"Deane Yang" <deane_yang@yahoo.com> 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.
Ideally the two expressions should be equivalent: 2/3 *A +1/3 * B == A + (1/3)*(B - A) = (2 * A + B ) / 3 etc If no multiplication or addition is allowed on points, this is not the case. (Welll.. its possible to work it at compile time, but I believe this is too restrictive) The points implementation is getting in the way of the expression. Expressions will fail for no good reason. OTOH These calculations work correctly if A and B are 'position-vectors'. regards Andy Little