# Is there any shorthand notation for linear interpolation?

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.

• The pic diagram programming language uses the notation a[p,q] for the point $a$ of the way between $p$ and $q$. I think metafont has something similar. – MJD Apr 17 '14 at 23:15
• @MJD Thanks. After a little searching, it looks like the pic notation is a<p,q> and metafont's is a[p,q], so they do have the same general form. – dfan Apr 17 '14 at 23:26
• pic also accepts a of the way between p and q, which I suppose demonstrates the lack of a common notation. – dfan Apr 17 '14 at 23:29