右移动间隙宽度一半的线段。
  3. 利用这些辅助线的交点构造路径，并根据对应线段延伸的斜率旋转小弧。

\documentclass[8pt,usenames,dvipsnames]{beamer}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.markings}
\DeclareMathOperator{\re}{Re}
\DeclareMathOperator{\im}{Im}
\begin{document} 
\begin{frame}[t]
\frametitle{A contour}
\begin{figure}
\centering
\begin{tikzpicture}[scale=0.7, every node/.style={scale=0.85},
dot/.style={circle,fill,inner sep=1pt}]
% Configurable parameters
\def\gap{0.2cm}
\def\bigradius{3cm}
\def\littleradius{0.25cm}
% Axes
\draw [help lines,->] (-1.25*\bigradius, 0) -- (1.25*\bigradius,0);
\draw [help lines,->] (0, -1.25*\bigradius) -- (0, 1.25*\bigradius);
% red path
\draw[red, dashed]  (0.5,-1) node[dot] (c1) {} --(1,0) node[dot] (c2){} 
-- (1.25*\bigradius,0) coordinate (c3);
\path let \p1=($(c2)-(c1)$), \n1={atan2(\y1,\x1)} in
 ($(c1)+(\n1:\gap/2+\littleradius/2)$) coordinate (c1')
 ($(c1')!\gap/2!90:(c2)$) coordinate (l1)
 ($(c2)!\gap/2!-90:(c1)$) coordinate (l2)
 ($(c2)!\gap/2!90:(c3)$) coordinate (l2')
 ($(c3)!\gap/2!-90:(c2)$) coordinate (l3)
 ($(c1')!\gap/2!-90:(c2)$) coordinate (r1)
 ($(c2)!\gap/2!90:(c1)$) coordinate (r2)
 ($(c2)!\gap/2!-90:(c3)$) coordinate (r2')
 ($(c3)!\gap/2!90:(c2)$) coordinate (r3);
% Path
\draw[line width=1pt,   decoration={ markings,
  mark=at position 0.06 with {\arrow[line width=0.9pt]{>}},
  mark=at position 0.2455 with {\arrow[line width=0.9pt]{>}},
  mark=at position 0.84 with {\arrow[line width=0.9pt]{>}},
  mark=at position 0.939 with {\arrow[line width=0.9pt]{>}}
  },
  postaction={decorate}]
  let
     \n1 = {asin(\gap/2/\bigradius)},
     \n2 = {asin(\gap/2/\littleradius)},
     \p1=($(c2)-(c1)$),
     \n3={atan2(\y1,\x1)}
  in (intersection of l1--l2 and l2'--l3) -- (\n1:\bigradius) 
  arc[start angle=\n1,end angle=360-\n1,radius=\bigradius]
  -- (intersection of r1--r2 and r2'--r3)
  -- (r1) 
  arc[start angle=-\n2+\n3,end angle=-360+\n2+\n3,radius=\littleradius]
  -- cycle
  ;

%Labels
\node at (3.6,-0.4){$\re(z)$};
\node at (-0.6,3.53) {$\im(z)$};
\end{tikzpicture}
\end{figure}
\end{frame}       
\end{document}

在此处输入图片描述

编辑：我调整了箭头的位置。

显然，人们可以使箭头更漂亮，甚至可以弯曲它们，但我不确定你是否想保留当前的箭头。

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