如何引入局部坐标系来减少代码？

Question

我编写了一个 C# 程序，通过 Latex 生成其输出。下面是所需 Latex 的一部分。有两个“范围”看起来非常相似，因此可以通过 C# for 循环生成以避免重复代码。范围必须尽可能相同。

我怀疑我可以为左右“范围”提供它们自己的本地（镜像？）坐标系。

我的问题是：有人可以指出我正确的方向来定义一个有用的范围局部坐标系，以便范围内的代码变得更加相同吗？

看一下矩形：那些减号很烦人......

我尝试了 xscale=-1/yscale=-1 选项，但似乎不起作用。

忘记节点标签吧。它们只是用来调试的。

\documentclass[11pt,a4paper]{article}
\usepackage[per-mode=symbol]{siunitx}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepackage{amssymb}
\usepackage{xcolor}
\usepackage{rotating}
\usepackage{tikz}
\tikzset{every picture/.style={line width=0.75pt}}
\usetikzlibrary{arrows.meta,calc,decorations.markings,math,quotes,angles,plotmarks}
\begin{document}
    \begin{figure}[h]
        \begin{tikzpicture}[x=0.75pt,y=0.75pt]
            \def \angleA {20} % left and right rotations
            \def \angleB {-30}
            \def \lengthA {50} % vector lengths
            \def \lengthB {60}
            \def \dist {300} % distance between A and B
            \coordinate (A) at (0,0);
            \coordinate (C) at (\lengthA,0);
            \path  (A)-- ++(\dist,0)  coordinate (B) -- ++(-\lengthB,0) coordinate(D);          
            \draw [black, dotted,thick](A)--(B); % connecting line          
            % the (fixed) resultant force vectors:
            \draw [-stealth,green] (A)-- (C) node [black, below]{\tiny{C}};
            \draw [-stealth,green] (B)-- (D) node [black, below]{\tiny{B}};
            \begin{scope}[rotate around={\angleA:(A)}]
                \draw[gray, fill=gray!40!white] (A)-- ++(0,100)-- ++(-5,0)-- ++(0,-200)-- ++(5,0)--cycle;
                % overlay C with G. G will be rotated 'away', C will remain where it is,
                % because it is outside the rotating scope:
                \coordinate (G) at (C);
                \draw [-stealth,blue] (A) -- (A|-G)  node [black,right] {\tiny{K}};
                % Save endpoint in a
                \draw [-stealth,red] (A)-- (A-|G) coordinate(a) node [black,right]{\tiny{G}};
                \pic[pic text=\tiny{$\ang{\angleA}$},blue,fill=cyan!30,draw, angle eccentricity=1.5,  angle radius=0.8cm]{angle=C--A--a};
            \end{scope}
            \begin{scope}[rotate around={\angleB:(B)}]
                \draw [gray, fill=gray!40!white] (B)-- ++(0,100)-- ++(5,0)-- ++(0,-200)-- ++(-5,0)--cycle;
                \coordinate (H) at (D);
                \draw [red,-stealth] (B)-- (B-|H) coordinate(a) node [black,left]{\tiny{H}};
                \draw [blue,-stealth] (B)-- (B|-H)  node [black,left]{\tiny{K}};
                \pic[pic text=\tiny{$\ang{\angleB}$},blue,fill=cyan!30,draw, angle eccentricity=1.5,angle       radius=0.8cm]{angle=a--B--D};
            \end{scope}
            \path (A)--(-0.3cm,0) node[left, red]{\textbf{A}};
            \path (B)-- ++(0.3cm,0) node[right, green!40!gray] {\textbf{B}};
        \end{tikzpicture}
    \end{figure}
\end{document}