"Deane Yang" <deane_yang@yahoo.com> wrote
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.
IMO there are a large number of cases eg when interpolating positions on a curve/surface where multiplication and addition is necessary.
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.
Thanks for that :-) I do feel that it is necessary to get the basics thrashed out as they are the simplest building blocks of a graphics system. regards Andy Little