如何用特定坐标处的箭头装饰路径？

Question

该手册的第 243 和 244 页可以找到以下文本摘录：

最后一句警告：装饰的排版可能相当慢，并且可能不准确。

和

由于 TEX 精度的限制，跨越输入段边界时的定位偶尔会出现不准确的情况。

也就是说，特征修饰的准确度是有限的，我们现在就来看看。下图是我通过代码构建的，位于本回答的末尾。

装饰不准确

黄色曲线是带有节点的相应控制曲线的表示。在这些曲线中，我们确定了交点并将其涂成红色。蓝点是这些相同交点的表示，但使用了装饰功能（很奇怪，是吧？）。绿色箭头是我发现的解决您的问题的方法。

这是一个缓慢的解决方案，因为我将路径与自身相交以将其变成一组节点。我相信一定有更优雅的方法来做到这一点。=)

etoolbox包用于方便变量的管理和比较。

此外，在比较时，还必须添加误差幅度。根据您要执行的操作，可能需要增加或减少此幅度。

\documentclass[border=2mm,tikz]{standalone}

\usepackage{calc}
\usepackage{etoolbox}

\usetikzlibrary{intersections, calc, shapes.arrows, decorations.markings}

\newcounter{cnt}
\newcommand\setpoint[2]{\csxdef{point#1}{#2}}
\newcommand\getpoint[1]{\csuse{point#1}}

\newcounter{curveindex}

\begin{document}
    \begin{tikzpicture} 

        \clip (-2,-2) rectangle (2,2);

        \draw [name path=curve 1] (-2,-1) .. controls (8,-1) and (-8,1) .. (2,1);
        \draw [name path=curve 2] (-1,-2) .. controls (-1,8) and (1,-8) .. (1,2);

        \path [name intersections={of=curve 1 and curve 1, name=i, total=\t, sort by = curve 1}] node {\xdef\totalone{\t}};
        \path [name intersections={of=curve 1 and curve 2, name=j, total=\t, sort by = curve 1}] node {\xdef\totaltwo{\t}};

        \pgfmathsetmacro{\myunit}{1/(\totalone)}

        \newdimen\xone
        \newdimen\yone
        \newdimen\xtwo
        \newdimen\ytwo

        \foreach \q in {1, ..., \totaltwo}
        {
            \pgfextractx{\xtwo}{\pgfpointanchor{j-\q}{center}}
            \pgfextracty{\ytwo}{\pgfpointanchor{j-\q}{center}}

            \foreach \p in {1, ..., \totalone}
            {
                \pgfextractx{\xone}{\pgfpointanchor{i-\p}{center}}
                \pgfextracty{\yone}{\pgfpointanchor{i-\p}{center}}

                \ifboolexpr{
                    test {\ifdimless{\xtwo - 0.5pt}{\xone}} and test {\ifdimless{\xone}{\xtwo + 0.5pt}}
                    and
                    test {\ifdimless{\ytwo - 0.5pt}{\yone}} and test {\ifdimless{\yone}{\ytwo + 0.5pt}}
                }{
                    \setpoint{\q}{\p}
                }{
                }
            }
        }

        \edef\mypath{}
        \pgfmathsetmacro{\lastbutone}{\totalone - 1}
        \foreach \k in {1, ..., \lastbutone}
        {
            \xdef\mypath{\mypath (i-\k) -- }
        }
        \edef\mypath{\mypath (i-\totalone)}

        \draw [yellow, line width = 1mm, opacity = 0.5] \mypath;

        \foreach \k in {1, ..., \totaltwo}
        {
            \pgfmathsetmacro{\positioning}{\getpoint{\k} * \myunit}
            \draw [decorate, decoration = {markings, mark = at position \positioning with {
                \node [
                    circle
                    , fill = blue
                    , inner sep = 1pt
                ]{};
            }}] \mypath;
        }

        \foreach \k in {1, ..., \totaltwo}
        {
           \node [
                circle
                , fill = red
                , inner sep = 1pt
                , opacity = 0.7
            ] at (i-\getpoint{\k}) {};
        }

        \foreach \k in {1, ..., \totaltwo}
        {
            \pgfmathsetmacro{\lastpoint}{\getpoint{\k} - 1}
            \draw [decorate, decoration = {markings, mark = at position -0.1pt with {
                \node [
                    single arrow
                    , fill = green
                    , anchor = east
                    , minimum size = 2mm
                    , inner sep = 1pt
                    , single arrow head extend = 2pt
                    , transform shape
                    , opacity = 0.8
                ]{};
            }}] (i-\lastpoint) -- (i-\getpoint{\k});
        }

    \end{tikzpicture}
\end{document}

Answer 1