贝塞尔曲线（相对）段的修饰

Question

我想修改贝塞尔曲线tikz，例如

\draw (0,0) .. controls +(87:2.3) and +(50:-0.7) .. (1,1);

这样，中间的部分就用点来绘制（而不是完整的实线），而起点和终点仍然是实线。我可以用下面的 MWE（见下文）从原则上解决这个问题，但参数pre length=和post length=必须在绝对坐标中定义。我如何更改它以指定相对位置（例如从路径长度的 0.3 到 0.8）？

具体来说，有一个\pgfdecoratedpathlength变量（TikZ 中曲线的长度)，但我不知道如何在dotted part of curve不出错的情况下将其包含在我的定义中。或者有其他更好的方法吗？

梅威瑟：

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.markings,calc}
\begin{document}

\begin{tikzpicture}[scale=1] % <- except of line/dot width drawing should be independent of scaling

\tikzset{
    dotted part of curve/.style args={between #1 and #2 with color #3}{
        #3,
        decorate,
        decoration={
            markings,
            mark=between positions 0 and 1 step 3*\pgflinewidth with{\fill[radius=\pgflinewidth,#3] (0,0) circle;},
            pre length=#1,
            post length=#2,
            pre=curveto,
            post=curveto,
            %post=moveto, % <-- alternate end: no drawing
        }
    },
    dotted part of curve/.default={between 0.5cm and 0.3cm with color red},
    % dotted part of curve/.default={between 0.3 and 0.8 with color red}, % <-- desired: relative positions
}

\draw (0,0) .. controls +(87:2.3) and +(50:-0.7) .. (1,1);
\draw[dotted part of curve] (0,0) .. controls +(87:2.3) and +(50:-0.7) .. (1,1);

\end{tikzpicture}
\end{document}

Answer 1

您可以使用\pgfdecoratedinputsegmentlength：

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\tikzset{
  dotted part of curve/.style args={between #1 and #2 with color #3}{
    postaction={decorate,draw,#3,
      decoration={
        markings,
        mark=between positions 0 and 1 step 3*\pgflinewidth 
          with{\fill[radius=\pgflinewidth,#3] (0,0) circle;},
        pre=curveto, pre length=#1*\pgfdecoratedinputsegmentlength,
        post=curveto, post length=(1-#2)*\pgfdecoratedinputsegmentlength
  }}},
  dotted part of curve/.default={between 0.3 and 0.8 with color red}
}

\begin{document}
\begin{tikzpicture}[scale=1] 
\draw
  [dotted part of curve]
  (0,0) .. controls +(87:2.3) and +(50:-0.7) .. (1,1);
\end{tikzpicture}
\end{document}

结果：

如果post=curveto替换为post=moveto结果变为

---

如果背景中不应该有黑线，您可以在上面的代码中\path使用：\draw

\path% <-
  [dotted part of curve]
  (0,0) .. controls +(87:2.3) and +(50:-0.7) .. (1,1);

或者

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\tikzset{
  dotted part of curve/.style args={between #1 and #2 with color #3}{
    decorate,
    #3,
    decoration={
      markings,
      mark=between positions 0 and 1 step 3*\pgflinewidth 
        with{\fill[radius=\pgflinewidth,#3] (0,0) circle;},
      pre=curveto, pre length=#1*\pgfdecoratedinputsegmentlength,
      post=curveto, post length=(1-#2)*\pgfdecoratedinputsegmentlength
  }},
  dotted part of curve/.default={between 0.3 and 0.8 with color red}
}

\begin{document}
\begin{tikzpicture}[scale=1] 
\draw
  [dotted part of curve]
  (0,0) .. controls +(87:2.3) and +(50:-0.7) .. (1,1);
\end{tikzpicture}
\end{document}

Answer 2

对于单条贝塞尔曲线，基本层\pgfpathcurvebetweentime命令可能很有用，而且肯定比装饰更有效。不幸的是，默认情况下没有 TikZ 界面，但下面显示了一种略显粗糙（但可用）的方法：

\documentclass[tikz,border=5]{standalone}
\tikzset{part curve/.style args={%
  from #1 to #2 curve #3 .. controls #4 and #5 .. #6}{insert path={
    #3 coordinate (@1) #4 coordinate (@2)
    #5 coordinate (@3) #6 coordinate (@4)
    \pgfextra{\pgfpathcurvebetweentime{#1}{#2}%
      {\pgfpointanchor{@1}{center}}{\pgfpointanchor{@2}{center}}%
      {\pgfpointanchor{@3}{center}}{\pgfpointanchor{@4}{center}}}
}}}
\begin{document}
\begin{tikzpicture}
\path
  (0,0) coordinate (P1)
  +(87:2.3) coordinate (P2)
  (1,1) coordinate (P4)
  +(50:-0.7) coordinate (P3);
\draw [help lines] (P1) .. controls (P2) and (P3) .. (P4);
\draw [red, thick,
  part curve={from 0.0 to 0.3 curve (P1) .. controls (P2) and (P3) .. (P4)}];
\draw [green!50!black, thick, dotted,
  part curve={from 0.3 to 0.8 curve (P1) .. controls (P2) and (P3) .. (P4)}];
\draw [blue, thick, dashed,
  part curve={from 0.8 to 1.0 curve (P1) .. controls (P2) and (P3) .. (P4)}];
\end{tikzpicture}
\end{document}