当我想要在 Tikz 中使用 plot 绘制曲线时，出现了一条直线

Question

我想要绘制的是如下图两个圆柱的相交曲线，但是画出来的却是一条直线，为了简单起见，只贴出绘制曲线的基本代码。

\documentclass{border=10pt}[standalone]

\usepackage{tikz}

\begin{document}

\tikzset{%

  math3d/.style={%%

                                       x={(-0.353cm,-0.353cm)},
                                       z={(0cm,1cm)},
                                       y={(1cm,0cm)},

  }%%


   }%

 \begin{tikzpicture}[math3d]

     \draw node[left] at (0,0,0) {$O$} coordinate (O);

     \draw[->](0,0,0)--(4,0,0);
     \draw node[below left] at (4,0,0) {$X$};

     \draw[->](0,0,0)--(0,5,0);
     \draw node[below right] at (0,5,0) {$Y$};

     \draw[->](0,0,0)--(0,0,5);
     \draw node[below right] at (0,0,5) {$Z$};

     %  curve as intersection of two cylinders
         \draw[variable=\t,samples=30,domain=0:0.5*pi,smooth] 
      plot ({2*cos(deg(\t))}, {2*sin(deg(\t))},{2*sin(deg(\t))}); %  

    \end{tikzpicture}

\end{document}

Answer 1

你选择了一个不合适的投影，曲线看起来像一条线。曲线由以下公式给出

\draw[variable=\t,samples=30,domain=0:0.5*pi,smooth] 
  plot ({2*cos(deg(\t))}, {2*sin(deg(\t))},{2*sin(deg(\t))});

因此它的y和z分量相等。但是，您选择的x是，使得x与成比例y+z，这样您就得到了一条线。为了安装另一个投影，您可以加载库perspective。以下动画显示，对于某些视角，曲线的投影可能看起来像一条线。

\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{perspective}
\begin{document}
\foreach \X in {100,105,...,130,125,120,...,105}
{\begin{tikzpicture}
\path[use as bounding box] (-3,-3) rectangle (6,6);
 \begin{scope}[3d view={\X }{20+15*sin((\X-100)*6)}]
     \draw node[left] at (0,0,0) {$O$} coordinate (O);
     \draw[->](0,0,0)--(4,0,0);
     \draw node[below left] at (4,0,0) {$X$};
     \draw[->](0,0,0)--(0,5,0);
     \draw node[below right] at (0,5,0) {$Y$};
     \draw[->](0,0,0)--(0,0,5);
     \draw node[below right] at (0,0,5) {$Z$};

     %  curve as intersection of two cylinders
     \draw[dashed] (2,0,0) -- (2,0,4) -- (0,0,4) -- (0,2,4)
      -- (0,2,2) -- (0,4,2) -- (0,4,0) -- (2,4,0) -- cycle
      plot[variable=\t,samples=30,domain=0:0.5*pi,smooth]
       ({2*sin(deg(\t))},4,{2*cos(deg(\t))});
     \draw 
      plot[variable=\t,samples=30,domain=0:0.5*pi,smooth]
       ({2*cos(deg(\t))}, {2*sin(deg(\t))},{2*sin(deg(\t))});
     \draw  plot[variable=\t,samples=30,domain=0:0.5*pi,smooth]
       ({2*cos(deg(\t))}, 0,{2*sin(deg(\t))}) -- 
      (0,2,2) -- (0,2,0)
       plot[variable=\t,samples=30,domain=0.5*pi:0,smooth]
       ({2*cos(deg(\t))},{2*sin(deg(\t))},0); 
 \end{scope} 
\end{tikzpicture}}
\end{document}