From: Cyril Concolato <cyril.concolato@telecom-paristech.fr>

Date: Mon, 04 Jun 2012 20:58:38 +0200

Message-ID: <4FCD055E.6090904@telecom-paristech.fr>

To: Dirk Schulze <dschulze@adobe.com>

CC: "Dr. Olaf Hoffmann" <Dr.O.Hoffmann@gmx.de>, "www-svg@w3.org" <www-svg@w3.org>, "public-fx@w3.org" <public-fx@w3.org>

Date: Mon, 04 Jun 2012 20:58:38 +0200

Message-ID: <4FCD055E.6090904@telecom-paristech.fr>

To: Dirk Schulze <dschulze@adobe.com>

CC: "Dr. Olaf Hoffmann" <Dr.O.Hoffmann@gmx.de>, "www-svg@w3.org" <www-svg@w3.org>, "public-fx@w3.org" <public-fx@w3.org>

Hi all, This thread is just too long for me at the moment, but I repeat what I said. I think that the neutral element for by animations should be the identity matrix. There is no mathematical problem. Adding a zero scale (or rotate, or translate, or skew, ...) is equivalent to post multiplying with the identity matrix. Cyril Le 6/2/2012 12:07 AM, Dirk Schulze a écrit : > On Jun 1, 2012, at 1:51 AM, Dr. Olaf Hoffmann wrote: > >> Cyril Concolato: >> >> >>> [CC] Adding 1 in the scale transformation means going from scale(X) to >> scale(X+1), therefore the neutral element is scale(0) which is the identity >> matrix. >> >> scale(0) is not the identity matrix, this is obviously scale(1,1), >> because >> (0,0) = scale(0,0) * (x,y) and for arbitrary x,y it is of course in most >> cases (x, y)<> (0,0); scale(0,0) is no representation of the identity matrix. >> but >> (x,y) = scale(1,1) * (x,y); scale(1,1) is a representation of the identity >> matrix. >> >> On the other hand the identity matrix has nothing to do with additive >> animation or the neutral element of addition, therefore there is no >> need, that it is the same. The identiy matrix is the neutral element >> of matrix multiplication, what is a completely different operation. > Like Cyril wrote, it was just a typo from him. > >> For the operation of addition of matrices M: 0:=scale(0,0) represents >> a neutral element M = M + 0 = 0 + M, but typically this is not very >> important for transformations in SVG or CSS. > I added a first draft of the definition for the 'neutral element of addition' to CSS Transforms [1]. The only problem that I see is with 'matrix', 'matrix3d' and 'perspective'. According to the definition of SMIL the values should be 0 (list of 0) as well. This would be a non-invertible matrix for 'matrix' and 'matrix3d' and a undefined matrix for 'perspective'. The interpolation chapter for matrices does not allow interpolation with non-invertible matrices [2]. Therefore 'by' animations on these transform functions will fall back to discrete animations and cause the element not to be displayed for half of the animation [3]. > > Of course it could be possible to linearly interpolate every component of a matrix, but since this is not the desired effect for most use cases, we use decomposing of matrices before interpolations. > > [1] http://dev.w3.org/csswg/css3-transforms/#neutral-element > [2] http://dev.w3.org/csswg/css3-transforms/#matrix-interpolation > [3] http://dev.w3.org/csswg/css3-transforms/#transform-function-lists > >> >> The scale function could have been defined in the passed in >> such a way, that the identity matrix results from the neutral >> element of addtion, this works for example in this way: >> scale(a,b) means scaling factors exp(a) and exp(b). >> But this would exclude mirroring and is maybe more >> difficult to estimate the effect for some authors. >> A Taylor expansion approximation by replacing >> exp(a) by (a+1) could save the mirroring, but not the >> intuitive understanding of scaling. >> Therefore there is no simple and intuitive solution to >> satisfy all expectations - and too late to change the >> definition anyway. > I would also think it gets to complicated for most authors. > >> Olaf >> > Greetings, > DirkReceived on Monday, 4 June 2012 18:59:16 UTC

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