[boost] Re: Probing interest in fixed dimension matrix class

From: Andy Little (andy_at_[hidden])
Date: 2005-06-02 12:36:42

"Deane Yang" <deane_yang_at_[hidden]> 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