From: Deane Yang (deane_yang_at_[hidden])
Date: 2005-06-02 11:22:00
Deane Yang wrote:
> Andy Little wrote:
>
>>
>> eg to find the point 1/3 rd way from the start of line(A , B) one could
>> calculate 2/3 *A +1/3 * B.
>>
>
> I think it is more natural to compute this as
>
> A + (1/3)*(B - A),
>
> where A and B are points and B - A is a vector. So you're really still
> just adding a vector to a point to get a new point. There is never a
> need to add or rescale points.
>
Now, to contradict myself, it is useful to rescale and add points in at
least one circumstance: when you want the "center of mass" or the
"average" of a set of points A1,..., An. In principle, you can do it as
B + [(A1-B) + .... + (An - B)]/n
but that's a lot of extra subtractions.
If I needed this (or a weighted average), I would probably encapsulate
it in a weighted average function (which would internally rescale and
add the points) and still disallow rescaling and adding points in my
library interface.
But I guess I now see why someone might just find it more convenient to
allow rescaling and adding points.