Reading "tikz Multi-segment Line of Varying Thickness" provides a good explanation to join segments, but it seems that the rounded corner transition is the only way to do this nicely?
I would like to join segments of different thickness with a nice sharp miter, getting similar results in the case of these two:
Lines of the same thickness have a nice miter:
\draw [very thick] (0.45,-0.2) to (0.45,0.17) to (0.75,-0.17) to (0.75,0.2);
But if I try to join a thick line to a thin line, there is an artifact:
\draw [very thick] (1.3,0.2) to (1,0) to (1.3,-0.2); \draw (1,0) to (1.3,-0.2) to (1.3,0.2) to (1,0);
The resulting mitre would appear thus (except not edited by hand):