tikz-3d 移动矩形

Question

考虑以下代码：

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{amsmath}

\newcommand{\ptsize}{1.5pt}

\usepackage{xcolor}
\definecolor{MyColor1}{rgb}{0.24, 0.59, 0.32}
\definecolor{MyColor2}{rgb}{0.85, 0.49, 0.19}
\definecolor{MyColor3}{rgb}{0.22, 0.42, 0.69}

\begin{document}
\tdplotsetmaincoords{75}{130}
\begin{tikzpicture}[tdplot_main_coords]

% Define all the nodes necessary for the drawing
\coordinate (alpha1) at (1,-1,0);
\coordinate (alpha2) at (0,1,-1);
\coordinate (alpha3) at (0,0,2);

\coordinate (12) at ($ (alpha1) + (alpha2) $);
\coordinate (23) at ($ (alpha2) + (alpha3) $);
\coordinate (123) at ($ (alpha1) + (alpha2) + (alpha3) $);
\coordinate (223) at ($ (alpha2) + (alpha2) + (alpha3) $);
\coordinate (1223) at ($ (alpha1) + (alpha2) + (alpha2) + (alpha3) $);
\coordinate (11223) at ($ (alpha1) + (alpha1) + (alpha2) + (alpha2) + (alpha3) $);

\coordinate (-alpha1) at (-1,1,0);
\coordinate (-alpha2) at (0,-1,1);
\coordinate (-alpha3) at (0,0,-2);

\coordinate (-12) at ($ (-alpha1) + (-alpha2) $);
\coordinate (-23) at ($ (-alpha2) + (-alpha3) $);
\coordinate (-123) at ($ (-alpha1) + (-alpha2) + (-alpha3) $);
\coordinate (-223) at ($ (-alpha2) + (-alpha2) + (-alpha3) $);
\coordinate (-1223) at ($ (-alpha1) + (-alpha2) + (-alpha2) + (-alpha3) $);
\coordinate (-11223) at ($ (-alpha1) + (-alpha1) + (-alpha2) + (-alpha2) + (-alpha3) $);

% Draw the black polygon
\begin{scope}[opacity=0.5]
    \draw (alpha3) -- (11223) -- (-alpha3) -- (-11223) -- (alpha3);
    \draw (alpha3) -- (223) -- (-alpha3) -- (-223) -- (alpha3);
\end{scope}

% Draw the nodes for the roots in appropriate colors
\begin{scope}[MyColor3]
    \draw[fill] (alpha3)  circle (\ptsize);
    \draw[fill] (-alpha3) circle (\ptsize);
\end{scope}

\begin{scope}[MyColor2]
    \draw[fill] (alpha1)  circle (\ptsize);
    \draw[fill] (223)     circle (\ptsize);
    \draw[fill] (1223)    circle (\ptsize);
    \draw[fill] (11223)   circle (\ptsize);
    \draw[fill] (-alpha1) circle (\ptsize);
    \draw[fill] (-223)    circle (\ptsize);
    \draw[fill] (-1223)   circle (\ptsize);
    \draw[fill] (-11223)  circle (\ptsize);
\end{scope}

\begin{scope}[MyColor1]
    \draw[fill] (alpha2) circle (\ptsize);
    \draw[fill] (12)      circle (\ptsize);
    \draw[fill] (23)      circle (\ptsize);
    \draw[fill] (123)     circle (\ptsize);
    \draw[fill] (-alpha2) circle (\ptsize);
    \draw[fill] (-12)     circle (\ptsize);
    \draw[fill] (-23)     circle (\ptsize);
    \draw[fill] (-123)    circle (\ptsize);
\end{scope}

% Draw the orange rectangle
\draw[MyColor2] (11223) -- (223) -- (-11223) -- (-223) -- (11223);

% Draw the upper green rectangle
\draw[MyColor1] (-alpha2) -- (123) -- (23) -- (-12) -- (-alpha2);

% Draw the upper green rectangle
\draw[MyColor1] (12) -- (-23) -- (-123) -- (alpha2) -- (12);

% Nodes for the names
\node (alpha1-name) at (1.4,-1,0) {$\alpha_1$};
\node (alpha2-name) at (0,1.4,-1) {$\alpha_2$};
\node (alpha3-name) at (0,0,2.3) {$\alpha_3$};

\begin{scope}[shift={(0,0,15)}]
    \draw[dashed] (alpha1) -- (1223) -- (-alpha1) -- (-1223) -- (alpha1);    
\end{scope}

\end{tikzpicture}
\end{document}

产生图片

z我目前正在尝试将虚线矩形沿图形的 -方向移动一定量。以下这我的尝试可以在上面的代码中找到

\begin{scope}[shift={(0,0,15)}]
    \draw[dashed] (alpha1) -- (1223) -- (-alpha1) -- (-1223) -- (alpha1);    
\end{scope}

但这不会产生任何变化。所以大概我误解了这个shift命令应该如何工作...理想情况下，我想在移位矩形的边缘定义新坐标，但我不确定是否可以做到这一点。

Answer 1

符号坐标不会以这种方式转换。您可以使用 来转换它们transform canvas，例如

\begin{scope}[transform canvas={shift={(0,0,2)}}]
    \draw[dashed] (alpha1) -- (1223) -- (-alpha1) -- (-1223) -- (alpha1);    
\end{scope}

但是，这有点危险，例如边界框无法正确计算。另一方面，tikz-3dplot加载calc库，因此您可以这样做

\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{amsmath}

\newcommand{\ptsize}{1.5pt}

\usepackage{xcolor}
\definecolor{MyColor1}{rgb}{0.24, 0.59, 0.32}
\definecolor{MyColor2}{rgb}{0.85, 0.49, 0.19}
\definecolor{MyColor3}{rgb}{0.22, 0.42, 0.69}

\begin{document}
\tdplotsetmaincoords{75}{130}
\begin{tikzpicture}[tdplot_main_coords]

% Define all the nodes necessary for the drawing
\coordinate (alpha1) at (1,-1,0);
\coordinate (alpha2) at (0,1,-1);
\coordinate (alpha3) at (0,0,2);

\coordinate (12) at ($ (alpha1) + (alpha2) $);
\coordinate (23) at ($ (alpha2) + (alpha3) $);
\coordinate (123) at ($ (alpha1) + (alpha2) + (alpha3) $);
\coordinate (223) at ($ (alpha2) + (alpha2) + (alpha3) $);
\coordinate (1223) at ($ (alpha1) + (alpha2) + (alpha2) + (alpha3) $);
\coordinate (11223) at ($ (alpha1) + (alpha1) + (alpha2) + (alpha2) + (alpha3) $);

\coordinate (-alpha1) at (-1,1,0);
\coordinate (-alpha2) at (0,-1,1);
\coordinate (-alpha3) at (0,0,-2);

\coordinate (-12) at ($ (-alpha1) + (-alpha2) $);
\coordinate (-23) at ($ (-alpha2) + (-alpha3) $);
\coordinate (-123) at ($ (-alpha1) + (-alpha2) + (-alpha3) $);
\coordinate (-223) at ($ (-alpha2) + (-alpha2) + (-alpha3) $);
\coordinate (-1223) at ($ (-alpha1) + (-alpha2) + (-alpha2) + (-alpha3) $);
\coordinate (-11223) at ($ (-alpha1) + (-alpha1) + (-alpha2) + (-alpha2) + (-alpha3) $);

% Draw the black polygon
\begin{scope}[opacity=0.5]
    \draw (alpha3) -- (11223) -- (-alpha3) -- (-11223) -- (alpha3);
    \draw (alpha3) -- (223) -- (-alpha3) -- (-223) -- (alpha3);
\end{scope}

% Draw the nodes for the roots in appropriate colors
\begin{scope}[MyColor3]
    \draw[fill] (alpha3)  circle (\ptsize);
    \draw[fill] (-alpha3) circle (\ptsize);
\end{scope}

\begin{scope}[MyColor2]
    \draw[fill] (alpha1)  circle (\ptsize);
    \draw[fill] (223)     circle (\ptsize);
    \draw[fill] (1223)    circle (\ptsize);
    \draw[fill] (11223)   circle (\ptsize);
    \draw[fill] (-alpha1) circle (\ptsize);
    \draw[fill] (-223)    circle (\ptsize);
    \draw[fill] (-1223)   circle (\ptsize);
    \draw[fill] (-11223)  circle (\ptsize);
\end{scope}

\begin{scope}[MyColor1]
    \draw[fill] (alpha2) circle[radius=\ptsize];
    \draw[fill] (12)      circle[radius=\ptsize];
    \draw[fill] (23)      circle[radius=\ptsize];
    \draw[fill] (123)     circle[radius=\ptsize];
    \draw[fill] (-alpha2) circle[radius=\ptsize];
    \draw[fill] (-12)     circle[radius=\ptsize];
    \draw[fill] (-23)     circle[radius=\ptsize];
    \draw[fill] (-123)    circle[radius=\ptsize];
\end{scope}

% Draw the orange rectangle
\draw[MyColor2] (11223) -- (223) -- (-11223) -- (-223) -- (11223);

% Draw the upper green rectangle
\draw[MyColor1] (-alpha2) -- (123) -- (23) -- (-12) -- (-alpha2);

% Draw the upper green rectangle
\draw[MyColor1] (12) -- (-23) -- (-123) -- (alpha2) -- (12);

% Nodes for the names
\node (alpha1-name) at (1.4,-1,0) {$\alpha_1$};
\node (alpha2-name) at (0,1.4,-1) {$\alpha_2$};
\node (alpha3-name) at (0,0,2.3) {$\alpha_3$};

%\begin{scope}[transform canvas={shift={(0,0,2)}}]
\draw[dashed] ($(alpha1)+(0,0,2)$) -- ($(1223)+(0,0,2)$) 
    -- ($(-alpha1)+(0,0,2)$) --($(-1223)+(0,0,2)$) -- cycle;    
%\end{scope}

\end{tikzpicture}
\end{document}

我移动了 2 而不是 15，因为 15 真的很远，但你也可以这样做。