将纸折叠图转换为 3D 对象或反之亦然

Question

我制作了这些命令来制作纸模型，我问是否可以在 tikz-3D 中或向后转换它们以获得 3D 视图。但绘制平面模型并在之后生成体积更容易。可以使用进行计算lualatex。如果你有想法可以遵循吗？

\documentclass[margin=2pt]{standalone}
\usepackage{tikz,xparse}
\usetikzlibrary{calc}

\tikzset{%
    patron/.style={%
        line join=round,
        rounded corners=.05pt,
        draw, thin},
    patron side/.style={patron},
    patron languette/.style={patron},
    }

\newcounter{NodePat}

\NewDocumentCommand{\PolygReg}{%
    O{3}    % nb de cotés
    m       % segment A/B
    O{A}    % nom générique
    }{%
    \foreach \a/\b in {#2} {%
    \path[patron side] let
    \p1 = ($(\a)!.5!(\b)$) ,
    \n1 = {veclen(\x1,\y1)} ,
    \p2 = ($(\p1)!1/tan(180/#1)!90:(\b)$)
    in
    (\a)--(\b)
    \foreach \i [%
        evaluate=\i as \j using (\i-1)*360/#1] in {3,...,#1} {%
        -- ($(\p2)!1!\j:(\a)$) coordinate (#3\theNodePat)
            \pgfextra{\stepcounter{NodePat}}
        }
         -- cycle ;
    }
}

\NewDocumentCommand{\Languette}{%
    O{.15}  % largeur
    D<>{45} % angle sur le premier node
    m       % les deux nodes
    D<>{45} % angle sur le second node
    O{A}
    }{%
    \foreach \b/\a in {#3} {%
    \path[patron languette] let
    \p1 = ($(#5\b)!#1/sin(#2)!-#2:(#5\a)$),
    \p2 = ($(#5\a)!#1/sin(#4)!#4:(#5\b)$)
    in
    (#5\a) -- (#5\b)
         -- (\p1)
         -- (\p2)
         -- cycle ; }
}


\makeatletter
\newcommand{\AffNodesPatron}[1][A]{%
    \newcount\X
    \X=1
    \loop
    \expandafter\ifx\csname pgf@sh@pi@A\the\X\endcsname\pgfpictureid
        \node[font={\footnotesize},red] at (A\the\X) {A\the\X} ;
        \advance \X by 1
    \else
        \X=0
    \fi
    \unless\ifnum \X=0
    \repeat
}
\makeatother

\begin{document}

\begin{tikzpicture}[scale=2]

\coordinate (A1) at (0,0) ;
\coordinate (A2) at (1,0) ;
\setcounter{NodePat}{3}

\PolygReg[4]{A1/A2}
\PolygReg{A3/A2,A5/A2,A5/A6,A5/A7}

\Languette{1/2,5/3,3/4,4/1}

%\AffNodesPatron

\end{tikzpicture}


\begin{tikzpicture}

\coordinate (A1) at (0,0) ;
\coordinate (A2) at (1,0) ;
\setcounter{NodePat}{3}

\PolygReg[6]{A1/A2,A4/A3,A6/A5,A2/A1}
\PolygReg[4]{A17/A16}
\PolygReg[6]{A20/A19,A20/A24,A23/A22,A21/A19}
\PolygReg[4]{A5/A4,A3/A2,A1/A6,A24/A23,A22/A21}

\Languette<30>{3/7,7/8,8/9,9/10,10/4,37/38,5/11,11/12,12/13,13/14,14/6,41/42,%
    42/1,15/16,16/19,21/45,22/29,32/23,28/20,17/18,2/39,39/40}<30>

%\AffNodesPatron

\end{tikzpicture}
\end{document}