Re: comments on Matrix

On 21/03/2013, at 10:25 AM, Benoit Jacob <jacob.benoit.1@gmail.com> wrote:

> 
> 
> 2013/3/20 Rik Cabanier <cabanier@gmail.com>
> and hearing that some of these mistakes are copied from other, already-blessed Web APIs is even more discomforting.
> 
> What you call a mistake (QR decomposition) is a well documented, fast alternative (I know at least 3 now that use this).
> From the paper you quoted:
> Also, the algorithms for QR are simple and efficient. The drawback is that the orthogonal matrix
> extracted is not particularly meaningful: it is not independent of the coordinate basis used, and so has no
> “physical” significance
> 
> This implies that the QR algorithm is fast but it doesn't produce results that you should use directly.
> So, we should use it for matrix interpolation but not to get the decomposed values out.
> 
> That's not what I get from this quote. This is saying that QR decomposition is simple and efficient to perform, but is not going to give good results for matrix interpolation, since that should definitely be coordinate-independent and "physically meaningful".

FWIW, this is the algorithm that CSS transforms uses for matrix interpolation (via decomposition). It's also the same as Core Animation. We have not had anyone complain about physical meaninglessness. We have had one person request interpolation purely by indices, which is definitely meaningless. The goal was to have something that looks "correct" the vast majority of times.

Dean