"Deane Yang" <deane_yang@yahoo.com> wrote in message news:d7nich$msv$1@sea.gmane.org...
Andy Little wrote:
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'.
What is the difference between a "point" and a "position-vector"?
I'm sure no expert on this but FWIW this is my understandoing: A position-vector is a work-around because it is not possible to have adequate C++ control of operations on points (in affine space), as previously explained. A position-vector is a just a vector, where one makes the assumption that all vectors are added to the Point (0,0) and any result is added to the Point (0,0) (I believe addtion of Point(0,0) to another point is valid as well as multiplication by 1. By suitable equation bending you can arrive to the above result) Therefore all vector ops are allowed. regards Andy Little