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我正在寻找

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我正在寻找

我正在寻找

我正在使用 TikZ 创建用于练习手写的备忘单。我想使用正弦波作为练习手写的图案，所以我想在同一页中显示水平和垂直正弦波。在我创建的备忘单中，我想绘制一组水平正弦波，它们从纸张的一端延伸到另一端，并且非常接近。在该组下方，我想绘制一组垂直正弦波。我使用 Inkscape 创建了以下图形来显示我正在寻找的内容。

在此处输入图片描述

我尝试过的方法

我知道如何使用 TikZ 绘制水平正弦波。请参阅下面的最小工作示例。

\documentclass{standalone}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
  \draw[opacity=0.2] (0,0) grid (10,2);
  \draw[red]  (0,1) sin (1, 2);
  \draw[blue] (1,2) cos (2, 1);
  \draw[red]  (2,1) sin (3, 0);
  \draw[blue] (3,0) cos (4, 1);
  \draw[red]  (4,1) sin (5, 2);
  \draw[blue] (5,2) cos (6, 1);
  \draw[red]  (6,1) sin (7, 0);
  \draw[blue] (7,0) cos (8, 1);
  \draw[red]  (8,1) sin (9, 2);
  \draw[blue] (9,2) cos (10,1);
\end{tikzpicture}
\end{document}

在此处输入图片描述

为了创建垂直正弦波，我尝试使用sin和cos并逐个指定坐标。但是，考虑到sin和cos函数的性质，这看起来不像第一个图形那么平滑。

%% This file is intended to be compiled by executing the following
%% commands:
%% $ pdflatex main

\documentclass{standalone}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
  \draw[opacity=0.2] (0,2) grid (10,-10);
  % Horizontal sine wave
  \draw[red]  (0,1) sin (1, 2);
  \draw[blue] (1,2) cos (2, 1);
  \draw[red]  (2,1) sin (3, 0);
  \draw[blue] (3,0) cos (4, 1);
  \draw[red]  (4,1) sin (5, 2);
  \draw[blue] (5,2) cos (6, 1);
  \draw[red]  (6,1) sin (7, 0);
  \draw[blue] (7,0) cos (8, 1);
  \draw[red]  (8,1) sin (9, 2);
  \draw[blue] (9,2) cos (10,1);
  % My attempt to draw a vertical sine wave (the result is not a
  % vertical sine wave)
  \draw[red]  (1,-0) cos  (2,-1);
  \draw[blue] (2,-1) sin  (1,-2);
  \draw[red]  (1,-2) cos  (0,-3);
  \draw[blue] (0,-3) sin  (1,-4);
  \draw[red]  (1,-4) cos  (2,-5);
  \draw[blue] (2,-5) sin  (1,-6);
  \draw[red]  (1,-6) cos  (0,-7);
  \draw[blue] (0,-7) sin  (1,-8);
  \draw[red]  (1,-8) cos  (2,-9);
  \draw[blue] (2,-9) sin  (1,-10);
\end{tikzpicture}
\end{document}

在此处输入图片描述

问题

如何在相同环境下在水平正弦波下方显示垂直正弦波tikzpicture？

答案不需要是上面显示的第一个图形的代码，它是我使用 Inkscape 创建的。在相同环境中，水平正弦波下方的垂直正弦波tikzpicture就足够了。

答案1

您是否考虑过旋转水平正弦波？

\documentclass{standalone}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
  \draw[opacity=0.2] (0,2) grid (10,-10);
  % Horizontal sine wave
  \draw[red]  (0,1) sin (1, 2);
  \draw[blue] (1,2) cos (2, 1);
  \draw[red]  (2,1) sin (3, 0);
  \draw[blue] (3,0) cos (4, 1);
  \draw[red]  (4,1) sin (5, 2);
  \draw[blue] (5,2) cos (6, 1);
  \draw[red]  (6,1) sin (7, 0);
  \draw[blue] (7,0) cos (8, 1);
  \draw[red]  (8,1) sin (9, 2);
  \draw[blue] (9,2) cos (10,1);
  % Vertical sine wave; draw horizontal & rotate
  \draw[red, rotate around={-90:(1.5,-1)}]  (0,-1) sin (1, -2);
  \draw[blue, rotate around={-90:(1.5,-1)}] (1,-2) cos (2, -1);
  \draw[red, rotate around={-90:(1.5,-1)}]  (2,-1) sin (3, -0);
  \draw[blue, rotate around={-90:(1.5,-1)}] (3,-0) cos (4, -1);
  \draw[red, rotate around={-90:(1.5,-1)}]  (4,-1) sin (5, -2);
  \draw[blue, rotate around={-90:(1.5,-1)}] (5,-2) cos (6, -1);
  \draw[red, rotate around={-90:(1.5,-1)}]  (6,-1) sin (7, -0);
  \draw[blue, rotate around={-90:(1.5,-1)}] (7,-0) cos (8, -1);
  \draw[red, rotate around={-90:(1.5,-1)}]  (8,-1) sin (9, -2);
  \draw[blue, rotate around={-90:(1.5,-1)}] (9,-2) cos (10,-1); 
\end{tikzpicture}
\end{document}

您也可以使用函数来捕获它们。

\begin{document}
    \begin{tikzpicture}
        \draw[opacity=0.2] (0,2) grid (10,-10);
        \draw[domain=0:10, smooth, samples=100, thick, red] plot (\x, {sin(pi/2 
        * \x r) + 1}); 
        \draw[domain=0:10, smooth, samples=100, thick, blue] plot ({sin(pi/2 * \x r) + 1}, -\x);

    \end{tikzpicture}
\end{document}

输出：

在此处输入图片描述

更进一步说，如果您想制作许多这样的图，我建议您创建一个函数，该函数接受起点和水平/垂直长度的输入，从而沿着它创建正弦波。

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