当我绘制这个三角形时，如何修复“尺寸太大”？

Question

我使用此代码绘制三角形。当我选择时a = b = c = 5，我得到了结果。

\documentclass[12pt, border = 1mm]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{intersections,calc,backgrounds}
\begin{document}
    \tdplotsetmaincoords{70}{80}
    \begin{tikzpicture}[tdplot_main_coords,line join = round, line cap = round]

    \pgfmathsetmacro{\a}{5} 
    \pgfmathsetmacro{\b}{5} 
    \pgfmathsetmacro{\c}{5} 
    \pgfmathsetmacro\myr{{sqrt(- pow(\a,2) *pow(\b,2)* pow(\c,2)/(pow(\a,4)  + pow(\b,4)  + pow(\c,4)- 2 *pow(\a,2) *pow(\b,2)  - 2*pow(\c,2) *pow(\b,2)-2*pow(\c,2) *pow(\a,2) ))}}
    \coordinate (A) at (0,0,0);
    \coordinate (B) at (\c,0,0);
    \coordinate (C) at  ({(pow(\b,2) + pow(\c,2) - pow(\a,2))/(2*\c)},{sqrt((\a+\b-\c) *(\a-\b+\c) *(-\a+\b+\c)* (\a+\b+\c))/(2*\c)},0);
    \coordinate (T) at  (\c/2, {\c* (\a*\a + \b*\b - \c*\c)/(2*sqrt((\a+\b-\c) *(\a-\b+\c)* (-\a+\b+\c)* (\a+\b+\c)))},0);

    \foreach \point/\position in {A/left,B/below,C/above,T/below}
    {
        \fill (\point) circle (1.8pt);
        \node[\position=3pt] at (\point) {$\point$};
    }
    \begin{scope}[canvas is xy plane at z=0]
    \draw[thick] (T) circle (\myr); 
    \end{scope} 
    \end{tikzpicture}
    \end{document}

如果我使用a = b = c = 6或更大的值，则无法获得结果。我该如何获得结果？

Answer 1

有一些标准方法来处理这个问题。其中之一是使用库fpu。（fpu在John Kormylo 的评论，但我没有那里提到的问题。）但是，正如你自己注意到的，在某些构造中，例如arc仅仅打开fpu可能会导致问题。为了让你更方便，我添加了一个宏\PgfmathsetmacroFPU，它在本地打开库，解析表达式，并将结果“走私”出组。因此，宏的定义将是本地的，就像普通的情况一样\pgfmathsetmacro。请注意，\pgfmathsmuggle已添加到较新版本的中pgf，因此如果您的 TeX 安装过时，它可能无法工作。对不起 overleaf 用户！有关走私的更多信息以及替代命令可以在以下答案中找到这个问题。

\documentclass[12pt, border = 1mm]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{intersections,calc,backgrounds,fpu} 
\newcommand{\PgfmathsetmacroFPU}[2]{\begingroup%
\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
\pgfmathsetmacro{#1}{#2}%
\pgfmathsmuggle#1\endgroup}
\begin{document}
\tdplotsetmaincoords{70}{80}
\begin{tikzpicture}[tdplot_main_coords,line join = round, line cap = round]
    \pgfmathsetmacro{\a}{6} 
    \pgfmathsetmacro{\b}{6} 
    \pgfmathsetmacro{\c}{6} 
    \PgfmathsetmacroFPU{\myr}{{sqrt(-
     pow(\a,2) *pow(\b,2)* pow(\c,2)/ (pow(\a,4)  + pow(\b,4)  + pow(\c,4)- 2
     *pow(\a,2) *pow(\b,2)  - 2*pow(\c,2) *pow(\b,2)-2*pow(\c,2) *pow(\a,2) ))}}
    \PgfmathsetmacroFPU{\Angleone}{-90} 
    \PgfmathsetmacroFPU{\Angletwo}{60}
    \coordinate (E) at ({\c/2 + \myr*cos(\Angleone)},{\c* (\a*\a + \b*\b -
     \c*\c)/(2*sqrt((\a+\b-\c) *(\a-\b+\c)* (-\a+\b+\c)* (\a+\b+\c))) +
     \myr*sin(\Angleone)},0 );  \coordinate (F) at ({\c/2 +
    \myr*cos(\Angletwo)},{\c* (\a*\a + \b*\b - \c*\c)/(2*sqrt((\a+\b-\c)
     *(\a-\b+\c)* (-\a+\b+\c)* (\a+\b+\c))) + \myr*sin(\Angletwo)},0 ); 
    \coordinate (A) at (0,0,0);
    \coordinate (B) at (\c,0,0);
    \coordinate (C) at  ({(pow(\b,2) + pow(\c,2) - pow(\a,2))/(2*\c)},{sqrt((\a+\b-\c) *(\a-\b+\c) *(-\a+\b+\c)* (\a+\b+\c))/(2*\c)},0);
    \coordinate (T) at  (\c/2, {\c* (\a*\a + \b*\b - \c*\c)/(2*sqrt((\a+\b-\c) *(\a-\b+\c)* (-\a+\b+\c)* (\a+\b+\c)))},0);
    \foreach \point/\position in {A/left,B/below,C/above,T/below}
    {
        \fill (\point) circle (1.8pt);
        \node[\position=3pt] at (\point) {$\point$};
    }
    \begin{scope}[canvas is xy plane at z=0]
    \draw[thick] (T) circle (\myr); 
    \end{scope}
    \pgfmathsetmacro{\Angleone}{-90} 
    \pgfmathsetmacro{\Angletwo}{60}  
    \draw[thick] (E) arc[start angle=\Angleone,end angle=\Angletwo,radius=\myr]; 
\end{tikzpicture}
\end{document}