我想画一个同时受到拉伸和扭转的立方体，如下图所示：
我已经尝试了扩展部分（附加代码），但不知道如何将其与扭转部分结合起来。
\documentclass[tikz,border=0mm]{standalone}
\usetikzlibrary{3d, perspective, calc, bending}
%
\definecolor{myRed}{RGB}{180,80,80}
\definecolor{myGreen}{RGB}{55,175,85}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[x=1cm, y=1cm, 3d view={65}{25}]
%-------------------------------------------------------------------------------
\def\h{1 * 5}
\def\w{1 * 5}
\def\d{1 * 5}
\coordinate (a) at ( 0, 0, 0);
\coordinate (b) at (\d, 0, 0);
\coordinate (c) at (\d,\w, 0);
\coordinate (d) at ( 0,\w, 0);
\coordinate (e) at ( 0, 0,\h);
\coordinate (f) at (\d, 0,\h);
\coordinate (g) at (\d,\w,\h);
\coordinate (h) at ( 0,\w,\h);
\coordinate (m) at (\d/2,\w/2,\h);
\tikzset{
face/.style = {fill opacity=0.5},
edge/.style = {draw, thin, line join=round},
top/.style = {edge,face,fill=black!30},
bottom/.style = {edge, face, fill=yellow!90},
side/.style = {edge, face, fill=myGreen!40},
label/.style = {fill=white, inner sep=0.5ex},
rot/.style={ultra thick,-{latex[bend]}},
fixedbot/.style = {edge, face, fill=black!50},
};
\draw[bottom,draw opacity=0.5] (a) -- (b) -- (c) -- (d) -- cycle;
\draw[thick, dashed, orange] (a) node[below left]{$\mathbf{A}$} -- (g) node[above right]{$\mathbf{B}$};
\draw[top] (e) -- (f) -- (g) -- (h) -- cycle;
\draw[side,draw opacity=0.2] (d) -- (a) -- (e) -- (h) -- cycle;
\draw[side,draw opacity=0.2] (c) -- (d) --(h) -- (g) -- cycle;
\draw[side,fill opacity=0.5] (a) -- (b) -- (f) -- (e) -- cycle;
\draw[side,fill opacity=0.5] (b) -- (c) -- (g) -- (f) -- cycle;
%BCs labels
\draw[draw=none] (e) -- (g) node[pos=0.8] {$\Omega_\mathsf{top}$};
\draw[draw=none] (a) -- (c) node[pos=0.5] {$\Omega_\mathsf{bottom}$};
%Coordinates
\draw[thick,-latex] (a) -- (2,0,0) node[above] {$x$};
\draw[thick,-latex] (a) -- (0,2,0) node[left=0.5ex] {$y$};
\draw[thick,-latex] (a) -- (0,0,2) node[left] {$z$};
\begin{scope}[canvas is xy plane at z=0]
\draw[help lines] (-1,-1) grid[step=5] (5.9,5.9);
\draw[latex-latex] (a |- 45:-2) -- (b |- 45:-2) node[midway,label] {$b$};
\end{scope}
\begin{scope}[canvas is yx plane at z=0]
\draw[latex-latex] (b |- 45:9) -- (c |- 45:9) node[midway,label] {$b$};
\end{scope}
\begin{scope}[canvas is zx plane at y=-1]
\draw[latex-latex] (a |- 45:-1) -- (e |- 45:-1) node[midway,above,label] {$b$};
\end{scope}
%--------------------------------------------------------------------------------
% Deformed cube
\begin{scope}[canvas is yx plane at z=6.0]
\coordinate (e1) at ( 0, 0,\h);
\coordinate (f1) at (\d, 0,\h);
\coordinate (g1) at (\d,\w,\h);
\coordinate (h1) at ( 0,\w,\h);
\draw[dash dot, top] (e1) -- (f1) -- (g1) -- (h1) -- cycle;
\draw[dash dot] (d) -- (a) -- (e1) -- (f1) -- cycle;
\draw[dash dot] (c) -- (d) -- (f1) -- (g1) -- cycle;
\draw[dash dot] (a) -- (b) -- (h1) -- (e1) -- cycle;
\draw[dash dot] (b) -- (c) -- (g1) -- (h1) -- cycle;
\end{scope}
%-------------------------------------------------------------------------------
\begin{scope}[canvas is zx plane at y=-1]
\draw[latex-latex] (e |- 45:-1) -- (e1 |- 45:-1) node[midway,label] {$\lambda_z$};
\end{scope}
%--------------------------------------------------------------------------------
\end{tikzpicture}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\end{document}
答案1
这是一种简单的方法，绘制一个绘制扭曲边缘的 3d 函数。只需几个\foreach命令即可。
\documentclass[border=2mm]{standalone}
\usepackage {tikz}
\usetikzlibrary{3d}
% colors
\definecolor{myRed} {RGB}{180, 80, 80}
\definecolor{myGreen}{RGB}{ 55,175, 85}
\begin{document}
\begin{tikzpicture}[x={(-0.5908cm,-0.4452cm)},y={(0.8068cm,-0.3260cm)},z={(0cm,0.8340cm)},line cap=round,line join=round]
\def\l {4} % length
\def\ra{40} % rotation angle
\def\ex{1} % extension
% green cube
\foreach\i in {0,1}
{%
\begin{scope}[canvas is xy plane at z=\i*\l]
\draw[myGreen] (-0.5*\l,-0.5*\l) rectangle (0.5*\l,0.5*\l);
\end{scope}
}
\foreach\i in {45,135,225,315}
{%
\draw[myGreen] (\i:{0.5*sqrt(2)*\l}) --++ (0,0,\l);
}
% distorted red cube
\begin{scope}[rotate around z=\ra,canvas is xy plane at z=\l+\ex]
\draw[myRed] (-0.5*\l,-0.5*\l) rectangle (0.5*\l,0.5*\l);
\end{scope}
\foreach\i in {45,135,225,315}
{%
\draw[myRed] plot[domain=0:1,samples=6,smooth] ({0.5*sqrt(2)*\l*cos(\x*\ra+\i)},{0.5*sqrt(2)*\l*sin(\x*\ra+\i)},{\x*(\l+\ex)});
}
% dashed lines (could be removed)
\foreach\i in {0.2,0.4,...,0.8}
{
\begin{scope}[rotate around z={\i*\ra},canvas is xy plane at z={\i*(\l+\ex)}]
\draw[very thin,myRed,dashed] (-0.5*\l,-0.5*\l) rectangle (0.5*\l,0.5*\l);
\end{scope}
}
\end{tikzpicture}
\end{document}
代码生成的结果如下：
答案2
根据您提供的代码，您只能通过沿 z 轴旋转来计算 e1、f1、g1 和 h1 的新坐标，然后在 3D 范围之外使用 绘制边缘[out=90,in=90]。在这里，我没有正确计算，只是让它稍微旋转了一下，只是为了看看它是如何工作的，但我认为添加正确的旋转微积分没什么大不了的。
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{3d, perspective, calc, bending}
%
\definecolor{myRed}{RGB}{180,80,80}
\definecolor{myGreen}{RGB}{55,175,85}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[x=1cm, y=1cm, 3d view={65}{25}]
%-------------------------------------------------------------------------------
\def\h{1 * 5}
\def\w{1 * 5}
\def\d{1 * 5}
\coordinate (a) at ( 0, 0, 0);
\coordinate (b) at (\d, 0, 0);
\coordinate (c) at (\d,\w, 0);
\coordinate (d) at ( 0,\w, 0);
\coordinate (e) at ( 0, 0,\h);
\coordinate (f) at (\d, 0,\h);
\coordinate (g) at (\d,\w,\h);
\coordinate (h) at ( 0,\w,\h);
\coordinate (m) at (\d/2,\w/2,\h);
\tikzset{
face/.style = {fill opacity=0.5},
edge/.style = {draw, thin, line join=round},
top/.style = {edge,face,fill=black!30},
bottom/.style = {edge, face, fill=yellow!90},
side/.style = {edge, face, fill=myGreen!40},
label/.style = {fill=white, inner sep=0.5ex},
rot/.style={ultra thick,-{latex[bend]}},
fixedbot/.style = {edge, face, fill=black!50},
};
\draw[bottom,draw opacity=0.5] (a) -- (b) -- (c) -- (d) -- cycle;
\draw[thick, dashed, orange] (a) node[below left]{$\mathbf{A}$} -- (g) node[above right]{$\mathbf{B}$};
\draw[top] (e) -- (f) -- (g) -- (h) -- cycle;
\draw[side,draw opacity=0.2] (d) -- (a) -- (e) -- (h) -- cycle;
\draw[side,draw opacity=0.2] (c) -- (d) --(h) -- (g) -- cycle;
\draw[side,fill opacity=0.5] (a) -- (b) -- (f) -- (e) -- cycle;
\draw[side,fill opacity=0.5] (b) -- (c) -- (g) -- (f) -- cycle;
%BCs labels
\draw[draw=none] (e) -- (g) node[pos=0.8] {$\Omega_\mathsf{top}$};
\draw[draw=none] (a) -- (c) node[pos=0.5] {$\Omega_\mathsf{bottom}$};
%Coordinates
\draw[thick,-latex] (a) -- (2,0,0) node[above] {$x$};
\draw[thick,-latex] (a) -- (0,2,0) node[left=0.5ex] {$y$};
\draw[thick,-latex] (a) -- (0,0,2) node[left] {$z$};
\begin{scope}[canvas is xy plane at z=0]
\draw[help lines] (-1,-1) grid[step=5] (5.9,5.9);
\draw[latex-latex] (a |- 45:-2) -- (b |- 45:-2) node[midway,label] {$b$};
\end{scope}
\begin{scope}[canvas is yx plane at z=0]
\draw[latex-latex] (b |- 45:9) -- (c |- 45:9) node[midway,label] {$b$};
\end{scope}
\begin{scope}[canvas is zx plane at y=-1]
\draw[latex-latex] (a |- 45:-1) -- (e |- 45:-1) node[midway,above,label] {$b$};
\end{scope}
%--------------------------------------------------------------------------------
% Deformed cube
\begin{scope}[canvas is yx plane at z=6.0]
% \coordinate (e1) at ( 0, 0,\h);
% \coordinate (f1) at (\d, 0,\h);
% \coordinate (g1) at (\d,\w,\h);
% \coordinate (h1) at ( 0,\w,\h);
\def\torsion{.7}
\coordinate (e1) at ( 0-\torsion, 0+\torsion,\h);
\coordinate (f1) at (\d-\torsion, 0-\torsion,\h);
\coordinate (g1) at (\d+\torsion,\w-\torsion,\h);
\coordinate (h1) at ( 0+\torsion,\w+\torsion,\h);
\draw[dash dot, top] (e1) -- (f1) -- (g1) -- (h1) -- cycle;
\draw[dash dot] (d) -- (a) -- (b) -- (c) -- cycle;
\end{scope}
\draw[dash dot] (a) to[out=90,in=-90] (e1);
\draw[dash dot] (b) to[out=90,in=-90] (h1);
\draw[dash dot] (c) to[out=90,in=-90] (g1);
\draw[dash dot] (d) to[out=90,in=-90] (f1);
%-------------------------------------------------------------------------------
\begin{scope}[canvas is zx plane at y=-1]
\draw[latex-latex] (e |- 45:-1) -- (e1 |- 45:-1) node[midway,label] {$\lambda_z$};
\end{scope}
%--------------------------------------------------------------------------------
\end{tikzpicture}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\end{document}
编辑：现在有了真正的旋转
在我之前的回答中，我所做的是将角坐标增加 0.7，这会导致顶部表面有所扩大。这是不准确的。我认为你更希望顶部正方形有真正的旋转，所以这就是我为实现这一点所做的。从绘图的角度来看，这并不是更好，但它更准确，所以你只需选择你喜欢的任何解决方案。
\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{3d, perspective, calc, bending}
%
\definecolor{myRed}{RGB}{180,80,80}
\definecolor{myGreen}{RGB}{55,175,85}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[x=1cm, y=1cm, 3d view={65}{25}]
%-------------------------------------------------------------------------------
\def\h{1 * 5}
\def\w{1 * 5}
\def\d{1 * 5}
\coordinate (a) at ( 0, 0, 0);
\coordinate (b) at (\d, 0, 0);
\coordinate (c) at (\d,\w, 0);
\coordinate (d) at ( 0,\w, 0);
\coordinate (e) at ( 0, 0,\h);
\coordinate (f) at (\d, 0,\h);
\coordinate (g) at (\d,\w,\h);
\coordinate (h) at ( 0,\w,\h);
\coordinate (m) at (\d/2,\w/2,\h);
\tikzset{
face/.style = {fill opacity=0.5},
edge/.style = {draw, thin, line join=round},
top/.style = {edge,face,fill=black!30},
bottom/.style = {edge, face, fill=yellow!90},
side/.style = {edge, face, fill=myGreen!40},
label/.style = {fill=white, inner sep=0.5ex},
rot/.style={ultra thick,-{latex[bend]}},
fixedbot/.style = {edge, face, fill=black!50},
};
\draw[bottom,draw opacity=0.5] (a) -- (b) -- (c) -- (d) -- cycle;
\draw[thick, dashed, orange] (a) node[below left]{$\mathbf{A}$} -- (g) node[above right]{$\mathbf{B}$};
\draw[top] (e) -- (f) -- (g) -- (h) -- cycle;
\draw[side,draw opacity=0.2] (d) -- (a) -- (e) -- (h) -- cycle;
\draw[side,draw opacity=0.2] (c) -- (d) --(h) -- (g) -- cycle;
\draw[side,fill opacity=0.5] (a) -- (b) -- (f) -- (e) -- cycle;
\draw[side,fill opacity=0.5] (b) -- (c) -- (g) -- (f) -- cycle;
%BCs labels
\draw[draw=none] (e) -- (g) node[pos=0.8] {$\Omega_\mathsf{top}$};
\draw[draw=none] (a) -- (c) node[pos=0.5] {$\Omega_\mathsf{bottom}$};
%Coordinates
\draw[thick,-latex] (a) -- (2,0,0) node[above] {$x$};
\draw[thick,-latex] (a) -- (0,2,0) node[left=0.5ex] {$y$};
\draw[thick,-latex] (a) -- (0,0,2) node[left] {$z$};
\begin{scope}[canvas is xy plane at z=0]
\draw[help lines] (-1,-1) grid[step=5] (5.9,5.9);
\draw[latex-latex] (a |- 45:-2) -- (b |- 45:-2) node[midway,label] {$b$};
\end{scope}
\begin{scope}[canvas is yx plane at z=0]
\draw[latex-latex] (b |- 45:9) -- (c |- 45:9) node[midway,label] {$b$};
\end{scope}
\begin{scope}[canvas is zx plane at y=-1]
\draw[latex-latex] (a |- 45:-1) -- (e |- 45:-1) node[midway,above,label] {$b$};
\end{scope}
%--------------------------------------------------------------------------------
% Deformed cube
\begin{scope}[canvas is yx plane at z=6.0]
\begin{scope}[rotate around={-15:(.5*\w ,0.5*\d)},canvas is xy plane at z=\h]
\path (0, 0,\h) coordinate (e1) -- (\d, 0,\h) coordinate (f1) -- (\d,\w,\h) coordinate (g1) -- ( 0,\w,\h) coordinate (h1);
\end{scope}
\draw[dash dot, top] (e1) -- (f1) -- (g1) -- (h1) -- cycle;
\draw[dash dot] (d) -- (a) -- (b) -- (c) -- cycle;
\end{scope}
\draw[dash dot] (a) to[out=90,in=-90] (e1);
\draw[dash dot] (b) to[out=90,in=-90] (h1);
\draw[dash dot] (c) to[out=90,in=-90] (g1);
\draw[dash dot] (d) to[out=90,in=-90] (f1);
%-------------------------------------------------------------------------------
\begin{scope}[canvas is zx plane at y=-1]
\draw[latex-latex] (e |- 45:-1) -- (e1 |- 45:-1) node[midway,label] {$\lambda_z$};
\end{scope}
%--------------------------------------------------------------------------------
\end{tikzpicture}
\end{document}