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如何将线弯曲成圆圈？

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如何将线弯曲成圆圈？

enter image description here

我正在尝试模仿上面的 GIF，但我很难让线像 GIF 那样弯曲到外圆。

\documentclass[tikz]{standalone}
\usepackage{tikz}

\usetikzlibrary{intersections}

\begin{document}
\foreach \x  in {0,0.1,...,1.1}
{
 \begin{tikzpicture}[scale=3]
 \draw (0,0) circle (1);
 \draw (-2.5,0)--(2.5,0); 
 \draw (0,-1.5)--(0,1.5);   
 \draw [red,very thick] (0,0)--(\x,0);      
 \end{tikzpicture}      
}

\foreach \angle  in {180,170,...,90}{
 \begin{tikzpicture}[scale=3]
 \draw (0,0) circle (1cm);
 \draw (-2.5,0)--(2.5,0); 
 \draw (0,-1.5)--(0,1.5);   
 \draw [red,very thick] (0,0)--(1,0);   
 \draw [red,very thick,xshift=1cm] (0,0) --(\angle:1);          
\end{tikzpicture}
}



 \foreach \angle in {0,10,20,30,40,50,57.35}
 {
\begin{tikzpicture}[scale=3]
\draw (0,0) circle (1cm);
\draw (-2.5,0)--(2.5,0); 
\draw (0,-1.5)--(0,1.5);    

\draw [red,very thick,xshift=1cm] (0,0) --(90:1);
\filldraw [yellow!80](60:1) circle(0.02);
\draw[blue!80,very thick] (1cm,0)
arc [start angle=0, end angle=57.35, radius=1cm];
\filldraw [red!80](57.35:1) circle(0.02);
\filldraw [red!80](0:1) circle(0.02);   

\draw[blue!80,very thick] (0,0) -- (\angle+57.35:1);

\draw[blue!80,very thick] (0,0) -- (\angle:1)
arc [start angle=\angle, end angle=\angle + 57.35, radius=1cm];
\filldraw [red!80](\angle:1) circle(0.02);
\filldraw [red!80](\angle+57.35:1) circle(0.02);    
\end{tikzpicture}
 }

\end{document}

这是我目前所做的。我能够找到线应该弯曲的坐标，即通过手动计算的角度。

enter image description here

答案1

基本上，你想画出具有特定尺寸的圆或椭圆的一部分。这被称为圆弧。

第一次尝试——直接调整解决方案

\documentclass[tikz]{standalone}
\usepackage{tikz}

\usetikzlibrary{intersections}

\begin{document}
\foreach \k  in {0,0.1,...,1.001}{
  \begin{tikzpicture}[scale=3]
  \draw [white, fill] (-2.5,-1.5) rectangle (2.5,1.5);% you probably don't need this, depending on gif creation. I just needed it for properly creating a gif with white background.
  \draw (0,0) circle (1cm);
  \draw (-2.5,0)--(2.5,0); 
  \draw (0,-1.5)--(0,1.5);   
  \draw [red,very thick] (0,0)--(1,0);
  \draw [red,very thick,xshift=1cm] (0,0) arc (0:1r:\k\space and 1.1884-0.1884*\k);
  \end{tikzpicture}
}
\end{document}

result

这将绘制一个椭圆的圆弧，并将其所属的椭圆的尺寸从宽度更改0为正确的圆形。这不会产生起始线和中间线的正确高度。为了快速解决这个问题，我引入了一个小小的解决方法：

圆弧的高度（最高点的 y 值）为。但如果是直线，sin(1)则应为，并减小到。因此，我在开始时相应地拉伸高度并进行线性插值。该数字实际上是为了校正弧长。1sin(1)1.1884sin(1)^-1

当然，你也可以做一些数学运算。

正确的方法

为了获得“正确”的线路而不用像上面那样的肮脏伎俩，您可以使用以下命令：

\documentclass[tikz]{standalone}
\usepackage{tikz}

\usetikzlibrary{intersections}
\def\zero{0}

\begin{document}
\foreach \k  in {0,0.1,...,1.001}{
  \begin{tikzpicture}[scale=3]
  \draw [white, fill] (-2.5,-1.5) rectangle (2.5,1.5);% you probably don't need this, depending on gif creation. I just needed it for properly creating a gif with white background.
  \draw (0,0) circle (1cm);
  \draw (-2.5,0)--(2.5,0); 
  \draw (0,-1.5)--(0,1.5);   
  \draw [red,very thick] (0,0)--(1,0);
  \ifx\k\zero
    \draw [red,very thick] (1,0)--(1,1);
  \else
    \draw[domain=0:\k r,smooth,variable=\t,red, very thick, xshift=1cm]  plot ({1/\k*cos(\t)-1/\k},{1/\k*sin(\t)});
  \fi
  \end{tikzpicture}
}
\end{document}

result2

此图生成1具有曲率的精确长度的线\k。我在这里使用了参数图，而不是arctikz 内置的图。

注解

为了制作这些动画，我使用了ImageMagick：

convert -delay 10 -loop 0 -background white -alpha remove the.pdf result.gif

可以使用以下方法创建更平滑的版本：

\foreach \k  in {0,0.04,...,1.001}{

而不是另一\foreach行。要微调相应的动画（并使其稍微大一些）：

convert -density 100 -loop 0 -background white -alpha remove -delay 100 the.pdf\[0\] -delay 4 the.pdf\[1-24\] -delay 100 the.pdf\[25\] result.gif

result

在这里，我手动选择了不同页面范围的延迟（以百分之一秒为单位），从零开始0，通过在 pdf 文件名后添加\[page\]。第一张图片和最后一张图片应显示 1 秒，其间所有内容显示 4/100 秒。

笔记：根据您的 shell，您可能不需要转义方括号，即使用the.pdf[..]而不是the.pdf\[..\]。感谢@AndréC 的提及。

笔记：虽然-background white -alpha remove图片中没有白色矩形作为背景应该可以正常工作，但它似乎并不总是能正常工作。所以我再次在代码中添加了矩形。

答案2

只是为了好玩，一个允许完成初始动画的代码，当然基于显示的优秀代码，以同样的方式我使用 Imagemagick 生成 gif 中的输出；原始文件有 113 帧 @ 105Kb，代码生成 110 帧 @ 648Kb，这可能会因 imagemagic 设置而异；但是，原始文件有一些具有特定延迟的帧，并且使用 imagemagick 声明它们的方式非常繁琐，特别是对于我使用 arara 进行编译的人来说，所以我使用了另一个程序（fireworks），它允许我在图形界面中编辑延迟，导出的文件自动压缩为 176Kb。

原始结果： enter image description here

延时编辑： enter image description here 梅威瑟：

% arara: pdflatex: {synctex: yes, action: nonstopmode}
% arara: animate: {density: 200, delay: 5, other: -background white -alpha remove}
% arara: showanimate
\documentclass[tikz,border=10pt]{standalone}
\usepackage{mathptmx} 
\definecolor{mygreen}{HTML}{019A01}
\usetikzlibrary{calc,arrows.meta}

\begin{document}
\begin{tikzpicture}[scale=2]% The initial frame 
    \path[draw,thick,gray!50] (0,0)
        edge (0:2)
        edge (90:1.2)
        edge (180:2)
        edge (270:1.2);
\end{tikzpicture}
\foreach \x  in {0.05 ,0.1 ,0.25 ,0.4 ,0.6,0.7,0.8,0.95}{%Radio 0 to 1 increment
\begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[red,thick] (0,0) -- (\x,0) coordinate (A);
    \fill[red](0,0) circle (1pt);
    \fill[red](A) circle (1pt);
\end{tikzpicture}   
}

\foreach \x  in {0,0.02,0.05,0.1,0.2,...,0.9,0.95,0.98,1}{% Draw the blue circle r=1
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360*\x:1);
    \draw[red,thick] (0,0) -- (360*\x:1) coordinate (A);
    \fill[red](0,0) circle (1pt);
    \fill[red](A) circle (1pt);
    \end{tikzpicture}   
}
\foreach \x  in {0,0.2,1,0.2}{% Show the radious label fading 
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \fill[red](0,0) circle (1pt);
    \fill[red](1,0) circle (1pt);
    \draw[red,thick,text opacity=\x] (0,0) -- (0:1) node[midway,anchor=south,font=\Huge]{r};
    \end{tikzpicture}   
}

\foreach \x  in {0,0.02,0.05,0.1,0.2,...,0.9,0.95,0.98,1}{%Rotate Radio from (1,0)
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \fill(0,0) circle (1pt);
    \fill[red](1,0) circle (1pt);
    \draw[red,thick] (1,0) -- ++(180-90*\x:1)coordinate (A);
    \fill[red](A) circle (1pt);
    \end{tikzpicture}   
}

\foreach \x  in {0,0.02,0.05,0.1,0.2,...,0.9,0.95,0.98,1}{%Nice bending @Nox trick
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \fill(0,0) circle (1pt);
    \fill[red](1,0) circle (1pt);
    \draw [red,xshift=1cm,thick] (0,0) arc (0:180/pi:\x\space and 1.1884-0.1884*\x) node[circle,fill,inner sep=1pt]{} circle (1pt);
    \end{tikzpicture}   
}
\foreach \x  in {0.1,0.2}{%Show 1 rad
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[red,thick](0:1) coordinate (A) arc (0:180/pi:1) coordinate (B);
    \draw[mygreen,fill,fill opacity=0.2*\x,draw opacity=\x](0,0)
        -- (0:0.2) arc (0:180/pi:0.2) -- cycle;
    \draw[mygreen,opacity=\x,thick] (0,0) edge(A) edge(B);
    \fill[red](A) circle (1pt);
    \fill[red](B) circle (1pt);
    \fill(0,0) circle (1pt);

    \end{tikzpicture}   
}

\foreach \x  in {0,0.2,1}{%Show text 1 rad
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[red,thick](0:1) coordinate (A) arc (0:180/pi:1) coordinate (B);
    \draw[mygreen,fill,fill opacity=0.2,draw opacity=1](0,0)
    -- (0:0.2) arc (0:180/pi:0.2) -- cycle;
    \draw[mygreen,opacity=1,thick] (0,0) edge(A) edge(B);
    \fill[red](A) circle (1pt);
    \fill[red](B) circle (1pt);
    \fill(0,0) circle (1pt);
    \draw node[mygreen,font=\LARGE,opacity=\x] at (0,-0.2){\bf 1 rad};
    \end{tikzpicture}   
}
\foreach \x  in {0.05 ,0.1 ,0.25 ,0.4 ,0.6,0.7,0.8,0.95}{%Show 1 rad
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[mygreen,thick] (0:1) arc (0:180/pi*\x:1);
    \draw[red,thick](180/pi*\x:1) coordinate (A) arc (180/pi*\x:180/pi+180/pi*\x:1) coordinate (B);
    \draw[mygreen,fill,fill opacity=0.2,draw opacity=1](0,0)
    -- (0:0.2) arc (0:180/pi+180/pi*\x:0.2) -- cycle;
    \draw[mygreen,opacity=1,thin] (0,0) -- (A);
    \draw[mygreen,opacity=1,thick] (0,0) edge(1,0) edge(B);
    \fill[red](A) circle (1pt);
    \fill[red](B) circle (1pt);
    \fill(0,0) circle (1pt);
    \fill[mygreen](1,0) circle (1pt);
    \draw node[mygreen,font=\LARGE,opacity=1-\x] at (0,-0.2){\bf 1 rad};
    \draw node[mygreen,font=\LARGE,opacity=\x] at (0,-0.2){\bf 2 rad};
    \end{tikzpicture}   
}
\foreach \x  in {0.05 ,0.1 ,0.25 ,0.4 ,0.6,0.7,0.8,0.95}{%Show 2 rad
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[mygreen,thick] (0:1) arc (0:180/pi+180/pi*\x:1);
    \draw[red,thick](180/pi+180/pi*\x:1) coordinate (A) arc (180/pi+180/pi*\x:360/pi+180/pi*\x:1) coordinate (B);
    \draw[mygreen,fill,fill opacity=0.2,draw opacity=1](0,0)
    -- (0:0.2) arc (0:360/pi+180/pi*\x:0.2) -- cycle;
    \draw[mygreen,opacity=1,thin] (0,0) edge (A) edge(180/pi:1);
    \draw[mygreen,opacity=1,thick] (0,0) edge(1,0) edge(B);
    \fill[red](A) circle (1pt);
    \fill[red](B) circle (1pt);
    \fill(0,0) circle (1pt);
    \fill[mygreen](1,0) circle (1pt);
    \fill[mygreen](180/pi:1) circle (0.75pt);
    \draw node[mygreen,font=\LARGE,opacity=1-\x] at (0,-0.2){\bf 2 rad};
    \draw node[mygreen,font=\LARGE,opacity=\x] at (0,-0.2){\bf 3 rad};
    \end{tikzpicture}   
}
\foreach \x  in {0.05 ,0.1 ,0.25 ,0.4 ,0.6,0.7,0.8,0.95}{%Show 3 rad
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[mygreen,thick] (0:1) arc (0:360/pi+180*\x-360/pi*\x:1);
    \draw[red,thick]
        (360/pi+180/pi*\x:1) coordinate (A) 
        arc (360/pi+180/pi*\x:360/pi+180/pi*\x+180*\x+180/pi-720/pi*\x:1) coordinate (B);
    \draw[mygreen,fill,fill opacity=0.2,draw opacity=1](0,0)
    -- (0:0.2) arc (0:360/pi+180/pi*\x:0.2) -- cycle;
    \draw[mygreen,opacity=1,thin] (0,0) edge (A) edge(180/pi:1) edge(360/pi:1);
    \draw[mygreen,opacity=1,thick] (0,0) edge(1,0) edge(B);
    \fill[red](A) circle (1pt);
    \fill[red](B) circle (1pt);
    \fill(0,0) circle (1pt);
    \fill[mygreen](1,0) circle (1pt);
    \fill[mygreen](180/pi:1) circle (0.75pt);
    \fill[mygreen](360/pi:1) circle (0.75pt);
    \draw node[mygreen,font=\LARGE,opacity=1-\x] at (0,-0.2){\bf 3 rad};
        \draw node[mygreen,font=\LARGE,opacity=\x] at (0,-0.2){\bf $\mathbf{\pi}$ rad};
    \end{tikzpicture}   
}
\foreach \x  in {0.4,0.8,1}{%Disapear lines
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[mygreen,thick] (0:1) arc (0:180:1);
    \draw[mygreen,fill,fill opacity=0.2,draw opacity=1](0,0)
    -- (0:0.2) arc (0:180:0.2) -- cycle;
    \draw[mygreen,opacity=1-\x,thin] (0,0) edge(180/pi:1) edge(360/pi:1) edge(540/pi:1);
    \draw[mygreen,opacity=1,thick] (0,0) edge(1,0) edge(-1,0);
    \fill(0,0) circle (1pt);
    \fill[mygreen](1,0) circle (1pt);
    \fill[mygreen,opacity=1-\x](180/pi:1) circle (0.75pt);
    \fill[mygreen,opacity=1-\x](360/pi:1) circle (0.75pt);
    \fill[mygreen,opacity=1-\x](540/pi:1) circle (0.75pt);
    \fill[mygreen](-1,0) circle (1pt);
    \draw node[mygreen,font=\LARGE,opacity=1] at (0,-0.2){\bf $\mathbf{\pi}$ rad};
    \end{tikzpicture}   
}
\foreach \x  in {0.05 ,0.1 ,0.25 ,0.4 ,0.6,0.7,0.8,0.95}{%Show move pi rad
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[mygreen,thick] (0:1) arc (0:180:1);
    \draw[mygreen,fill,fill opacity=0.2,draw opacity=1](0,0)
    -- (0:0.2) arc (0:180:0.2) -- cycle;
    \draw[mygreen,opacity=1,thick] (0,0) edge(1,0) edge(-1,0);
    \fill(0,0) circle (1pt);
    \fill[mygreen](1,0) circle (1pt);
    \fill[mygreen](-1,0) circle (1pt);
    \draw node[mygreen,font=\LARGE] at (0,0.7*\x-0.2){\bf $\mathbf{\pi}$ rad};
    \end{tikzpicture}   
}
\foreach \x  in {0.05 ,0.1 ,0.25 ,0.4 ,0.6,0.7,0.8,0.95}{%Show  2 pi rad
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[mygreen,thick] (0:1) arc (0:180+180*\x:1) coordinate (a);
    \draw[mygreen,fill,fill opacity=0.2,draw opacity=1](0,0)
    -- (0:0.2) arc (0:180+180*\x:0.2) -- cycle;
    \draw[mygreen,opacity=1,thick] (0,0) edge(1,0) edge(-1,0) edge(a);
    \fill(0,0) circle (1pt);
    \fill[mygreen](1,0) circle (1pt);
    \fill[mygreen](a) circle (1pt);
    \fill[mygreen](-1,0) circle (0.75pt);
    \draw node[mygreen,font=\LARGE,opacity=1-\x] at (0,0.5){\bf $\mathbf{\pi}$ rad};
    \draw node[mygreen,font=\LARGE,opacity=\x] at (0,0.5){\bf $\mathbf{2\pi}$ rad};
    \end{tikzpicture}   
}
\foreach \x  in {0.4,0.6,0.8,1}{%Show  2 pi rad
    \begin{tikzpicture}[scale=2]
    \path[draw,thick,gray!50] (0,0)
    edge (0:2)
    edge (90:1.2)
    edge (180:2)
    edge (270:1.2);
    \draw[blue] (0:1) arc (0:360:1);
    \draw[mygreen,thick] (0:1) arc (0:360:1) coordinate (a);
    \draw[mygreen,fill,fill opacity=0.2-0.2*\x,draw opacity=1-\x](0,0)
    -- (0:0.2) arc (0:360:0.2) -- cycle;
    \draw[mygreen,opacity=1-\x,thick] (0,0) edge(1,0) edge(-1,0) edge(a);
    \fill(0,0) circle (1pt);
    \fill[mygreen,opacity=1-\x](1,0) circle (1pt);
    \fill[mygreen,opacity=1-\x](a) circle (1pt);
    \fill[mygreen,opacity=1-\x](-1,0) circle (0.75pt);
    \draw node[mygreen,font=\LARGE] at (0,0.5){\bf $\mathbf{2\pi}$ rad};
    \end{tikzpicture}   
}
\end{document}

答案3

根据 nox 的良好回答，这是一个仅绘制圆段而不是椭圆的版本：它用于确定以不同角度开始的pgfmath弧长圆段的半径。1(1,0)

\documentclass[tikz]{standalone}
\usepackage{tikz,ifthen}

\begin{document}
\foreach \x  in {0,0.05,...,1.001}{
    \begin{tikzpicture}[scale=3]
    \draw [white, fill] (-2.5,-1.5) rectangle (2.5,1.5);% you probably don't need this, I just needed it for properly creating a gif with white background
    \draw (0,0) circle (1cm);
    \draw (-2.5,0)--(2.5,0); 
    \draw (0,-1.5)--(0,1.5);   
    \draw [red,very thick] (0,0)--(1,0);
    \ifthenelse{\equal\x0}{
      \draw [red,very thick] (1,0)--(1,1);
    }{
      \draw [red,very thick,xshift=1cm] (0,0) arc (0:deg(\x):1/\x);
    }
    \end{tikzpicture}
}
\end{document}

enter image description here

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