TikZ path decorated with coil or snake

Question

A recurrent question on the forum is... How to draw a decorated path without a straight segment at the end?

Usually the path described are straight lines (See post1, post2 or post3), but there are also solutions for semi circle paths (see post4).

I'm interested in drawing a general path, decorated with a coil and a snake (with an entire number of wave length). I found an interesting solution for snake decoration HERE, however, no clue for coil decoration is given.

Question

How could a general path be decorated with a coil? constrained to have an entire number of wave length.

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Update

It has been pointed out by percusse different problems in the definition of my question. So, I'll be less aggressive...

Question v.2.0

Assume that we have a sufficiently smooth path (without vertices or abrupt changes). Additionally, we want the end-points of the path to be centred on the amplitude of the coil. If possible, instead of giving a "wave length" for the coil, we'd like to control the number of turns.

How would such a construction be defined?

Answer 1

Here is one idea that don't work very well (because of the precision problems).

1. Take the length of the path
2. set the coil segment length ot 1/n of this length and decorate ...

Here is one experimentation.

\documentclass[varwidth,border=7mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{decorations.markings,decorations.pathmorphing}
\tikzset{
  get length/.style = {
    preaction={decorate,
      decoration={ markings,
        mark = at position 1 with
        {
          \pgfkeysgetvalue{/pgf/decoration/mark info/distance from start}{\len}
          \xdef\pathlen{\len}
        }
      }
    }
  }
}

\begin{document}
  \begin{tikzpicture}
  \draw [get length] (0,0) circle(3);
  \draw[decoration={coil,amplitude=3mm,segment length={\pathlen /200}},
        decorate] (0,0) circle(3);
  \end{tikzpicture}
\end{document}