TikZ：添加到椭圆 2 的法线和切向量

Question

在Tikz：曲线的单位切向量，Jake 帮助为椭圆添加了切向量。然而，在那道题中，椭圆的半长轴和短轴与 x 轴和 y 轴成一线。

在这个问题中TikZ：通过两点绘制椭圆，Percusse 帮助构建了一个随机椭圆弧，我在这里使用的就是这个。所以我们不知道半长轴和短轴的排列。也许我们可以找到它的旋转，但我100%还没有找到。

在缺乏这些信息的情况下，我的问题是如何向以 结束的路径添加法线和切线向量P2？

杰克的答案可以调整吗，或者我们是否需要采用不同的方法，因为椭圆方向的模糊性？

  \documentclass[tikz]{standalone}
  \usetikzlibrary{arrows,calc}

  \begin{document}

  \begin{tikzpicture}[
    dot/.style = {outer sep = +0pt, inner sep = +0pt, shape = circle, draw = black, label = {#1}},
    small dot/.style = {minimum size = 1pt, dot = {#1}},
    big dot/.style = {minimum size = 2pt, dot = {#1}},
    line join = round, line cap = round, >=triangle 45
    ]
    \node[ fill = black, big dot = {below: \(F\)}] (F) at (0, 0) {};
    \node[ fill = black, big dot = {below: \(P_1\)}] (P1)  at (2, 0) {};
    \node[ fill = black, big dot = {above right=.25cm:\(P_2\)}] (P2) at (-2, 2) {};    

    \begin{pgfinterruptboundingbox}                  
    \begin{scope}[decoration = {markings,
        mark = at position 0.5 with {\arrow{>}}
      }]
      \clip (2, 0) -- (-2, 0) -- (-2, 4) -- (2, 4) -- cycle;
      \draw[name path global = ellp, postaction = decorate] let
        \p0 = ($(P2) - (F)$),
        \p1 = ($(P1) - (P2)$)
      in (P2|-P1) ++ (\x1, 0) arc (0:100: \x1 and \y0);                                         
  \end{scope}
\end{pgfinterruptboundingbox}

\path[name path = aux1] (P2) circle [radius = 1bp];
\draw[name intersections = {of = ellp and aux1}, -latex] (P2) --
($(intersection-2)!.75cm!(intersection-1)$);


  \end{tikzpicture}
  \end{document} 

Answer 1

您可以使用与在Tikz：曲线的单位切向量获取切向矢量：

如果您已经定义了一个非常小的圆路径aux1，例如，围绕切线/法线点，则可以找到此圆与曲线之间的交点。两个交点之间的连接线将大致与曲线相切。要绘制法线，可以使用calc旋转线的语法：

(P2) -- ($(P2)!0.75cm!-90:($(intersection-2)!.75cm!(intersection-1)$)$)

---

  \documentclass[tikz, border=5mm]{standalone}
  \usetikzlibrary{arrows,calc, decorations.markings, intersections}

  \begin{document}

  \begin{tikzpicture}[
    dot/.style = {outer sep = +0pt, inner sep = +0pt, shape = circle, draw = black, label = {#1}},
    small dot/.style = {minimum size = 1pt, dot = {#1}},
    big dot/.style = {minimum size = 2pt, dot = {#1}},
    line join = round, line cap = round, >=triangle 45
    ]
    \node[ fill = black, big dot = {below: \(F\)}] (F) at (0, 0) {};
    \node[ fill = black, big dot = {below: \(P_1\)}] (P1)  at (2, 0) {};
    \node[ fill = black, big dot = {above right=.25cm:\(P_2\)}] (P2) at (-2, 2) {};    

    \begin{pgfinterruptboundingbox}                  
    \begin{scope}[decoration = {markings,
        mark = at position 0.5 with {\arrow{>}}
      }]
      \clip (2, 0) -- (-2, 0) -- (-2, 4) -- (2, 4) -- cycle;
      \draw[name path global = ellp, postaction = decorate] let
        \p0 = ($(P2) - (F)$),
        \p1 = ($(P1) - (P2)$)
      in (P2|-P1) ++ (\x1, 0) arc (0:100: \x1 and \y0);                                         
  \end{scope}
\end{pgfinterruptboundingbox}

\path[name path = aux1] (P2) circle [radius = 1bp];
\draw[name intersections = {of = ellp and aux1}, -latex] (P2) --
($(intersection-2)!.75cm!(intersection-1)$);
\draw [-latex] (P2) --
($(P2)!0.75cm!-90:($(intersection-2)!.75cm!(intersection-1)$)$);


  \end{tikzpicture}
  \end{document}