This might be really simple, but I'm stuck.
Suppose I have 3 triangles with areas A0, A1, A2. I want to compute a weighted average for these values. To do that, I divide each area by the sum of all areas. This way I obtain weights w0, w1, w2 such that w0 + w1 + w2 = 1.
Now, what I want is that the smaller the triangle's area, the BIGGER its weight (i.e. smaller values get higher weights). How can I modify the formula to achieve this, while maintaining the sum of all weights equal to 1?
Best Answer
Let $v_0 = (1/w_0), \;v_1 = (1/w_1), \;v_2 = (1/w_2),$
and let $t = v_0 + v_1 + v_2.$
Then simply scale $v_0, v_1, v_2$ by
$u_0 = (v_0/t), \;u_1 = (v_1/t), \;u_2 = (v_2/t).$