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TikZ：当我使用 draw let ... in 命令绘制一个简单的圆弧时，我得到的尺寸太大

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TikZ：当我使用 draw let ... in 命令绘制一个简单的圆弧时，我得到的尺寸太大 
\documentclass[convert = false, border = 2cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc, intersections}

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

  \begin{pgfinterruptboundingbox}
    \path[name path = line1] (O) -- (15:5cm);

    \draw (O) -- (-45:4.5cm) coordinate (P1);

    \path[name path = line2] (P1) -- +(0, 5cm);
    \path[name intersections = {of = line1 and line2, by = P2}];
  \end{pgfinterruptboundingbox}

  \draw let
    \p0 = (P1),
    \p1 = (P2),
    \p2 = (O),
    \n1 = {atan2(\x1 - \x0, \y1 - \y0)},
    \n2 = {atan2(\x2 - \x0, \y2 - \y0)},
    \n3 = {.75cm}
  in (P1) +(\n1:\n3) arc[radius = \n3, start angle = \n1, end angle = \n2];
\end{tikzpicture}
\end{document}

上述代码产生以下错误：

ERROR: Dimension too large.

--- TeX said ---
<recently read> \pgfmath@x

l.22     \n1 = {atan2(\x1 - \x0, \y1 - \y0)}
                                            ,
--- HELP ---
From the .log file...

I can't work with sizes bigger than about 19 feet.
Continue and I'll use the largest value I can

代码没有任何异常，我无法找出导致此问题的原因。我在图形周围画了一个边界框，它完全在页面内。

此外，它指向的线是一个圆弧，半径为，.75cm因此也可以大于19英尺。

答案1

这是由于atan2实现中的数值不稳定性造成的，自 2013-07-19 起，该问题已在 TikZ 的 CVS 版本中得到修复。

如果 y 分量太大，函数会因 y 和 x 分量之间的差异过大而崩溃。以下示例说明了这一点：

\documentclass{article}
\usepackage{tikz}

\begin{document}

\pgfmathparse{atan2(0.01,1000)}    % Crashes
\pgfmathparse{atan2(0.001,100)}    % Crashes
\pgfmathparse{atan2(0.01,100)}     % Is fine
\pgfmathparse{atan2(0.0001,10)}    % Is fine
\pgfmathparse{atan2(0.0000001,10)} % Is fine

\end{document}

为避免这种情况，您可以通过将两个分量除以 y 分量来使 y 分量等于 1。如果您使用的 TikZ 的 CVS 版本比 2013-07-19 更新，则无需执行此操作。

\documentclass[convert = false, border = 2cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc, intersections}

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

  \begin{pgfinterruptboundingbox}
    \path[name path = line1] (O) -- (15:5cm);

    \draw (O) -- (-45:4.5cm) coordinate (P1);

    \path[name path = line2] (P1) -- +(0, 5cm);
    \path[name intersections = {of = line1 and line2, by = P2}];
  \end{pgfinterruptboundingbox}

  \draw let
    \p0 = (P1),
    \p1 = (P2),
    \p2 = (O),
    \n1 = {atan2((\x1 - \x0)/(\y1 - \y0), 1)},
    \n2 = {atan2(\x2 - \x0, \y2 - \y0)},
    \n3 = {.75cm}
  in (P1) +(\n1:\n3) arc[radius = \n3, start angle = \n1, end angle = \n2];
\end{tikzpicture}
\end{document}

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