Crossings in tikz knots package

Finding the intersections in a knot diagram is a lengthy process so the knots library makes a few optimisations, which can be turned off if needed. These are:

1. By default, it only looks at intersections between separate paths. consider self intersections=true overrides this.
2. When looking at self intersections then it has to split the path into sections and consider intersections between these sections. Successive sections obviously intersect at their end points, these are considered spurious intersections and would crowd out the wanted ones so by default it ignores intersections that are near an endpoint of a section. What it considers to be "near" is determined by end tolerance=<dimen> (for simplicity, it uses the l^1 norm).
3. Ignoring endpoint intersections can be disabled altogether by the key ignore endpoint intersections=false.

Here are three solutions. The first adjusts the path so that the intersection is not near an section endpoint (that is, near a specified point on the path). The second uses a smaller adjustment and adjusts end tolerance=<dimen> as well. The third uses the key ignore endpoint intersections=false on the original path.

documentclass{article}

usepackage{tikz}
usetikzlibrary{knots}

title{Untitled}
author{}
date{2020-11-11}
begin{document}
maketitle


begin{tikzpicture}
begin{knot}[clip width=10, clip radius=15pt, consider self intersections]
  strand[thick] (0,0)
    to[out=up, in=down] (0,0.5) 
    to[out=up, in=left] (0.5,1.5)
    to[out=right, in=up]  (1,1)
    to[out=down, in=right]  (0.5,0.5)
    to[out=left, in=down]  (0,1.5)
    to[out=up, in=down]  (0,2);
end{knot}
end{tikzpicture}


begin{tikzpicture}
begin{knot}[clip width=10, clip radius=15pt, consider self intersections, end tolerance=3pt]
  strand[thick] (0,0)
    to[out=up, in=down] (0,0.7) 
    to[out=up, in=left] (0.5,1.5)
    to[out=right, in=up]  (1,1)
    to[out=down, in=right]  (0.5,0.5)
    to[out=left, in=down]  (0,1.3)
    to[out=up, in=down]  (0,2);
end{knot}
end{tikzpicture}

begin{tikzpicture}[scale=0.75]
begin{knot}[clip width=5, clip radius=8pt, consider self intersections, ignore endpoint intersections=false]
  strand[thick] (0,0)
    to[out=up, in=down] (0,1)
    to[out=up, in=left] (0.5,1.5)
    to[out=right, in=up]  (1,1)
    to[out=down, in=right]  (0.5,0.5)
    to[out=left, in=down]  (0,1)
    to[out=up, in=down]  (0,2);
end{knot}
end{tikzpicture}


end{document}