在平面上放置名称并在 3D 图中绘制圆形曲线

Question

我需要一些帮助来制作一张与此类似的图像，但是使用 LaTeX 语言：

为此我尝试了以下代码：

\documentclass{standalone}

\usepackage{tikz}
\usepackage{tikz-3dplot}

\begin{document}

\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[scale=3,tdplot_main_coords]
    %\draw[thin] (0,0,0) -- ({1.2*\x},{sqrt(3)*1.2*\x},0) node[below] {$y=\sqrt{3}x$};
    \filldraw[
        draw=red!20,%
        fill=red!20,%
    ]          (0,0,0)
            -- (1,0,0)
            -- (1,0,1)
            -- (0,0,1)
            -- cycle;

    \filldraw[
        draw=blue!20,%
        fill=blue!20,%
    ]          (0,0,0)
            -- (0,1,0)
            -- (0,1,1)
            -- (0,0,1)
            -- cycle;

    \filldraw[
        draw=green!20,%
        fill=green!20,%
    ]          (0,0,0)
            -- (0,1,0)
            -- (1,1,0)
            -- (1,0,0)
            -- cycle;

\draw[thin][red] (0,0,0) -- (1,1,1) node[below] {$ \alpha(t) $};

\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$ t(s) $};
\draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$ n(s) $};
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$ b(s) $};

\end{tikzpicture}
\end{document}

生成以下图像：

遗憾的是，这与我的愿望相去甚远。所以，我会告诉你我想做的事情，但我不知道该怎么做：

1. 我用红色绘制了一个圆形曲线，而不是圆形曲线。
2. 将名称放在平面上：矫正平面、正常平面和密切平面。

我正在寻找这样的东西：

Answer 1

像这样？您可以按照通常的方式放置节点并绘制曲线。

\documentclass{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}
  [
    scale=3,
    tdplot_main_coords,
    my label/.style={font=\sffamily, midway, anchor=mid},
  ]
  %\draw[thin] (0,0,0) -- ({1.2*\x},{sqrt(3)*1.2*\x},0) node[below] {$y=\sqrt{3}x$};
  \filldraw[
  draw=red!20,%
  fill=red!20,%
  ] (0,0,0)
  -- (1,0,0)
  -- (1,0,1)
  -- (0,0,1)
  -- cycle;

  \filldraw[
  draw=blue!20,%
  fill=blue!20,%
  ] (0,0,0)
  -- (0,1,0)
  -- (0,1,1)
  -- (0,0,1)
  -- cycle;

  \filldraw[
  draw=green!20,%
  fill=green!20,%
  ] (0,0,0)
  -- (0,1,0)
  -- (1,1,0)
  -- (1,0,0)
  -- cycle;

  \draw [thin, red] (0,0,0) .. controls +(-.5,0,.25) and +(1,.25,-.2) .. (1,1,1) node[pos=.75,right] {$ \alpha(t) $};

  \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$ t(s) $};
  \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$ n(s) $};
  \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$ b(s) $};

  \path [] (0,0,.75) -- (0,1,.75) node  [my label] {normal plane};
  \path [] (.5,0,0) -- (.5,1,0) node  [my label] {osculating plane};
  \path [] (.75,0,0) -- (.75,0,1) node  [my label, align=center] {rectifying\\plane};
\end{tikzpicture}
\end{document}