TikZ実例集〜3D編

TikZで作った図

POINT

• TikZを使うと，TeX環境で簡単にきれいな図を作成することができる．
• TikZで作成した図（3D）のソースコードを紹介！
• TikZ実例集〜2Dグラフ編 - Notes_JP

記事のために作った図のTeXコード（TikZを利用）を，備忘録として残します．

ベクトルの回転（3次元）

作成した図：

ベクトルの回転(3次元)

この図は，以下の記事で使っています：
回転行列（3次元） - Notes_JP

▶クリックしてソースコードを表示

\begin{figure}[htbp]
  % 左の図
  \begin{minipage}{0.3\hsize} 
    \begin{center}
      \begin{tikzpicture}[scale=1.5, rotate=0]
        \begin{axis}[
            title={3D Rotation},
            view={60}{30},
            axis lines=none,
            ticks=none,
            xmin=-30, xmax=50, ymin=0-30, ymax=50, zmin=0, zmax=50,
          ]
          %
          \node at(axis cs:0,0,0) [anchor=north]{$\boldsymbol{O}$};
          %
          \draw[-stealth,thick] (axis cs:0,0,0) -- (axis cs:0,0,50);
          \node at(axis cs:0,0,{50/2}) [anchor=east]{$(\boldsymbol{r}\cdot\boldsymbol{n})\boldsymbol{n}$};
          %
          \draw[-stealth,thick] (axis cs:0,0,0) -- (axis cs:30,0,50);
          \node at(axis cs:30,0,50) [anchor=north east]{$\boldsymbol{r}$};      
          \draw[-stealth,thick] (axis cs:0,0,0) -- (axis cs:{30/2},{30*sqrt(3)/2},50);
          \node at(axis cs:{30/2},{30*sqrt(3)/2},50) [anchor=west]{$\boldsymbol{r^\prime}$};    
          %
          \draw[thin,gray] (axis cs:0,0,50) circle (300);
          \fill[orange, opacity=.5, thin] (axis cs:0,0,50) circle (300);
          %
          \draw[-stealth,red,very thick] (axis cs:0,0,50) -- (axis cs:0,0,60);
          \node at(axis cs:0,0,60) [anchor=north west]{$\boldsymbol{n}$};     
          %
          \draw[-stealth,dashed] (axis cs:0,0,50) -- (axis cs:30,0,50);
          \draw[-stealth,dashed] (axis cs:0,0,50) -- (axis cs:{30/2},{30*sqrt(3)/2},50);
          \draw [thin,->](axis cs:10,0,50) arc (0:60:100);
          \node at(axis cs:3,8,50) [anchor=north west]{$\theta$};      
        \end{axis}
      \end{tikzpicture}
    \end{center}
  \end{minipage}
  %中央の空間
  \begin{minipage}{0.2\hsize}
    \begin{center}
    \end{center}
  \end{minipage}
  % 右の図
  \begin{minipage}{0.3\hsize}
    \begin{center}
      \begin{tikzpicture}[scale=2]
        %円
        \draw[thin,gray] (0,0) circle (1);
        \fill[orange, opacity=.5, thin] (0,0) circle (1);
        %
        \draw [thin,->](0:1/4) arc (0:60:1/4);
        \node at(40:1/4) [anchor=west]{$\theta$};
        % ベクトル
        \draw [very thick,-stealth,dashed](0,0)--(1,0)node [anchor=west]{$\color{red}{\boldsymbol{r}-(\boldsymbol{r}\cdot\boldsymbol{n})\boldsymbol{n}}$};
        \draw [very thick,-stealth,dashed](0,0)--(1/2,{sqrt(3)/2})node [anchor=west]{$\left[\color{red}{\boldsymbol{r}-(\boldsymbol{r}\cdot\boldsymbol{n})\boldsymbol{n}}\right]\cos\theta+\left(\color{blue}{\boldsymbol{n}\times\boldsymbol{r}}\right)\sin\theta$};
        \draw [very thick,-stealth](0,0)--(0,1)node [anchor=south]{$\color{blue}{\boldsymbol{n}\times\boldsymbol{r}}$};
        %直角記号
        \draw[thin] (0,0.1) -- (0.1,0.1) -- (0.1,0);
      \end{tikzpicture}
    \end{center}
  \end{minipage}   
\end{figure}

回転体

TikZ, pgfplotで作成しました．

その1

作成した図：

回転体の図1

この図は，以下の記事で使っています：
曲面積の計算における派生公式の活用法 - Notes_JP

▶クリックしてソースコードを表示

\begin{center}
  \begin{tikzpicture}[scale=2]
    \begin{axis}[
        title={Rotation of $f(x)$},
        colormap/greenyellow,
        view={30}{30},%15,30
        axis lines=center,
        ticks=none,
        xmin=0, xmax=2.5, ymin=-40, ymax=60, zmin=-40, zmax=40,
        xlabel=$x$, ylabel=$y$, zlabel=$z$,
        every axis x label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=west,
        },
        every axis y label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=west,
        },
        every axis z label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=south,
        }
      ]
      \addplot3[
        %            mesh,
        surf,
        opacity=0.5,
        shader=faceted,
        samples=20,
        domain=0:2,y domain=0:2*pi,
        z buffer=sort]
      (x,{(60/(x+2))* cos(deg(y))},{(60/(x+2)) * sin(deg(y))});
      %
      \draw[red, domain=0:pi/4, samples=200]plot(axis cs:0,{10* cos(deg(\x))}, {10* sin(deg(\x))});
      \node at(axis cs:0,5,8) [anchor=west]{$\theta$};     
      %
      \draw[-stealth,red,thin] (axis cs:0,0,0) -- (axis cs:0,{30*cos(deg(pi/4))},{30*sin(deg(pi/4))});
      \draw[dashed,thin] (axis cs:0,{30*cos(deg(pi/4))},0) -- (axis cs:0,{30*cos(deg(pi/4))},{30*sin(deg(pi/4))});
      \draw[dashed,thin] (axis cs:0,0,{30*sin(deg(pi/4))}) -- (axis cs:0,{30*cos(deg(pi/4))},{30*sin(deg(pi/4))});
    \end{axis}
  \end{tikzpicture}
\end{center}

参考記事：

• PGFplots 3d: Creating a filled solid of revolution - TeX - LaTeX Stack Exchange
• pgfplot: 3D version of a plane and its the gradient vector - TeX - LaTeX Stack Exchange
• tikz pgf - Naming 3D axes in pgfplots - TeX - LaTeX Stack Exchange
• How can I adjust the position of xlabel and ylabel with pgfplots? - TeX - LaTeX Stack Exchange

その2

上の図にいくつか図を追加すると，次のような図も作成できます．

回転体の図2

▶クリックしてソースコードを表示

\begin{center}
  \begin{tikzpicture}[scale=2]
    \begin{axis}[
        title={Rotation of $f(x)$},
        colormap/greenyellow,
        view={30}{30},%15,30
        axis lines=center,
        ticks=none,
        xmin=0, xmax=2.5, ymin=-40, ymax=60, zmin=-40, zmax=40,
        xlabel=$x$, ylabel=$y$, zlabel=$z$,
        every axis x label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=west,
        },
        every axis y label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=west,
        },
        every axis z label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=south,
        }
      ]
      \addplot3[
        %            mesh,
        surf,
        opacity=0.5,
        shader=faceted,
        samples=20,
        domain=0:2,y domain=0:2*pi,
        z buffer=sort]
      (x,{(60/(x+2))* cos(deg(y))},{(60/(x+2)) * sin(deg(y))});
      %
      \draw[red, domain=0:pi/4, samples=200]plot(axis cs:0,{10* cos(deg(\x))}, {10* sin(deg(\x))});
      \node at(axis cs:0,5,8) [anchor=west]{$\theta$};     
      %
      \draw[-stealth, red, domain=0:11*pi/4, samples=200]plot(axis cs:2.3,{6*cos(deg(\x))},{6*sin(deg(\x))});      
      %
      \draw[-stealth,red,thin] (axis cs:0,0,0) -- (axis cs:0,{30*cos(deg(pi/4))},{30*sin(deg(pi/4))});
      \draw[dashed,thin] (axis cs:0,{30*cos(deg(pi/4))},0) -- (axis cs:0,{30*cos(deg(pi/4))},{30*sin(deg(pi/4))});
      \draw[dashed,thin] (axis cs:0,0,{30*sin(deg(pi/4))}) -- (axis cs:0,{30*cos(deg(pi/4))},{30*sin(deg(pi/4))});
      %
      \filldraw[orange, opacity=0.5, domain=0:2, samples=200]plot(axis cs:\x,{(60/(\x+2))},0) -- (axis cs:2,15,0) -- (axis cs:2,0,0)-- (axis cs:0,0,0) --(axis cs:0,30,0);
    \end{axis}
  \end{tikzpicture}
\end{center}

その3

作成した図：

回転体の図3

この図は，以下の記事で使っています：
バームクーヘン積分 - Notes_JP

▶クリックして1つ目のソースコードを表示

\begin{center}
  \begin{tikzpicture}[scale=2]
    \begin{axis}[
%        title={Rotation of $f(x)$},
        colormap/greenyellow,
        hide axis,
        view={0}{30},%15,30
        axis lines=center,
        ticks=none,
        xmin=-2.5, xmax=3, ymin=-2.5, ymax=2.5, zmin=0, zmax=2
      ]
      %
      \addplot3[
        surf,
        opacity=0.5,
        shader=faceted,
        samples=30,
        domain=0:1,y domain=0:2*pi %,z buffer=sort
      ]
      ({cos(deg(y))},{sin(deg(y))},{x});
      %
      \addplot3[
        %            mesh,
        surf,
        opacity=0.5,
        shader=faceted,
        samples=30,
        domain=1:2,y domain=0:2*pi %,z buffer=sort
      ]
      ({x*cos(deg(y))},{x*sin(deg(y))},{3/(x^3+2)});
      %
      \addplot3[
        surf,
        opacity=0.5,
        shader=faceted,
        samples=30,
        domain=0:3/10,y domain=0:2*pi %,z buffer=sort
      ]
      ({2*cos(deg(y))},{2*sin(deg(y))},{x});
      %
      \filldraw[green, opacity=0.5, domain=1:2, samples=200]plot(axis cs:\x,0,{(3/(\x^3+2))}) -- (axis cs:2,0,3/10) -- (axis cs:2,0,0)-- (axis cs:1,0,0) --(axis cs:1,0,1);
      \draw[thin,domain=1:2, samples=200]plot(axis cs:\x,0,{(3/(\x^3+2))}) -- (axis cs:2,0,3/10) -- (axis cs:2,0,0)-- (axis cs:1,0,0) --(axis cs:1,0,1);     
      %
      \draw[-stealth](axis cs:0,0,0) -- (axis cs:2.5,0,0)node[anchor=west]{$x$};
      \draw[-stealth](axis cs:0,0,0) -- (axis cs:0,0,1.6)node[anchor=south]{$y$};
      \draw[-stealth, red, domain=-pi/4:7*pi/4, samples=200]plot(axis cs:{0.2*cos(deg(\x))}, {0.2*sin(deg(\x))},1.4);
      \node at(axis cs:1,0,0)[anchor=south west]{$a$};
      \node at(axis cs:2,0,0)[anchor=south west]{$b$};
      \node at(axis cs:1,0,1)[anchor=west]{$\;y=f(x)$};     
    \end{axis}
  \end{tikzpicture}
\end{center}

▶クリックして2つ目のソースコードを表示

\begin{center}
  \begin{tikzpicture}[scale=2]
    \begin{axis}[
%        title={Rotation of $f(x)$},
        colormap/greenyellow,
        hide axis,
        view={0}{30},%15,30
        axis lines=center,
        ticks=none,
        xmin=-2.5, xmax=3, ymin=-2.5, ymax=2.5, zmin=0, zmax=2
      ]
      % 点線(奥:0~pi)
      \draw[thin, dashed, domain=0:pi, samples=200]plot(axis cs:{cos(deg(\x))}, {sin(deg(\x))},0);
      \draw[thin, dashed, domain=0:pi, samples=200]plot(axis cs:{cos(deg(\x))}, {sin(deg(\x))},1);
      \draw[thin, dashed, domain=0:pi, samples=200]plot(axis cs:{2*cos(deg(\x))}, {2*sin(deg(\x))},0);
      \draw[thin, dashed, domain=0:pi, samples=200]plot(axis cs:{2*cos(deg(\x))}, {2*sin(deg(\x))},3/10);
      %
      \addplot3[
        surf,
        opacity=0.5,
        shader=faceted,
        samples=30,
        domain=0:24/43,y domain=0:2*pi %,z buffer=sort
      ]
      ({1.5*cos(deg(y))},{1.5*sin(deg(y))},{x});
      %
      \addplot3[
        %            mesh,
        surf,
        opacity=0.5,
        shader=faceted,
        samples=30,
        domain=1.5:1.6,y domain=0:2*pi %,z buffer=sort
      ]
      ({x*cos(deg(y))},{x*sin(deg(y))},{3/(x^3+2)});    
      %
      \addplot3[
        surf,
        opacity=0.5,
        shader=faceted,
        samples=30,
        domain=0:125/254,y domain=0:2*pi %,z buffer=sort
      ]
      ({1.6*cos(deg(y))},{1.6*sin(deg(y))},{x});
      %
      \filldraw[green, opacity=0.3, domain=1:2, samples=200]plot(axis cs:\x,0,{(3/(\x^3+2))}) -- (axis cs:2,0,3/10) -- (axis cs:2,0,0)-- (axis cs:1,0,0) --(axis cs:1,0,1);      
      \draw[thin, domain=1.5:1.6, samples=200]plot(axis cs:\x,0,{(3/(\x^3+2))}) -- (axis cs:1.6,0,125/254) -- (axis cs:1.6,0,0) -- (axis cs:1.5,0,0)-- (axis cs:1.5,0,24/43);
      % 点線(手前:pi~2pi)
      \draw[thin, dashed, opacity=0.5, domain=pi:2*pi, samples=200]plot(axis cs:{cos(deg(\x))}, {sin(deg(\x))},0);
      \draw[thin, dashed, domain=pi:2*pi, samples=200]plot(axis cs:{cos(deg(\x))}, {sin(deg(\x))},1);
      \draw[thin, dashed](axis cs:1,0,1) -- (axis cs:1,0,0);
      \draw[thin, dashed](axis cs:-1,0,1) -- (axis cs:-1,0,0);
      \draw[thin, dashed, domain=pi:2*pi, samples=200]plot(axis cs:{2*cos(deg(\x))}, {2*sin(deg(\x))},0);
      \draw[thin, dashed, domain=pi:2*pi, samples=200]plot(axis cs:{2*cos(deg(\x))}, {2*sin(deg(\x))},3/10);
      \draw[thin, dashed, domain=1:2, samples=200]plot(axis cs:\x,0,{(3/(\x^3+2))}) -- (axis cs:2,0,0);
      \draw[thin, dashed, domain=1:2, samples=200]plot(axis cs:{-\x},0,{(3/(\x^3+2))}) -- (axis cs:-2,0,0);  
      % 断面
      \draw[-stealth](axis cs:0,0,0) -- (axis cs:2.5,0,0)node[anchor=west]{$x$};
      \draw[-stealth](axis cs:0,0,0) -- (axis cs:0,0,1.6)node[anchor=south]{$y$};
      \draw[-stealth, red, domain=-pi/4:7*pi/4, samples=200]plot(axis cs:{0.2*cos(deg(\x))}, {0.2*sin(deg(\x))},1.4);
      %
      \node at(axis cs:1.5,0,0)[anchor=south east]{$x$};
      \node at(axis cs:1.55,0,0)[anchor=north]{$\mathrm{d}x$};
      \draw[dashed](axis cs:0,0,24/43)node[anchor=east]{$f(x)$} -- (axis cs:1.5,0,24/43);
    \end{axis}
  \end{tikzpicture}
\end{center}

応力テンソルの図

作成した図：

この図は，以下の記事で使っています：
テンソルと行列が混同される理由 - Notes_JP

▶クリックしてソースコードを表示

\begin{center}
  \begin{tikzpicture}[scale=2.5]
    \begin{axis}[
        title={Stress Tensor},
        view={60}{30},
        axis lines=center,
        ticks=none,
        xmin=0, xmax=50, ymin=0, ymax=50, zmin=0, zmax=50,
        xlabel=$x$, ylabel=$y$, zlabel=$z$,
        every axis x label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=west,
        },
        every axis y label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=west,
        },
        every axis z label/.style={
          at={(ticklabel* cs:1.05)},
          anchor=south,
        }
      ]
      %
      \node at(axis cs:20,20,20) [anchor=west]{$\boldsymbol{n}$};
      \draw[-stealth,red,very thick] (axis cs:10,10,10) -- (axis cs:20,20,20);
      \draw[thin] (axis cs:30,0,0) -- (axis cs:0,30,0);
      \draw[thin] (axis cs:30,0,0) -- (axis cs:0,0,30);
      \draw[thin] (axis cs:0,30,0) -- (axis cs:0,0,30);
      \fill[orange, opacity=.2] (axis cs:30,0,0) -- (axis cs:0,30,0) -- (axis cs:0,0,30);
    \end{axis}
  \end{tikzpicture}
\end{center}

ローレンツ変換

作成した図：

2つの慣性系

この図は，以下の記事で使っています：
速度の変換則（ローレンツ変換） - Notes_JP

▶クリックしてソースコードを表示

\begin{center}
  \begin{tikzpicture}[scale=2]
    \draw [white](0,-1.5)--(0,1.5);
    %\node [anchor=north west] at (0,1.5) {$t>0$};
    \draw [very thick, -stealth](0,{-3/8})--(0.6,{-3/8}) node [anchor=north]{$\bm{V}$};
    % K
    \draw [very thick, -stealth]({-1/8},{-1/8})--(1/2,1/2) node [anchor=east]{$y\,$};
    \draw [very thick, -stealth](-1/4,0)--(1,0) node [anchor=north]{$x$};
    \draw [very thick, -stealth](0,-1/4)--(0,1) node [anchor=east]{$z$};
    \node [anchor=north west] at (0,0) {$O$};
    % K'
    \draw [-stealth, gray]({-1/8+0.6},{-1/8})--({1/2+0.6},1/2) node [anchor=east]{$y^{\prime}$};
    \draw [-stealth, gray]({-1/4+0.6},0)--({1+0.6},0) node [anchor=north]{$x^{\prime}$};
    \draw [-stealth, gray](0.6,-1/4)--(0.6,1) node [anchor=east]{$z^{\prime}$};
    \node [gray, anchor=north west] at (0.6,0) {$O^{\prime}$};  
  \end{tikzpicture}
\end{center}