沿曲线绘制与切向量平行的向量

Question

我正在尝试复制下图，该图与广义相对论中的矢量平行传输有关，在扭转空间中，两个矢量相加后如何交换会产生无法闭合的平行四边形，闭合之间的空间就是扭转的量度。

这是我想复制的图：

这是我迄今为止所做的尝试：

我的问题是，是否有一种方便的方法可以在曲线最顶端绘制与切向量平行的向量，然后在曲线的其余部分等距地绘制这些相等大小的平行向量？

我知道我可以借助一些 GUI（例如 TikZEdt）来实现这一点，但我仍然想知道是否有不使用 GUI 的解决方案。

我迄今为止的代码：

\documentclass{standalone}

\usepackage{tikz}
\usepackage{graphicx}
\usetikzlibrary{arrows,decorations.markings}

\begin{document}

\begin{tikzpicture}[
    tangent/.style={
        decoration={
            markings,% switch on markings
            mark=
                at position #1
                with
                {
                    \coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
                    \coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
                    \coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
                }
        },
        postaction=decorate
    },
    use tangent/.style={
        shift=(tangent point-#1),
        x=(tangent unit vector-#1),
        y=(tangent orthogonal unit vector-#1)
    },
    use tangent/.default=1
]

\draw[
    tangent=0,
    tangent=0.125,
    tangent=0.25,
    tangent=0.375,
    red,line width=1pt] (-0.8,-0.725) .. controls (-0.975,0.3) and (-0.825,1.6) .. (0.05,2.125) .. controls (0.95,1.825) and (1.425,0.525) .. (1.175,-0.65) .. controls (0.3,-0.825) and (0.05,-0.775) .. cycle;

\draw [blue, thick, use tangent, -stealth] (0,0) -- (1.1,0);
\draw [blue, thick, use tangent=2, -stealth] (0,0) -- (1.1,0);
\draw [blue, thick, use tangent=3, -stealth] (0,0) -- (1.1,0);
\draw [blue, thick, use tangent=4, -stealth] (0,0) coordinate (a) -- (1.1,0) coordinate (b);
\end{tikzpicture}

\end{document}

与绘制切向量有关的部分代码取自 Jake 在这篇文章中的回答：如何在 TikZ 中绘制路径上任意点的切线

Answer 1

如果您基本上想绘制与切线处绘制的矢量平行的矢量，则可以使用calc节点并进行简单计算。对于曲线上的每个位置，您基本上取坐标，添加切线矢量的终点并减去其起点。

\documentclass[]{article}
\usepackage{tikz}
\usetikzlibrary{arrows,decorations.markings,through,calc,angles,quotes}
\begin{document}
\begin{tikzpicture}[% ateb: https://tex.stackexchange.com/a/700977/ i gwestiwn SolidMark: https://tex.stackexchange.com/q/700974/ sy'n defnyddio côd o ateb Jake: https://tex.stackexchange.com/a/25940/
  tangent/.style={
    decoration={
      markings,% switch on markings
      mark=
      at position #1
      with
      {
        \coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
        \coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
        \coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
      }
    },
    postaction=decorate
  },
  use tangent/.style={
    shift=(tangent point-#1),
    x=(tangent unit vector-#1),
    y=(tangent orthogonal unit vector-#1)
  },
  use tangent/.default=1
  ]
  
  \draw[
  tangent=0,
  tangent=0.125,
  tangent=0.25,
  tangent=0.375,
  red,line width=1pt] (-0.8,-0.725) coordinate (c0) coordinate (C)
  .. controls (-0.975,0.3) and (-0.825,1.6) .. (0.05,2.125) 
  .. controls (0.95,1.825) and (1.425,0.525) .. coordinate [pos=0.3333] (c1) coordinate [pos=0.6667] (c2)  (1.175,-0.65) coordinate  (c3)
  .. controls (0.3,-0.825) and (0.05,-0.775) .. 
  coordinate [pos=0.5] (c4) cycle ;
  
  \draw [blue, thick, use tangent, -stealth] (0,0) -- (1.1,0) coordinate (A);
  \draw [blue, thick, use tangent=2, -stealth] (0,0) -- (1.1,0);
  \draw [blue, thick, use tangent=3, -stealth] (0,0) -- (1.1,0);
  \draw [blue, thick, use tangent=4, -stealth] (0,0) coordinate (a) -- (1.1,0) coordinate (b);
  
  \foreach \i in {0,...,4} \draw [blue,thick,-stealth] (c\i) -- ++($(b)-(a)$) coordinate (b\i);
  \coordinate (B) at (b0);
  \path pic [draw,"$\alpha$"] {angle=B--C--A};
  
  \node [draw] at (0,0) [circle through={(a)}] {};
\end{tikzpicture}

\end{document}