Path with opacity gradient in tikz

Question

Inspired by this question, I would like to draw a infinity symbol whose opacity changes along the path, what I can achieve so far is this:

\documentclass[tikz]{standalone}

\usetikzlibrary{decorations.markings}

\pagecolor{yellow}

\definecolor{col1}{RGB}{127,127,127}
\definecolor{col2}{RGB}{240,240,240}

\begin{document}

\begin{tikzpicture}
    \path[postaction={
        decorate,
        decoration={
            markings,
            mark=between positions 0 and \pgfdecoratedpathlength step 0.5pt with {
                \pgfmathsetmacro\myval{multiply(divide(
                    \pgfkeysvalueof{/pgf/decoration/mark info/distance from start}, \pgfdecoratedpathlength),100)};
                \pgfsetfillcolor{col1!\myval!col2};
                \pgfpathcircle{\pgfpointorigin}{0.1cm};
                \pgfusepath{fill};}
}}] plot[smooth cycle] coordinates{(0,0.7)(-0.2,0.35)(0,0)(1,0.7)(1.2,0.35)(1,0)};
\end{tikzpicture}

\end{document}

However there are two problems with it:

(1) This is drown with color gradient, not opacity gradient, thus for example if I use this picture in a paper with yellow background, it is still gray and white, not gray and yellow.

(2) The edge of the path, as you can see, is not smooth, it seems as if the edge is some kind of wave. (I think it is because the color gradient is achieved by drawing many many circles and so the line looks not very straight. However I don't know how to fix this except reduce the step 0.5pt, but if I do so the drawing process would be very slow.)

Is there any easier way to draw this picture correctly?

Answer 1

I draw the symbol with two fadings, and experiment with lining them up at the right side.

This solution is obvious not optimal. The fading is not along the path, but west to east. There is a color difference and render artefact where the lines meet at the right side. There is a problem where the lines intersect - if it was just transparency, it could have been solved with a transparency group.

\documentclass[tikz]{standalone}
\usetikzlibrary {fadings, patterns}
\begin{document}
\begin{tikzpicture}
\pattern[pattern=checkerboard,pattern color=yellow](-1,-0.5) rectangle (1,0.5);
\begin{scope}
  \clip(-1,-0.5)--(0,-0.5)--(0.5,0)--(1,0)--(1,0.5)--(0,0.5)--(-0.5,0)--(-1,0)--cycle;
  \draw[darkgray, line width=5.5, path fading=west, fading transform={xscale=2, xshift=10},  line cap=round] plot[smooth] coordinates{(-0.7,0.02)(-0.5,-0.35)(0.5,0.35)(0.7,-0.02)};
\end{scope}
\begin{scope}
  \clip (-1,-0.5)--(1,-0.5)--(1,0)--(0.5,0)--(0,0.5)--(-1,0.5)--cycle;
  \draw[darkgray, line width=5.5, path fading=east, fading transform={xscale=2, xshift=10},  line cap=round] plot[smooth] coordinates{(-0.7,0)(-0.5,0.35)(0.5,-0.35)(0.7,0.02)}; 
\end{scope}
\end{tikzpicture}
\end{document}

---

Edit:

This is just to demonstrate that it is possible to cut one path completely out of the other

\documentclass[tikz]{standalone}
\usetikzlibrary{fadings, patterns}
\begin{tikzfadingfrompicture}[name=myfading]
\clip(-1,-0.5)--(0,-0.5)--(0.5,0)--(1,0)--(1,0.5)--(0,0.5)--(-0.5,0)--(-1,0)--cycle;
\draw[white, line width=5.5, path fading=west, fading transform={xscale=2, xshift=10},  line cap=round] plot[smooth] coordinates{(-0.7,0.02)(-0.5,-0.35)(0.5,0.35)(0.7,-0.02)};
\draw[line width=5.5, line cap=round] plot[smooth] coordinates{(-0.7,0)(-0.5,0.35)(0.5,-0.35)(0.7,0.02)}; 
\end{tikzfadingfrompicture}
\begin{document}
\begin{tikzpicture}
\pattern[pattern=checkerboard,pattern color=yellow](-1,-0.5) rectangle (1,0.6);
\fill[path fading=myfading, left color = white, right color = gray] (-1,-1) rectangle (1,1);
\end{tikzpicture}
\end{document}

This could solve the overlap problem, but whenever I try to use tikzfadingfrompicture, I get strange scaling problems due to my lack of understanding. -see https://tex.stackexchange.com/a/551723/8650