On Wed, Mar 20, 2013 at 4:32 PM, Dean Jackson <dino@apple.com> wrote: > > 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. > > Yes, Flash and some of our tools also use this algorithm and AFAIK it works fine.
Received on Wednesday, 20 March 2013 23:36:57 UTC