From: Benoit Jacob <jacob.benoit.1@gmail.com>

Date: Thu, 21 Mar 2013 11:14:25 -0400

Message-ID: <CAJTmd9ppHYn0QtCto+bddgcxBUW6AzJ1N7rpGiY5SWLJLG0xag@mail.gmail.com>

To: Dirk Schulze <dschulze@adobe.com>

Cc: Rik Cabanier <cabanier@gmail.com>, "public-fx@w3.org" <public-fx@w3.org>

Date: Thu, 21 Mar 2013 11:14:25 -0400

Message-ID: <CAJTmd9ppHYn0QtCto+bddgcxBUW6AzJ1N7rpGiY5SWLJLG0xag@mail.gmail.com>

To: Dirk Schulze <dschulze@adobe.com>

Cc: Rik Cabanier <cabanier@gmail.com>, "public-fx@w3.org" <public-fx@w3.org>

2013/3/21 Dirk Schulze <dschulze@adobe.com> > > On Mar 21, 2013, at 6:01 AM, Benoit Jacob <jacob.benoit.1@gmail.com> > wrote: > > > > > > > 2013/3/21 Rik Cabanier <cabanier@gmail.com> > > > > > > On Wed, Mar 20, 2013 at 8:38 PM, Benoit Jacob <jacob.benoit.1@gmail.com> > wrote: > > > > > > 2013/3/20 Rik Cabanier <cabanier@gmail.com> > > > > > > On Wed, Mar 20, 2013 at 6:29 PM, Benoit Jacob <jacob.benoit.1@gmail.com> > wrote: > > > > > > 2013/3/20 Rik Cabanier <cabanier@gmail.com> > > > > > > On Tue, Mar 19, 2013 at 6:38 PM, Benoit Jacob <jacob.benoit.1@gmail.com> > wrote: > > Hi, > > > > Seeing that a matrix API was being discussed ( > https://dvcs.w3.org/hg/FXTF/raw-file/default/matrix/index.html), I > thought I'd take a look and chime in. > > > > Here are the first few things that scare me, glancing at the current > draft: > > > > 1. Some functions like inverse() throw on singular matrices. The problem > is it's impossible to define very firmly what singular means, in > floating-point arithmetic --- except perhaps by prescribing a mandatory > order in which the arithmetic operations inside of inverse() are performed, > which would be insane --- so saying that inverse() throws on singular > matrices means in effect that there are realistic matrices on which it is > implementation-defined whether inverse() throws or not. The consensus in > all the serious matrix libraries that I've seen, for closed-form matrix > inversion, is to just blindly perform the computation --- in the worst case > you'll get Inf or NaN values in the result, which you will have anyway on > some input matrices unless you mandate unduly expensive checks. More > generally, I would never throw on singular-ness in any function, and in the > case of 4x4 matrices and closed-form computations I wouldn't attempt to > report on singular-ness otherwise than by inf/nan values. > > > > Are you suggesting that the user should check all the values to make > sure that the matrix inversion didn't fail? That seems very expensive. > > Can you point us to an algorithm for inversion that you think the spec > should include? > > > > No, I'm saying that we should _not_ check anything, or if we do (say in > a separate "checked inverse" method), it should be in a graceful way e.g. > an output boolean parameter, not throwing an exception which by default > halts the program. That's what I meant by "The consensus[...] is to just > blindly perform the computation --- in the worst case you'll get Inf or NaN > values in the result" above. > > > > That's certainly tempting! I can see how that's easier (and less > disrupting). > > > > I checked 2 of our internal libraries, as well as Cairo, Skia and Flash > and they all refuse to calculate the matrix if it's not invertible. So, not > all matrix libraries do as you suggest. > > SVGMatrix is also documented to throw. > > These are all matrix classes designed for graphics so I *think* it makes > sense to follow what they did. > > > > I had dedicated matrix libraries in mind, rather than the casual > incidental matrix computation in something like Cairo. > > > > So, are you saying the matrix class should not throw? > > > > Yes. Matrices are just a generalization of numbers (which are 1x1 > matrices). Numbers don't throw --- not even 1/0 or 0/0. Matrices should > not, either. > That is not correct. Mathematically, a matrix is different from a number. I just phrased a personal opinion there, with which you may disagree, but that viewpoint has served me well as far as I'm concerned. > Even if a one element matrix has special additional behaviors over a multi > element matrix. This is not an argument for a special treatment. Especially > for inverse() I do care more about backward compatibility to SVGMatrix[1]. > There is content activity using it. Earlier in this thread someone asked me to clarify what I meant by basic mistakes in SVGMatrix. That would be one. Throwing defaults to killing the program, and that shouldn't happen by default as a result of floating-point imprecision. > As Rik mentioned in previous postings, this is not much different to the > treatment of transformation matrices in graphics libraries anyway. Again, > we are not talking about matrices in general, but matrices used in computer > graphics. And items of NaN and Infinity just theoretically make sense. > I'm afraid there might be a misconception that graphics would have its own requirements on matrix computations that would make it stand apart from scientific software doing matrix computations. I don't think that's the case. In my experience, when graphics code did things differently than scientific matrix libraries, that was typically a consequence if its author being more skilled in graphics than in matrix math. Benoit > > Greetings, > Dirk > > [1] http://www.w3.org/TR/SVG/coords.html#__svg__SVGMatrix__inverseReceived on Thursday, 21 March 2013 15:14:54 UTC

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