Tikz：沿曲线增加点间距

Question

我有由 3 个点创建的虚线，但我希望曲线上的点密度不断增加。我设法创建了一个点图案，但间距是固定的。一般情况下，我没有曲线方程。

是否可以使用 tikz 直接控制曲线上点的密度？也许有一个功能？

\documentclass[8pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{calc}
\usepgfplotslibrary{fillbetween}

% Dot pattern
\tikzset{
    dot diameter/.store in=\dot@diameter,
    dot diameter=2pt,
    dot spacing/.store in=\dot@spacing,
    dot spacing=3pt,
    dots/.style={
        line width=\dot@diameter,
        line cap=round,
        dash pattern=on 0pt off \dot@spacing
    }
}

\begin{document}
        \begin{tikzpicture}
        \coordinate (z) at (0.9,-1);
 
        % Dots along a curve
        \draw[draw=black,dots] plot [smooth,tension=1] coordinates { ($(z)+(-0.5,-1)$) ($(z)+(0.1,-0.5)$) ($(0,0)$) };

        \end{tikzpicture}
\end{document}

谢谢 ！

Answer 1

是的，可以这样做。下面有两个选项：要么将位置传递给列表，要么为间距定义一个函数。第二个选项的语法是

variable dots={<function>}{<samples>}

例如

variable dots={2*\x/(10+\x)}{1,...,7}

其中，默认情况下，函数是 的函数\x。代码已注释。dimension too large使用 还可以避免错误fpu。

\documentclass[8pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.markings,fpu}

\tikzset{dot diameter/.initial=2pt,
add marking position/.code={\edef\x{#1}%
\pgfmathparse{spacingfunction(\x)}%
\ifx\mymarkpositions\empty
\edef\mymarkpositions{\pgfmathresult}
\else
\edef\mymarkpositions{\mymarkpositions,\pgfmathresult}%
\fi},variable dots/.code 2 args={%
\tikzset{declare function={spacingfunction(\x)=#1;}}%
\let\mymarkpositions\empty%
\tikzset{add marking position/.list={#2}}%
%\typeout{\mymarkpositions}
\tikzset{postaction={decorate,decoration={markings,%
my mark/.list/.expanded={\mymarkpositions}}}}}}
\tikzset{/pgf/decoration/my mark/.code=\tikzset{/pgf/decoration/mark={at position #1 with 
    {\fill circle[radius=\pgfkeysvalueof{/tikz/dot diameter}];}}}}
\begin{document}
\begin{tikzpicture}
 \coordinate (z) at (0.9,-1);
 % Dots along a curve
 \draw[/pgf/fpu/install only={reciprocal},%<- only to avoid "dimension too large" errors
    draw=black,postaction={decorate,decoration={markings,
    my mark/.list={0.18181,0.33333,0.46153,0.57143,0.66666,0.75,0.82352}%<- explicit list
    }}] 
    plot [smooth,tension=1] coordinates 
 { ($(z)+(-0.5,-1)$) ($(z)+(0.1,-0.5)$) ($(0,0)$) };
\end{tikzpicture}

\begin{tikzpicture}
 \coordinate (z) at (0.9,-1);
 % Dots along a curve
 \draw[/pgf/fpu/install only={reciprocal},%<- only to avoid "dimension too large" errors
    draw=black,variable dots={2*\x/(10+\x)}%<- function
    {1,...,7}]%<- arguments 
    plot [smooth,tension=1] coordinates 
 { ($(z)+(-0.5,-1)$) ($(z)+(0.1,-0.5)$) ($(0,0)$) };
\end{tikzpicture}

\end{document}