MW> On Fri, 5 Nov 2004 23:54:30 +0000, Val Samko <boost@digiways.com> wrote:
Once again, in geometry, vector and point are practically the same thing. MW> Not really - you can only represent a point by its radius/position MW> vector wrt a given coordinate system.
I thought we are only talking about Cartesian coordinates? Does anyone really need a gui library for radial coordinate system? :) MW> Radius vector and point are not the same thing, though. For instance, MW> there is no meaning behind multiplying a point by a scalar. More MW> formal, points are not members of any vector space, so you can't apply MW> operations which are only defined on vectors on them. We are not talking about abstract points here. They are points in nD space, and each of them is represented by a corresponding vector. You may apply any operations defined in your space to your points/vectors. MW> The point (pun intended) is, that the resulting type is NOT a point. MW> "point-point" has a different meaning than "vector-vector". In C++ sence - yes, it's a different point. In mathematical sense, point-point depends on how this operation is defined in your particular space, and in Euclidean space, the result of this operations is the same as difference of corresponding vectors. If you need a distance, you need a norm, i.e. ||pointA-pointB||.
RD> So in a mathematical sense, the difference between size and position is RD> entirely relevant, it's just that some libraries (not mentioning names) RD> do not adhere to the above mathematical rules.
There are no mathematical rules, which say that a point in nD Cartesian coordinate system is not just a set of corresponding distances along each axe. MW> A point can be *specified* by means of a vector, but it's not the same.
Please see http://mathworld.wolfram.com/EuclideanSpace.html "Euclidean n-space (Cartesian space) is commonly denoted R^n. ... R^n is a vector space". So, any point in nD Cartesian space IS a vector. Valentin Samko http://val.samko.info