It is quite common for me to encounter or manipulate expressions of the form $$ x + \alpha(y-x) $$ or equivalently $$ (1 - \alpha) x + \alpha y $$ where any of the expressions ($\alpha, x, y$) may be rather complicated. I am not happy with either the repetition of expressions or the fact that so many symbols are required for the very simple ternary operation "$\alpha$ of the way from $x$ to $y$". In my own notes (not intended for reading by anyone but myself), I've taken to writing this as $$ x \overset\alpha\rightharpoondown y $$ which I think is both clearer and more elegant. Has anyone proposed a similar notation for this concept? I assume that even if such a proposal has been made, it hasn't caught on, since my internet searching hasn't turned anything up, but if there is even a minimally standard notation, I'd be interested to learn it.
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picdiagram programming language uses the notationa[p,q]for the point $a$ of the way between $p$ and $q$. I thinkmetafonthas something similar. – MJD Apr 17 '14 at 23:15picnotation isa<p,q>andmetafont's isa[p,q], so they do have the same general form. – dfan Apr 17 '14 at 23:26picalso acceptsa of the way between p and q, which I suppose demonstrates the lack of a common notation. – dfan Apr 17 '14 at 23:29