使用 tikz 从绘图表装饰绘图（绘制通用点）

Question

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……

Answer 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}

曲线排序表

-2.00000 4.00000 0.00000 
-1.99747 3.98998 0.00000 
-1.99494 3.97996 0.00000 
-1.99241 3.96994 0.00000 
-1.98988 3.95992 0.00000 
-1.98735 3.94990 0.00000 
-1.98482 3.93988 0.00000 
-1.98229 3.92986 0.00000 
-1.97976 3.91984 0.00000 
-1.97722 3.90982 0.00000 
-1.97469 3.89980 0.00000 
-1.97216 3.88978 0.00000 
-1.96963 3.87976 0.00000 
-1.96710 3.86974 0.00000 
-1.96457 3.85972 0.00000 
-1.96204 3.84970 0.00000 
-1.95960 3.84002 0.00000 
-1.95951 3.83968 0.00000 
-1.95693 3.82966 0.00000 
-1.95434 3.81964 0.00000 
-1.95176 3.80962 0.00000 
-1.94918 3.79960 0.00000 
-1.94659 3.78958 0.00000 
-1.94401 3.77956 0.00000 
-1.94143 3.76954 0.00000 
-1.93884 3.75952 0.00000 
-1.93626 3.74950 0.00000 
-1.93368 3.73948 0.00000 
-1.93109 3.72946 0.00000 
-1.92851 3.71944 0.00000 
-1.92593 3.70942 0.00000 
-1.92334 3.69940 0.00000 
-1.92076 3.68938 0.00000 
-1.91919 3.68330 0.00000 
-1.91815 3.67936 0.00000 
-1.91552 3.66934 0.00000 
-1.91288 3.65932 0.00000 
-1.91024 3.64930 0.00000 
-1.90760 3.63928 0.00000 
-1.90496 3.62926 0.00000 
-1.90233 3.61924 0.00000 
-1.89969 3.60922 0.00000 
-1.89705 3.59920 0.00000 
-1.89441 3.58918 0.00000 
-1.89177 3.57916 0.00000 
-1.88913 3.56914 0.00000 
-1.88650 3.55912 0.00000 
-1.88386 3.54910 0.00000 
-1.88122 3.53908 0.00000 
-1.87879 3.52984 0.00000 
-1.87858 3.52906 0.00000 
-1.87588 3.51904 0.00000 
-1.87319 3.50902 0.00000 
-1.87049 3.49900 0.00000 
-1.86779 3.48898 0.00000 
-1.86510 3.47896 0.00000 
-1.86240 3.46894 0.00000 
-1.85971 3.45892 0.00000 
-1.85701 3.44890 0.00000 
-1.85432 3.43888 0.00000 
-1.85162 3.42886 0.00000 
-1.84892 3.41884 0.00000 
-1.84623 3.40882 0.00000 
-1.84353 3.39880 0.00000 
-1.84084 3.38878 0.00000 
-1.83838 3.37966 0.00000 
-1.83814 3.37876 0.00000 
-1.83538 3.36874 0.00000 
-1.83263 3.35872 0.00000 
-1.82987 3.34870 0.00000 
-1.82711 3.33868 0.00000 
-1.82436 3.32866 0.00000 
-1.82160 3.31864 0.00000 
-1.81885 3.30862 0.00000 
-1.81609 3.29860 0.00000 
-1.81334 3.28858 0.00000 
-1.81058 3.27856 0.00000 
-1.80783 3.26854 0.00000 
-1.80507 3.25852 0.00000 
-1.80232 3.24850 0.00000 
-1.79956 3.23848 0.00000 
-1.79798 3.23273 0.00000 
-1.79678 3.22846 0.00000 
-1.79396 3.21844 0.00000 
-1.79114 3.20842 0.00000 
-1.78832 3.19840 0.00000 
-1.78551 3.18838 0.00000 
-1.78269 3.17836 0.00000 
-1.77987 3.16834 0.00000 
-1.77705 3.15832 0.00000 
-1.77423 3.14830 0.00000 
-1.77141 3.13828 0.00000 
-1.76860 3.12826 0.00000 
-1.76578 3.11824 0.00000 
-1.76296 3.10822 0.00000 
-1.76014 3.09820 0.00000 
-1.75758 3.08907 0.00000 
-1.75732 3.08818 0.00000 
-1.75443 3.07816 0.00000
-1.75443 3.07816 0.00000 
-1.75155 3.06814 0.00000 
-1.74867 3.05812 0.00000 
-1.74578 3.04810 0.00000 
-1.74290 3.03808 0.00000 
-1.74002 3.02806 0.00000 
-1.73713 3.01804 0.00000 
-1.73425 3.00802 0.00000 
-1.73136 2.99800 0.00000 
-1.72848 2.98798 0.00000 
-1.72560 2.97796 0.00000 
-1.72271 2.96794 0.00000 
-1.71983 2.95792 0.00000 
-1.71717 2.94868 0.00000 
-1.71694 2.94790 0.00000 
-1.71399 2.93788 0.00000 
-1.71104 2.92786 0.00000 
-1.70808 2.91784 0.00000 
-1.70513 2.90782 0.00000 
-1.70218 2.89780 0.00000 
-1.69923 2.88778 0.00000 
-1.69627 2.87776 0.00000 
-1.69332 2.86774 0.00000 
-1.69037 2.85772 0.00000 
-1.68742 2.84770 0.00000 
-1.68447 2.83768 0.00000 
-1.68151 2.82766 0.00000 
-1.67856 2.81764 0.00000 
-1.67677 2.81155 0.00000 
-1.67558 2.80762 0.00000 
-1.67256 2.79760 0.00000 
-1.66953 2.78758 0.00000 
-1.66651 2.77756 0.00000 
-1.66348 2.76754 0.00000 
-1.66046 2.75752 0.00000 
-1.65743 2.74749 0.00000 
-1.65441 2.73747 0.00000 
-1.65139 2.72745 0.00000 
-1.64836 2.71743 0.00000 
-1.64534 2.70741 0.00000 
-1.64231 2.69739 0.00000 
-1.63929 2.68737 0.00000 
-1.63636 2.67769 0.00000 
-1.63626 2.67735 0.00000 
-1.63316 2.66733 0.00000 
-1.63006 2.65731 0.00000 
-1.62696 2.64729 0.00000 
-1.62386 2.63727 0.00000 
-1.62076 2.62725 0.00000 
-1.61766 2.61723 0.00000 
-1.61456 2.60721 0.00000 
-1.61146 2.59719 0.00000 
-1.60836 2.58717 0.00000 
-1.60526 2.57715 0.00000 
-1.60216 2.56713 0.00000 
-1.59906 2.55711 0.00000 
-1.59596 2.54709 0.00000 
-1.59278 2.53707 0.00000 
-1.58960 2.52705 0.00000 
-1.58642 2.51703 0.00000 
-1.58324 2.50701 0.00000 
-1.58006 2.49699 0.00000 
-1.57689 2.48697 0.00000 
-1.57371 2.47695 0.00000 
-1.57053 2.46693 0.00000 
-1.56735 2.45691 0.00000 
-1.56417 2.44689 0.00000 
-1.56099 2.43687 0.00000 
-1.55781 2.42685 0.00000 
-1.55556 2.41975 0.00000 
-1.55460 2.41683 0.00000 
-1.55134 2.40681 0.00000 
-1.54808 2.39679 0.00000 
-1.54482 2.38677 0.00000 
-1.54155 2.37675 0.00000 
-1.53829 2.36673 0.00000 
-1.53503 2.35671 0.00000 
-1.53176 2.34669 0.00000 
-1.52850 2.33667 0.00000 
-1.52524 2.32665 0.00000 
-1.52197 2.31663 0.00000 
-1.51871 2.30661 0.00000 
-1.51545 2.29659 0.00000 
-1.51515 2.29568 0.00000 
-1.51210 2.28657 0.00000 
-1.50875 2.27655 0.00000 
-1.50540 2.26653 0.00000 
-1.50205 2.25651 0.00000 
-1.49870 2.24649 0.00000 
-1.49535 2.23647 0.00000 
-1.49200 2.22645 0.00000 
-1.48865 2.21643 0.00000 
-1.48529 2.20641 0.00000 
-1.48194 2.19639 0.00000 
-1.47859 2.18637 0.00000 
-1.47524 2.17635 0.00000 
-1.47475 2.17488 0.00000 
-1.47181 2.16633 0.00000 
-1.46836 2.15631 0.00000 
-1.46836 2.15631 0.00000 
-1.46492 2.14629 0.00000 
-1.46148 2.13627 0.00000 
-1.45803 2.12625 0.00000 
-1.45459 2.11623 0.00000 
-1.45114 2.10621 0.00000 
-1.44770 2.09619 0.00000 
-1.44425 2.08617 0.00000 
-1.44081 2.07615 0.00000 
-1.43737 2.06613 0.00000 
-1.43434 2.05734 0.00000 
-1.43391 2.05611 0.00000 
-1.43037 2.04609 0.00000 
-1.42682 2.03607 0.00000 
-1.42328 2.02605 0.00000 
-1.41974 2.01603 0.00000 
-1.41619 2.00601 0.00000 
-1.41265 1.99599 0.00000 
-1.40911 1.98597 0.00000 
-1.40557 1.97595 0.00000 
-1.40202 1.96593 0.00000 
-1.39848 1.95591 0.00000 
-1.39494 1.94589 0.00000 
-1.39394 1.94307 0.00000 
-1.39132 1.93587 0.00000 
-1.38767 1.92585 0.00000 
-1.38403 1.91583 0.00000 
-1.38038 1.90581 0.00000 
-1.37673 1.89579 0.00000 
-1.37309 1.88577 0.00000 
-1.36944 1.87575 0.00000 
-1.36579 1.86573 0.00000 
-1.36214 1.85571 0.00000 
-1.35850 1.84569 0.00000 
-1.35485 1.83567 0.00000 
-1.35354 1.83206 0.00000 
-1.35113 1.82565 0.00000 
-1.34738 1.81563 0.00000 
-1.34362 1.80561 0.00000 
-1.33986 1.79559 0.00000 
-1.33610 1.78557 0.00000 
-1.33235 1.77555 0.00000 
-1.32859 1.76553 0.00000 
-1.32483 1.75551 0.00000 
-1.32107 1.74549 0.00000 
-1.31732 1.73547 0.00000 
-1.31356 1.72545 0.00000 
-1.31313 1.72431 0.00000 
-1.30970 1.71543 0.00000 
-1.30582 1.70541 0.00000 
-1.30195 1.69539 0.00000 
-1.29807 1.68537 0.00000 
-1.29420 1.67535 0.00000 
-1.29032 1.66533 0.00000 
-1.28645 1.65531 0.00000 
-1.28257 1.64529 0.00000 
-1.27870 1.63527 0.00000 
-1.27482 1.62525 0.00000 
-1.27273 1.61983 0.00000 
-1.27089 1.61523 0.00000 
-1.26689 1.60521 0.00000 
-1.26289 1.59519 0.00000 
-1.25889 1.58517 0.00000 
-1.25489 1.57515 0.00000 
-1.25089 1.56513 0.00000 
-1.24689 1.55511 0.00000 
-1.24289 1.54509 0.00000 
-1.23889 1.53507 0.00000 
-1.23489 1.52505 0.00000 
-1.23232 1.51862 0.00000 
-1.23084 1.51503 0.00000 
-1.22671 1.50501 0.00000 
-1.22258 1.49499 0.00000 
-1.21844 1.48497 0.00000 
-1.21431 1.47495 0.00000 
-1.21018 1.46493 0.00000 
-1.20604 1.45491 0.00000 
-1.20191 1.44489 0.00000 
-1.19778 1.43487 0.00000 
-1.19364 1.42485 0.00000 
-1.19192 1.42067 0.00000 
-1.18943 1.41483 0.00000 
-1.18515 1.40481 0.00000 
-1.18087 1.39479 0.00000 
-1.17660 1.38477 0.00000 
-1.17232 1.37475 0.00000 
-1.16805 1.36473 0.00000 
-1.16377 1.35471 0.00000 
-1.15950 1.34469 0.00000 
-1.15522 1.33467 0.00000 
-1.15152 1.32599 0.00000 
-1.15092 1.32465 0.00000 
-1.14650 1.31463 0.00000 
-1.14207 1.30461 0.00000 
-1.13764 1.29459 0.00000 
-1.13321 1.28457 0.00000 
-1.12878 1.27455 0.00000 
-1.12435 1.26453 0.00000 
-1.11992 1.25451 0.00000 
-1.11992 1.25451 0.00000 
-1.11550 1.24449 0.00000 
-1.11111 1.23457 0.00000 
-1.11107 1.23447 0.00000 
-1.10647 1.22445 0.00000 
-1.10188 1.21443 0.00000 
-1.09729 1.20441 0.00000 
-1.09270 1.19439 0.00000 
-1.08810 1.18437 0.00000 
-1.08351 1.17435 0.00000 
-1.07892 1.16433 0.00000 
-1.07433 1.15431 0.00000 
-1.07071 1.14641 0.00000 
-1.06970 1.14429 0.00000 
-1.06493 1.13427 0.00000 
-1.06016 1.12425 0.00000 
-1.05539 1.11423 0.00000 
-1.05062 1.10421 0.00000 
-1.04585 1.09419 0.00000 
-1.04108 1.08417 0.00000 
-1.03631 1.07415 0.00000 
-1.03154 1.06413 0.00000 
-1.03030 1.06152 0.00000 
-1.02663 1.05411 0.00000 
-1.02167 1.04409 0.00000 
-1.01671 1.03407 0.00000 
-1.01175 1.02405 0.00000 
-1.00679 1.01403 0.00000 
-1.00183 1.00401 0.00000 
-0.99687 0.99399 0.00000 
-0.99191 0.98397 0.00000 
-0.98990 0.97990 0.00000 
-0.98683 0.97395 0.00000 
-0.98166 0.96393 0.00000 
-0.97650 0.95391 0.00000 
-0.97133 0.94389 0.00000 
-0.96616 0.93387 0.00000 
-0.96100 0.92385 0.00000 
-0.95583 0.91383 0.00000 
-0.95066 0.90381 0.00000 
-0.94949 0.90154 0.00000 
-0.94532 0.89379 0.00000 
-0.93993 0.88377 0.00000 
-0.93454 0.87375 0.00000 
-0.92915 0.86373 0.00000 
-0.92376 0.85371 0.00000 
-0.91837 0.84369 0.00000 
-0.91298 0.83367 0.00000 
-0.90909 0.82645 0.00000 
-0.90752 0.82365 0.00000 
-0.90188 0.81363 0.00000 
-0.89624 0.80361 0.00000 
-0.89061 0.79359 0.00000 
-0.88497 0.78357 0.00000 
-0.87934 0.77355 0.00000 
-0.87370 0.76353 0.00000 
-0.86869 0.75462 0.00000 
-0.86803 0.75351 0.00000 
-0.86213 0.74349 0.00000 
-0.85622 0.73347 0.00000 
-0.85032 0.72345 0.00000 
-0.84441 0.71343 0.00000 
-0.83851 0.70341 0.00000 
-0.83260 0.69339 0.00000 
-0.82828 0.68605 0.00000 
-0.82662 0.68337 0.00000 
-0.82042 0.67335 0.00000 
-0.81422 0.66333 0.00000 
-0.80802 0.65331 0.00000 
-0.80182 0.64329 0.00000 
-0.79562 0.63327 0.00000 
-0.78942 0.62325 0.00000 
-0.78788 0.62075 0.00000 
-0.78298 0.61323 0.00000 
-0.77645 0.60321 0.00000 
-0.76992 0.59319 0.00000 
-0.76340 0.58317 0.00000 
-0.75687 0.57315 0.00000 
-0.75035 0.56313 0.00000 
-0.74747 0.55872 0.00000 
-0.74362 0.55311 0.00000 
-0.73673 0.54309 0.00000 
-0.72984 0.53307 0.00000 
-0.72295 0.52305 0.00000 
-0.71606 0.51303 0.00000 
-0.70917 0.50301 0.00000 
-0.70707 0.49995 0.00000 
-0.70200 0.49299 0.00000 
-0.69471 0.48297 0.00000 
-0.68741 0.47295 0.00000 
-0.68012 0.46293 0.00000 
-0.67283 0.45291 0.00000 
-0.66667 0.44444 0.00000 
-0.66546 0.44289 0.00000 
-0.65771 0.43287 0.00000 
-0.64996 0.42285 0.00000 
-0.64221 0.41283 0.00000 
-0.63446 0.40281 0.00000 
-0.62671 0.39279 0.00000 
-0.62671 0.39279 0.00000 
-0.62626 0.39220 0.00000 
-0.61848 0.38277 0.00000 
-0.61021 0.37275 0.00000 
-0.60194 0.36273 0.00000 
-0.59368 0.35271 0.00000 
-0.58586 0.34323 0.00000 
-0.58538 0.34269 0.00000 
-0.57652 0.33267 0.00000 
-0.56766 0.32265 0.00000 
-0.55881 0.31263 0.00000 
-0.54995 0.30261 0.00000 
-0.54545 0.29752 0.00000 
-0.54076 0.29259 0.00000 
-0.53122 0.28257 0.00000 
-0.52168 0.27255 0.00000 
-0.51214 0.26253 0.00000 
-0.50505 0.25508 0.00000 
-0.50240 0.25251 0.00000 
-0.49207 0.24248 0.00000 
-0.48173 0.23246 0.00000 
-0.47140 0.22244 0.00000 
-0.46465 0.21590 0.00000 
-0.46074 0.21242 0.00000 
-0.44947 0.20240 0.00000 
-0.43820 0.19238 0.00000 
-0.42692 0.18236 0.00000 
-0.42424 0.17998 0.00000 
-0.41479 0.17234 0.00000 
-0.40239 0.16232 0.00000 
-0.38999 0.15230 0.00000 
-0.38384 0.14733 0.00000 
-0.37690 0.14228 0.00000 
-0.36312 0.13226 0.00000 
-0.34934 0.12224 0.00000 
-0.34343 0.11795 0.00000 
-0.33458 0.11222 0.00000 
-0.31908 0.10220 0.00000 
-0.30358 0.09218 0.00000 
-0.30303 0.09183 0.00000 
-0.28595 0.08216 0.00000 
-0.26823 0.07214 0.00000 
-0.26263 0.06897 0.00000 
-0.24850 0.06212 0.00000 
-0.22784 0.05210 0.00000 
-0.22222 0.04938 0.00000 
-0.20416 0.04208 0.00000 
-0.18182 0.03306 0.00000 
-0.17874 0.03206 0.00000 
-0.14774 0.02204 0.00000 
-0.14141 0.02000 0.00000 
-0.10852 0.01202 0.00000 
-0.10101 0.01020 0.00000 
-0.06061 0.00367 0.00000 
-0.03995 0.00200 0.00000 
-0.02020 0.00041 0.00000 
0.02020 0.00041 0.00000 
0.03995 0.00200 0.00000 
0.06061 0.00367 0.00000 
0.10101 0.01020 0.00000 
0.10852 0.01202 0.00000 
0.14141 0.02000 0.00000 
0.14774 0.02204 0.00000 
0.17874 0.03206 0.00000 
0.18182 0.03306 0.00000 
0.20416 0.04208 0.00000 
0.22222 0.04938 0.00000 
0.22784 0.05210 0.00000 
0.24850 0.06212 0.00000 
0.26263 0.06897 0.00000 
0.26823 0.07214 0.00000 
0.28595 0.08216 0.00000 
0.30303 0.09183 0.00000 
0.30358 0.09218 0.00000 
0.31908 0.10220 0.00000 
0.33458 0.11222 0.00000 
0.34343 0.11795 0.00000 
0.34934 0.12224 0.00000 
0.36312 0.13226 0.00000 
0.37690 0.14228 0.00000 
0.38384 0.14733 0.00000 
0.38999 0.15230 0.00000 
0.40239 0.16232 0.00000 
0.41479 0.17234 0.00000 
0.42424 0.17998 0.00000 
0.42692 0.18236 0.00000 
0.43820 0.19238 0.00000 
0.44947 0.20240 0.00000 
0.46074 0.21242 0.00000 
0.46465 0.21590 0.00000 
0.47140 0.22244 0.00000 
0.48173 0.23246 0.00000 
0.49207 0.24248 0.00000 
0.50240 0.25251 0.00000 
0.50505 0.25508 0.00000 
0.51214 0.26253 0.00000 
0.52168 0.27255 0.00000 
0.53122 0.28257 0.00000 
0.54076 0.29259 0.00000 
0.54076 0.29259 0.00000 
0.54545 0.29752 0.00000 
0.54995 0.30261 0.00000 
0.55881 0.31263 0.00000 
0.56766 0.32265 0.00000 
0.57652 0.33267 0.00000 
0.58538 0.34269 0.00000 
0.58586 0.34323 0.00000 
0.59368 0.35271 0.00000 
0.60194 0.36273 0.00000 
0.61021 0.37275 0.00000 
0.61848 0.38277 0.00000 
0.62626 0.39220 0.00000 
0.62671 0.39279 0.00000 
0.63446 0.40281 0.00000 
0.64221 0.41283 0.00000 
0.64996 0.42285 0.00000 
0.65771 0.43287 0.00000 
0.66546 0.44289 0.00000 
0.66667 0.44444 0.00000 
0.67283 0.45291 0.00000 
0.68012 0.46293 0.00000 
0.68741 0.47295 0.00000 
0.69471 0.48297 0.00000 
0.70200 0.49299 0.00000 
0.70707 0.49995 0.00000 
0.70917 0.50301 0.00000 
0.71606 0.51303 0.00000 
0.72295 0.52305 0.00000 
0.72984 0.53307 0.00000 
0.73673 0.54309 0.00000 
0.74362 0.55311 0.00000 
0.74747 0.55872 0.00000 
0.75035 0.56313 0.00000 
0.75687 0.57315 0.00000 
0.76340 0.58317 0.00000 
0.76992 0.59319 0.00000 
0.77645 0.60321 0.00000 
0.78298 0.61323 0.00000 
0.78788 0.62075 0.00000 
0.78942 0.62325 0.00000 
0.79562 0.63327 0.00000 
0.80182 0.64329 0.00000 
0.80802 0.65331 0.00000 
0.81422 0.66333 0.00000 
0.82042 0.67335 0.00000 
0.82662 0.68337 0.00000 
0.82828 0.68605 0.00000 
0.83260 0.69339 0.00000 
0.83851 0.70341 0.00000 
0.84441 0.71343 0.00000 
0.85032 0.72345 0.00000 
0.85622 0.73347 0.00000 
0.86213 0.74349 0.00000 
0.86803 0.75351 0.00000 
0.86869 0.75462 0.00000 
0.87370 0.76353 0.00000 
0.87934 0.77355 0.00000 
0.88497 0.78357 0.00000 
0.89061 0.79359 0.00000 
0.89624 0.80361 0.00000 
0.90188 0.81363 0.00000 
0.90752 0.82365 0.00000 
0.90909 0.82645 0.00000 
0.91298 0.83367 0.00000 
0.91837 0.84369 0.00000 
0.92376 0.85371 0.00000 
0.92915 0.86373 0.00000 
0.93454 0.87375 0.00000 
0.93993 0.88377 0.00000 
0.94532 0.89379 0.00000 
0.94949 0.90154 0.00000 
0.95066 0.90381 0.00000 
0.95583 0.91383 0.00000 
0.96100 0.92385 0.00000 
0.96616 0.93387 0.00000 
0.97133 0.94389 0.00000 
0.97650 0.95391 0.00000 
0.98166 0.96393 0.00000 
0.98683 0.97395 0.00000 
0.98990 0.97990 0.00000 
0.99191 0.98397 0.00000 
0.99687 0.99399 0.00000 
1.00183 1.00401 0.00000 
1.00679 1.01403 0.00000 
1.01175 1.02405 0.00000 
1.01671 1.03407 0.00000 
1.02167 1.04409 0.00000 
1.02663 1.05411 0.00000 
1.03030 1.06152 0.00000 
1.03154 1.06413 0.00000 
1.03631 1.07415 0.00000 
1.04108 1.08417 0.00000 
1.04585 1.09419 0.00000 
1.05062 1.10421 0.00000 
1.05539 1.11423 0.00000 
1.06016 1.12425 0.00000 
1.06493 1.13427 0.00000 
1.06970 1.14429 0.00000 
1.06970 1.14429 0.00000 
1.07071 1.14641 0.00000 
1.07433 1.15431 0.00000 
1.07892 1.16433 0.00000 
1.08351 1.17435 0.00000 
1.08810 1.18437 0.00000 
1.09270 1.19439 0.00000 
1.09729 1.20441 0.00000 
1.10188 1.21443 0.00000 
1.10647 1.22445 0.00000 
1.11107 1.23447 0.00000 
1.11111 1.23457 0.00000 
1.11550 1.24449 0.00000 
1.11992 1.25451 0.00000 
1.12435 1.26453 0.00000 
1.12878 1.27455 0.00000 
1.13321 1.28457 0.00000 
1.13764 1.29459 0.00000 
1.14207 1.30461 0.00000 
1.14650 1.31463 0.00000 
1.15092 1.32465 0.00000 
1.15152 1.32599 0.00000 
1.15522 1.33467 0.00000 
1.15950 1.34469 0.00000 
1.16377 1.35471 0.00000 
1.16805 1.36473 0.00000 
1.17232 1.37475 0.00000 
1.17660 1.38477 0.00000 
1.18087 1.39479 0.00000 
1.18515 1.40481 0.00000 
1.18943 1.41483 0.00000 
1.19192 1.42067 0.00000 
1.19364 1.42485 0.00000 
1.19778 1.43487 0.00000 
1.20191 1.44489 0.00000 
1.20604 1.45491 0.00000 
1.21018 1.46493 0.00000 
1.21431 1.47495 0.00000 
1.21844 1.48497 0.00000 
1.22258 1.49499 0.00000 
1.22671 1.50501 0.00000 
1.23084 1.51503 0.00000 
1.23232 1.51862 0.00000 
1.23489 1.52505 0.00000 
1.23889 1.53507 0.00000 
1.24289 1.54509 0.00000 
1.24689 1.55511 0.00000 
1.25089 1.56513 0.00000 
1.25489 1.57515 0.00000 
1.25889 1.58517 0.00000 
1.26289 1.59519 0.00000 
1.26689 1.60521 0.00000 
1.27089 1.61523 0.00000 
1.27273 1.61983 0.00000 
1.27482 1.62525 0.00000 
1.27870 1.63527 0.00000 
1.28257 1.64529 0.00000 
1.28645 1.65531 0.00000 
1.29032 1.66533 0.00000 
1.29420 1.67535 0.00000 
1.29807 1.68537 0.00000 
1.30195 1.69539 0.00000 
1.30582 1.70541 0.00000 
1.30970 1.71543 0.00000 
1.31313 1.72431 0.00000 
1.31356 1.72545 0.00000 
1.31732 1.73547 0.00000 
1.32107 1.74549 0.00000 
1.32483 1.75551 0.00000 
1.32859 1.76553 0.00000 
1.33235 1.77555 0.00000 
1.33610 1.78557 0.00000 
1.33986 1.79559 0.00000 
1.34362 1.80561 0.00000 
1.34738 1.81563 0.00000 
1.35113 1.82565 0.00000 
1.35354 1.83206 0.00000 
1.35485 1.83567 0.00000 
1.35850 1.84569 0.00000 
1.36214 1.85571 0.00000 
1.36579 1.86573 0.00000 
1.36944 1.87575 0.00000 
1.37309 1.88577 0.00000 
1.37673 1.89579 0.00000 
1.38038 1.90581 0.00000 
1.38403 1.91583 0.00000 
1.38767 1.92585 0.00000 
1.39132 1.93587 0.00000 
1.39394 1.94307 0.00000 
1.39494 1.94589 0.00000 
1.39848 1.95591 0.00000 
1.40202 1.96593 0.00000 
1.40557 1.97595 0.00000 
1.40911 1.98597 0.00000 
1.41265 1.99599 0.00000 
1.41619 2.00601 0.00000 
1.41974 2.01603 0.00000 
1.42328 2.02605 0.00000 
1.42682 2.03607 0.00000 
1.42682 2.03607 0.00000 
1.43037 2.04609 0.00000 
1.43391 2.05611 0.00000 
1.43434 2.05734 0.00000 
1.43737 2.06613 0.00000 
1.44081 2.07615 0.00000 
1.44425 2.08617 0.00000 
1.44770 2.09619 0.00000 
1.45114 2.10621 0.00000 
1.45459 2.11623 0.00000 
1.45803 2.12625 0.00000 
1.46148 2.13627 0.00000 
1.46492 2.14629 0.00000 
1.46836 2.15631 0.00000 
1.47181 2.16633 0.00000 
1.47475 2.17488 0.00000 
1.47524 2.17635 0.00000 
1.47859 2.18637 0.00000 
1.48194 2.19639 0.00000 
1.48529 2.20641 0.00000 
1.48865 2.21643 0.00000 
1.49200 2.22645 0.00000 
1.49535 2.23647 0.00000 
1.49870 2.24649 0.00000 
1.50205 2.25651 0.00000 
1.50540 2.26653 0.00000 
1.50875 2.27655 0.00000 
1.51210 2.28657 0.00000 
1.51515 2.29568 0.00000 
1.51545 2.29659 0.00000 
1.51871 2.30661 0.00000 
1.52197 2.31663 0.00000 
1.52524 2.32665 0.00000 
1.52850 2.33667 0.00000 
1.53176 2.34669 0.00000 
1.53503 2.35671 0.00000 
1.53829 2.36673 0.00000 
1.54155 2.37675 0.00000 
1.54482 2.38677 0.00000 
1.54808 2.39679 0.00000 
1.55134 2.40681 0.00000 
1.55460 2.41683 0.00000 
1.55556 2.41975 0.00000 
1.55781 2.42685 0.00000 
1.56099 2.43687 0.00000 
1.56417 2.44689 0.00000 
1.56735 2.45691 0.00000 
1.57053 2.46693 0.00000 
1.57371 2.47695 0.00000 
1.57689 2.48697 0.00000 
1.58006 2.49699 0.00000 
1.58324 2.50701 0.00000 
1.58642 2.51703 0.00000 
1.58960 2.52705 0.00000 
1.59278 2.53707 0.00000 
1.59596 2.54709 0.00000 
1.59906 2.55711 0.00000 
1.60216 2.56713 0.00000 
1.60526 2.57715 0.00000 
1.60836 2.58717 0.00000 
1.61146 2.59719 0.00000 
1.61456 2.60721 0.00000 
1.61766 2.61723 0.00000 
1.62076 2.62725 0.00000 
1.62386 2.63727 0.00000 
1.62696 2.64729 0.00000 
1.63006 2.65731 0.00000 
1.63316 2.66733 0.00000 
1.63626 2.67735 0.00000 
1.63636 2.67769 0.00000 
1.63929 2.68737 0.00000 
1.64231 2.69739 0.00000 
1.64534 2.70741 0.00000 
1.64836 2.71743 0.00000 
1.65139 2.72745 0.00000 
1.65441 2.73747 0.00000 
1.65743 2.74749 0.00000 
1.66046 2.75752 0.00000 
1.66348 2.76754 0.00000 
1.66651 2.77756 0.00000 
1.66953 2.78758 0.00000 
1.67256 2.79760 0.00000 
1.67558 2.80762 0.00000 
1.67677 2.81155 0.00000 
1.67856 2.81764 0.00000 
1.68151 2.82766 0.00000 
1.68447 2.83768 0.00000 
1.68742 2.84770 0.00000 
1.69037 2.85772 0.00000 
1.69332 2.86774 0.00000 
1.69627 2.87776 0.00000 
1.69923 2.88778 0.00000 
1.70218 2.89780 0.00000 
1.70513 2.90782 0.00000 
1.70808 2.91784 0.00000 
1.71104 2.92786 0.00000 
1.71399 2.93788 0.00000 
1.71694 2.94790 0.00000 
1.71717 2.94868 0.00000 
1.71717 2.94868 0.00000 
1.71983 2.95792 0.00000 
1.72271 2.96794 0.00000 
1.72560 2.97796 0.00000 
1.72848 2.98798 0.00000 
1.73136 2.99800 0.00000 
1.73425 3.00802 0.00000 
1.73713 3.01804 0.00000 
1.74002 3.02806 0.00000 
1.74290 3.03808 0.00000 
1.74578 3.04810 0.00000 
1.74867 3.05812 0.00000 
1.75155 3.06814 0.00000 
1.75443 3.07816 0.00000 
1.75732 3.08818 0.00000 
1.75758 3.08907 0.00000 
1.76014 3.09820 0.00000 
1.76296 3.10822 0.00000 
1.76578 3.11824 0.00000 
1.76860 3.12826 0.00000 
1.77141 3.13828 0.00000 
1.77423 3.14830 0.00000 
1.77705 3.15832 0.00000 
1.77987 3.16834 0.00000 
1.78269 3.17836 0.00000 
1.78551 3.18838 0.00000 
1.78832 3.19840 0.00000 
1.79114 3.20842 0.00000 
1.79396 3.21844 0.00000 
1.79678 3.22846 0.00000 
1.79798 3.23273 0.00000 
1.79956 3.23848 0.00000 
1.80232 3.24850 0.00000 
1.80507 3.25852 0.00000 
1.80783 3.26854 0.00000 
1.81058 3.27856 0.00000 
1.81334 3.28858 0.00000 
1.81609 3.29860 0.00000 
1.81885 3.30862 0.00000 
1.82160 3.31864 0.00000 
1.82436 3.32866 0.00000 
1.82711 3.33868 0.00000 
1.82987 3.34870 0.00000 
1.83263 3.35872 0.00000 
1.83538 3.36874 0.00000 
1.83814 3.37876 0.00000 
1.83838 3.37966 0.00000 
1.84084 3.38878 0.00000 
1.84353 3.39880 0.00000 
1.84623 3.40882 0.00000 
1.84892 3.41884 0.00000 
1.85162 3.42886 0.00000 
1.85432 3.43888 0.00000 
1.85701 3.44890 0.00000 
1.85971 3.45892 0.00000 
1.86240 3.46894 0.00000 
1.86510 3.47896 0.00000 
1.86779 3.48898 0.00000 
1.87049 3.49900 0.00000 
1.87319 3.50902 0.00000 
1.87588 3.51904 0.00000 
1.87858 3.52906 0.00000 
1.87879 3.52984 0.00000 
1.88122 3.53908 0.00000 
1.88386 3.54910 0.00000 
1.88650 3.55912 0.00000 
1.88913 3.56914 0.00000 
1.89177 3.57916 0.00000 
1.89441 3.58918 0.00000 
1.89705 3.59920 0.00000 
1.89969 3.60922 0.00000 
1.90233 3.61924 0.00000 
1.90496 3.62926 0.00000 
1.90760 3.63928 0.00000 
1.91024 3.64930 0.00000 
1.91288 3.65932 0.00000 
1.91552 3.66934 0.00000 
1.91815 3.67936 0.00000 
1.91919 3.68330 0.00000 
1.92076 3.68938 0.00000 
1.92334 3.69940 0.00000 
1.92593 3.70942 0.00000 
1.92851 3.71944 0.00000 
1.93109 3.72946 0.00000 
1.93368 3.73948 0.00000 
1.93626 3.74950 0.00000 
1.93884 3.75952 0.00000 
1.94143 3.76954 0.00000 
1.94401 3.77956 0.00000 
1.94659 3.78958 0.00000 
1.94918 3.79960 0.00000 
1.95176 3.80962 0.00000 
1.95434 3.81964 0.00000 
1.95693 3.82966 0.00000 
1.95951 3.83968 0.00000 
1.95960 3.84002 0.00000 
1.96204 3.84970 0.00000 
1.96457 3.85972 0.00000 
1.96710 3.86974 0.00000 
1.96710 3.86974 0.00000 
1.96963 3.87976 0.00000 
1.97216 3.88978 0.00000 
1.97469 3.89980 0.00000 
1.97722 3.90982 0.00000 
1.97976 3.91984 0.00000 
1.98229 3.92986 0.00000 
1.98482 3.93988 0.00000 
1.98735 3.94990 0.00000 
1.98988 3.95992 0.00000 
1.99241 3.96994 0.00000 
1.99494 3.97996 0.00000 
1.99747 3.98998 0.00000 
2.00000 4.00000 0.00000 

Answer 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}