我想绘制曲线的所谓“通用点”，其中曲线本身是curve.table使用gnuplot 表绘制的tikz。这基本上相当于将图变形为波浪形或卷曲形。
通用点是代数几何中的一个概念，表示曲线上“无处不在”的点。它通常由曲线上的某个超粗点、各种大小的散点或波浪形、卷曲或盘绕的线表示。不幸的是（也令人震惊），我在五分钟内能找到的唯一这种可视化示例来自wiki/Zariski 拓扑#示例：
我更喜欢波浪线或一些散射点，但我想这也行。
这是我目前所拥有的一个例子：
\documentclass[border=3]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw plot[smooth,scale=0.5] file {curve.table};
\end{tikzpicture}
\end{document}
这里，curve.table指的是我使用生成的抛物线gnuplot，数据在这里pastebin/ZJDWcXcc如果你需要它。因此，此 tex 代码产生以下内容：
我想修改该抛物线，使其变得弯曲/波浪形/卷曲/盘绕或上面有一些散点。我该怎么做？
Tikz 的设施装饰是一个候选。问题是 tikz 似乎只能修饰路径。我也不想用 tikz 本身来绘图，因为 tikz 似乎无法绘制零组方程（或者可以吗？），而且随着曲线变得越来越复杂，对它们进行参数化根本不是一个选择……
答案1
您在问题下方的最后一条评论中谈到的断开源自 的分段性质curve.table。它包含从末尾开始的一个段，然后是该段之前的段，依此类推。因此 TikZ 开始为每个段进行修饰。
通过对表格进行排序，所有东西都被装饰成一个整体，断开连接的地方也消失了。
排序是通过
sort -h curve.table > curve-sorted.table
在Linux下。然后我用文本编辑器删除了中间的空行和注释行。
代码：
\documentclass[border=3]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}
\begin{document}
\begin{tikzpicture}
\draw[decorate,decoration={coil,aspect=0.8,amplitude=1.5pt,segment length=2.5pt}] plot[scale=0.5] file {curve.table};
\node at (0,-0.5) {unsorted};
\end{tikzpicture}
\hspace{1cm}
\begin{tikzpicture}
\draw[decorate,decoration={coil,aspect=0.8,amplitude=1.5pt,segment length=2.5pt}] plot[scale=0.5] file {curve-sorted.table};
\node at (0,-0.5) {sorted};
\end{tikzpicture}
\end{document}
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答案2
我不知道如何使用 TikZ 来实现，但我建议使用一个简短的代码pstricks，更具体地说是使用pst-coil：
\documentclass{article}
\usepackage[showframe, margin = 5mm]{geometry}
\usepackage{pstricks-add, pst-coil}% auto-pst-pdf
\begin{document}
\noindent
\psset{unit = 0.8cm}
\begin{pspicture}(0.4,-2)(25,2)
\psset{coilheight = 1.75}
\psCoil{280}{6000}
\dotnodes[dotsize =15pt](3.1,-0.25){2}(6.60,-0.25){3}(12.375,-0.25){5}(18.56,-0.25){7}
\foreach \n in{2,3,5,7} {\nput{-90}{\n}{(\n)}}
\rput(21,1){$(0)$}
\end{pspicture}
\end{document}
