ピラミッドの後ろに破線の円弧を描くにはどうすればいいですか?

ピラミッドの後ろに破線の円弧を描くにはどうすればいいですか?

この絵のように描こうとしていますここに画像の説明を入力してください

私は試した

\documentclass[border=2 mm,12pt]{standalone}
\usepackage{fouriernc}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\begin{document}
    \tdplotsetmaincoords{70}{180}
    \begin{tikzpicture}[tdplot_main_coords,line join = round, line cap = round]
        \coordinate (A) at (0,0,0);
        \coordinate (S) at (7/2,{-7*sqrt(3)/6},14/3);
        \coordinate (C) at (7,0,0);
        \coordinate (B) at  ({65/14},{15*sqrt(3)/14},0);
        \coordinate (I) at  (7/2,{-7*sqrt(3)/6},0) ;

        \draw[very thick] (A) -- (B) (B) -- (C)  (S) --  (A) (S) --(B) (S) -- (C) ;

        \draw[dashed ] (C) -- (A) (I) -- (A) (I) -- (B) (I) --(C) (S) --(I) ;
        \draw[very thick] (I) circle ({7/sqrt(3)});
        \foreach \point/\position in {A/below,B/below,C/below,
            I/below,S/above}
        {
            \fill (\point) circle (1.5pt);
            \node[\position=3pt] at (\point) {$\point$};
        }
          \end{tikzpicture}
  \end{document}

そして

ここに画像の説明を入力してください

ピラミッドの後ろに破線の円弧を描くにはどうすればいいですか?

答え1

常にうまくいくのはreverseclip騙す

\documentclass[border=2 mm,12pt]{standalone}
\usepackage{fouriernc}
\usepackage{tikz}
\usepackage{tikz-3dplot}
% based on https://tex.stackexchange.com/a/12033/121799
\tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle 
  (current bounding box.north east)} }}
\begin{document}
    \tdplotsetmaincoords{70}{180}
    \begin{tikzpicture}[tdplot_main_coords,line join = round, line cap = round]
        \coordinate (A) at (0,0,0);
        \coordinate (S) at (7/2,{-7*sqrt(3)/6},14/3);
        \coordinate (C) at (7,0,0);
        \coordinate (B) at  ({65/14},{15*sqrt(3)/14},0);
        \coordinate (I) at  (7/2,{-7*sqrt(3)/6},0) ;

        \draw[very thick] (A) -- (B) (B) -- (C)  (S) --  (A) (S) --(B) (S) -- (C) ;

        \draw[dashed ] (C) -- (A) (I) -- (A) (I) -- (B) (I) --(C) (S) --(I) ;
        \path (I) circle ({1.01*7/sqrt(3)});
        \begin{scope}
         \clip (S) -- (C) -- (B) -- (A) -- cycle [reverseclip];
         \draw[very thick] (I) circle ({7/sqrt(3)});
        \end{scope}
        \begin{scope}
         \clip (S) -- (C) -- (B) -- (A);
         \draw[dashed] (I) circle ({7/sqrt(3)});
        \end{scope}
        \foreach \point/\position in {A/below,B/below,C/below,
            I/below,S/above}
        {
            \fill (\point) circle (1.5pt);
            \node[\position=3pt] at (\point) {$\point$};
        }
    \end{tikzpicture}
\end{document}

ここに画像の説明を入力してください

答え2

ライブラリを使用するとintersections、コードは次のようになります (必要な行を赤で強調表示しています)。

ここに画像の説明を入力してください

\documentclass[border=2 mm,12pt]{standalone}
\usepackage{fouriernc}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{intersections}
\colorlet{bgcolor}{white}

\tikzset{
    overdraw/.style={preaction={draw,bgcolor,line width=#1}},
    overdraw/.default=2pt
}

\begin{document}
    \tdplotsetmaincoords{70}{180}
    \begin{tikzpicture}[tdplot_main_coords,line join = round, line cap = round]
        \coordinate (A) at (0,0,0);
        \coordinate (S) at (7/2,{-7*sqrt(3)/6},14/3);
        \coordinate (C) at (7,0,0);
        \coordinate (B) at  ({65/14},{15*sqrt(3)/14},0);
        \coordinate (I) at  (7/2,{-7*sqrt(3)/6},0) ;

        \draw[very thick] (A) -- (B) (B) -- (C) (S) --(B);
        \draw[very thick,name path=SC] (S) -- (C);
        \draw[very thick,name path=SA] (S) --  (A);

        \draw[very thick,name path=CIR] (I) circle ({7/sqrt(3)});

        \path [name intersections={of=SC and CIR, by={C,C'}}];
        \path [name intersections={of=SA and CIR, by={D,D'}}];
        \draw[red,dashed,overdraw] (C') to [bend right=-10] (D'); %to draw the curved path
        \draw[dashed] (C) -- (A) (I) -- (A) (I) -- (B) (I) --(C) (S) --(I) ;
        \foreach \point/\position in {A/below,B/below,C/below,
            I/below,S/above}
        {
            \fill (\point) circle (1.5pt);
            \node[\position=3pt] at (\point) {$\point$};
        }
          \end{tikzpicture}
  \end{document} 

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