TikZ 数学中的奇怪行为

Question

我正在制作一个 Tikz 图形，它使用 sin 和 cos 函数。目前，我使用 Python 脚本来计算六个函数参数，这些参数被提供给 Tikz “g” 函数，如下所示：

\documentclass{article}


\usepackage{tikz}
\usepackage{adjustbox}
\usetikzlibrary{calc,shadings,shadows,shapes.arrows,positioning, shadows,arrows, trees,fit,shadings,calc,arrows,shapes,shadows,shapes.arrows,decorations.markings, decorations.pathreplacing}


\newcommand*{\g}[6]{
\begin{tikzpicture}[]
  \coordinate (needle_a) at (#1, #2);
  \coordinate (needle_b) at (#3, #4);
  \coordinate (needle_c) at (#5, #6);
  \draw [top color=white, bottom color=orange, shading angle=45] (needle_a) -- (needle_b) -- (needle_c) -- cycle;
\end{tikzpicture}}


\newcommand*{\f}[1]{
\begin{tikzpicture}[]

  \pgfmathparse{#1}
  \pgfmathsetmacro{\angle}{\pgfmathresult}

  \pgfmathparse{cos(\angle + 0.314) * 0.1}
  \pgfmathsetmacro{\mya}{\pgfmathresult}

  \pgfmathparse{sin(\angle + 0.314) * 0.1 + 0.15}
  \pgfmathsetmacro{\myb}{\pgfmathresult}

  \pgfmathparse{cos(\angle - 0.314) * 0.1}
  \pgfmathsetmacro{\myc}{\pgfmathresult}

  \pgfmathparse{sin(\angle - 0.314) * 0.1 + 0.15}
  \pgfmathsetmacro{\myd}{\pgfmathresult}

  \pgfmathparse{cos(\angle) * 0.5}
  \pgfmathsetmacro{\mye}{\pgfmathresult}

  \pgfmathparse{sin(\angle) * 0.5 + 0.15}
  \pgfmathsetmacro{\myf}{\pgfmathresult}

  \coordinate (needle_a) at (\mya, \myb);
  \coordinate (needle_b) at (\myc, \myd);
  \coordinate (needle_c) at (\mye, \myf);

  \draw [top color=white, bottom color=orange, shading angle=45] (needle_a) -- (needle_b) -- (needle_c) -- cycle;

\end{tikzpicture}}

\begin{document}
  \begin{figure}
    \centering
    \begin{adjustbox}{width=0.8\textwidth}
    \begin{tikzpicture}[]
      \node [scale=2.5] (s1) at (0, 0) {\g{0.088}{0.198}{0.099}{0.137}{0.491}{0.244}};
    \end{tikzpicture}
    \end{adjustbox}
    \caption{g}
  \end{figure}
  \begin{figure}
    \centering
    \begin{adjustbox}{width=0.8\textwidth}
    \begin{tikzpicture}[]
      \node [scale=2.5] (s2) at (0, 0) {\f{0.188}};
    \end{tikzpicture}
    \end{adjustbox}
    \caption{f}
  \end{figure}
\end{document}

然而，这些参数都是基于单个数值（即角度），并按如下方式计算：

a = math.cos(angle + 0.314) * 0.1
b = math.sin(angle + 0.314) * 0.1 + 0.15
c = math.cos(angle - 0.314) * 0.1
d = math.sin(angle - 0.314) * 0.1 + 0.15
e = math.cos(angle) * 0.5
f = math.sin(angle) * 0.5 + 0.15

因此，我认为直接在 Tikz 中计算这些值会很好，而不必依赖额外的脚本。我尝试在“f”函数中实现这一点，该函数只接受一个参数，但由于某种原因，它不能按预期工作。我在下面添加了结果图片。理论上，两个图应该看起来一样。

谢谢你的帮助，斯文

Answer 1

您必须使用\deg(angle)或将角度转换为度数\angle r：

\documentclass{article}
\usepackage{tikz}
\usepackage{adjustbox}

\newcommand*{\g}[6]{
\begin{tikzpicture}[]
  \coordinate (needle_a) at (#1, #2);
  \coordinate (needle_b) at (#3, #4);
  \coordinate (needle_c) at (#5, #6);
  \draw [top color=white, bottom color=orange, shading angle=45] (needle_a) -- (needle_b) -- (needle_c) -- cycle;
\end{tikzpicture}}

\newcommand*{\f}[1]{%
\begin{tikzpicture}[]
  \pgfmathsetmacro{\angle}{#1 r}
%
  \pgfmathsetmacro{\mya}{cos(\angle + 0.314 r) * 0.1}
  \pgfmathsetmacro{\myb}{sin(\angle + 0.314 r) * 0.1 + 0.15}
  \pgfmathsetmacro{\myc}{cos(\angle - 0.314 r) * 0.1}
  \pgfmathsetmacro{\myd}{sin(\angle - 0.314 r) * 0.1 + 0.15}
  \pgfmathsetmacro{\mye}{cos(\angle) * 0.5}
  \pgfmathsetmacro{\myf}{sin(\angle) * 0.5 + 0.15}
%
  \coordinate (needle_a) at (\mya, \myb);
  \coordinate (needle_b) at (\myc, \myd);
  \coordinate (needle_c) at (\mye, \myf);
%
  \draw [top color=white, bottom color=orange, shading angle=45]
    (needle_a) -- (needle_b) -- (needle_c) -- cycle;
\end{tikzpicture}}

\begin{document}
  \begin{figure}
    \centering
    \begin{adjustbox}{width=0.8\textwidth}
    \begin{tikzpicture}[]
      \node [scale=2.5] (s1) at (0, 0) {\g{0.088}{0.198}{0.099}{0.137}{0.491}{0.244}};
    \end{tikzpicture}
    \end{adjustbox}
    \caption{g}
  \end{figure}
  \begin{figure}
    \centering
    \begin{adjustbox}{width=0.8\textwidth}
    \begin{tikzpicture}[]
      \node [scale=2.5] (s2) at (0, 0) {\f{0.188}};
    \end{tikzpicture}
    \end{adjustbox}
    \caption{f}
  \end{figure}
\end{document}