TikZ：使用名称交叉点来定义节点

Question

两个问题：

1. 这些从交叉点定义的节点出了什么问题？
2. 能否使用\foreach语法自动找到第二点的其他向量？我没搞明白。

---

\documentclass[tikz]{standalone}
\usepackage{amsmath}

\usetikzlibrary{intersections}
\usetikzlibrary{calc}

%  Used for both ellipses and circles                                               
\tikzset{%                                                                          
  partial ellipse/.style args = {#1:#2:#3}{%                                        
    insert path = {+ (#1:#3) arc (#1:#2:#3)}
  }
}

%  unit vectors                                                                     
\newcommand{\unit}[1]{\hat{\mathbf{#1}}}

\begin{document}
\begin{tikzpicture}
  \coordinate (O) at (0, 0);

  \draw[-latex] (O) -- (4, 0) node[pos = 1.1, font = \scriptsize] {\(x\)};
  \draw[-latex] (O) -- (0, 4) node[pos = 1.1, font = \scriptsize] {\(y\)};
  \draw[blue, name path = arc] (O) [partial ellipse = -15:75:3];


  \foreach \i/\angle in {1/60, 2/30}{
    \path[name path global = line\i] (O) -- (\angle:3.5);
    \path[name intersections = {of = arc and line\i, by = P\i}];
    \path[name path global = circ\i] (P\i) circle[radius = 1bp];

    \filldraw[black] (P\i) circle[radius = .025cm];
  }

  \node[coordinate, name intersections = {of = circ1 and arc}] (A1) at
  (intersection-1) {};
  \node[coordinate, name intersections = {of = circ1 and arc}] (A2) at
  (intersection-2) {};
  \draw[name intersections = {of = circ1 and arc}, -latex] (P1) --
  ($(A2)!.75cm!(A1)$) node[pos = 1.125, font = \tiny] {\(\unit{u}\)} coordinate
  (B1);

  \draw[-latex] (P1) -- ($(P1)!.75cm!-270:(B1)$) node[pos = 1.125,
  font = \tiny] {\(\unit{n}\)};
\end{tikzpicture}
\end{document}

从图中我们可以看到，第一个点绘制正确，只是存在相关错误。

Answer 1

对于现在遇到的错误，只需在 \foreach 循环中使用以下代码（pgf-manual p.496）：

\path[name path global/.expanded = line\i] (O) -- (\angle:3.5);
\path[name intersections/.expanded = {of = arc and line\i, by = P\i}];
\path[name path global/.expanded = circ\i] (P\i) circle[radius = 1bp];

\foreach这将允许您在循环外使用循环内定义的路径。

---

如果只是复制循环内的最后一个命令，\foreach则会出现以下错误：

! Paragraph ended before \tikz@intersect@path@names@parse was complete.

这是因为of键 (\tikz@intersect@path@names@parse) 需要周围的空格，and如果您使用 ，则空格显然会被剥离of = circ\i and arc，因此您需要使用of = {circ\i} and arc。

\documentclass[tikz]{standalone}
\usepackage{amsmath}

\usetikzlibrary{intersections}
\usetikzlibrary{calc}

%  Used for both ellipses and circles                                               
\tikzset{%                                                                          
  partial ellipse/.style args = {#1:#2:#3}{%                                        
    insert path = {+ (#1:#3) arc (#1:#2:#3)}
  }
}

%  unit vectors                                                                     
\newcommand{\unit}[1]{\hat{\mathbf{#1}}}

\begin{document}
\begin{tikzpicture}
  \coordinate (O) at (0, 0);

  \draw[-latex] (O) -- (4, 0) node[pos = 1.1, font = \scriptsize] {\(x\)};
  \draw[-latex] (O) -- (0, 4) node[pos = 1.1, font = \scriptsize] {\(y\)};
  \draw[blue, name path = arc] (O) [partial ellipse = -15:75:3];


  \foreach \i/\angle in {1/60, 2/30 }{
    \path[name path global= line\i] (O) -- (\angle:3.5);
    \path[name intersections = {of = arc and line\i, by = P\i}];
    \path[name path global = circ\i] (P\i) circle[radius = 1bp];
    \filldraw[black] (P\i) circle[radius = .025cm];
    \node[coordinate, name intersections = {of = {circ\i} and arc}] (A1) at  (intersection-1) {};
    \node[coordinate, name intersections = {of = {circ\i} and arc}] (A2) at  (intersection-2) {};
    \draw[name intersections/.expanded = {of = {circ\i} and arc}, -latex] (P\i) -- ($(A2)!.75cm!(A1)$) node[pos = 1.125, font = \tiny] {\(\unit{u}\)} coordinate (B1);
  \draw[-latex] (P\i) -- ($(P\i)!.75cm!-270:(B1)$) node[pos = 1.125, font = \tiny] {\(\unit{n}\)};
  }


\end{tikzpicture}
\end{document}