RE: [boost] proposal for efficient geom. vector class

From: Noah Stein (Noah_at_[hidden])
Date: 2003-05-22 10:50:40

> -----Original Message-----
> From: boost-bounces_at_[hidden]
> [mailto:boost-bounces_at_[hidden]]On Behalf Of Reece Dunn
> Sent: Thursday, May 22, 2003 6:54 AM
> To: boost_at_[hidden]
> Subject: Re: [boost] proposal for efficient geom. vector class

> As for the point/vector/matrix from a non-graphics point-of-view,
> I agree:
> it should be applicable to any application that makes use of points,
> vectors, etc.
>
> Regarding point = point +/- vector, a vector is a representation of a
> distance (hence why it can be created via point - point), so the above
> operations translate a point by a certain distance. Having point
> = point +/-
> point does not make sence, because a point is a *location* not a
> *distance*.

point = point +/- point might make sense.  It depends upon the vector space
you're using.  In an affine space, you would be correct - you can't add
points together.  Well, even in that space, it can be useful from time to
time: finding the midpoint [(p1+p2)/2] or some other barycentric
combination.  In a Grassman space, any point +/- point combination is a
valid operation.  The paper I referenced in my last e-mail provides a great
discussion of this  very point:

http://portal.acm.org/citation.cfm?doid=504789.504792

-- Noah