From: Michael Walter (michael.walter_at_[hidden])
Date: 2004-11-05 19:42:51
On Fri, 5 Nov 2004 23:54:30 +0000, Val Samko <boost_at_[hidden]> wrote:
> Once again, in geometry, vector and point are practically the same thing.
Not really - you can only represent a point by its radius/position
vector wrt a given coordinate system.
Radius vector and point are not the same thing, though. For instance,
there is no meaning behind multiplying a point by a scalar. More
formal, points are not members of any vector space, so you can't apply
operations which are only defined on vectors on them.
> RD> If you do point - point, then the resulting type is a size type that
> RD> represents the distance between the two points.
> Just like size - size.
The point (pun intended) is, that the resulting type is NOT a point.
"point-point" has a different meaning than "vector-vector".
> 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.
A point can be *specified* by means of a vector, but it's not the same.
Another important.. point would be that o
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