From: Dirk Schulze <dschulze@adobe.com>

Date: Mon, 4 Jun 2012 12:06:24 -0700

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

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>

Message-ID: <F25A2602-119B-42EB-B3A5-C5D9D401F53B@adobe.com>

Date: Mon, 4 Jun 2012 12:06:24 -0700

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

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>

Message-ID: <F25A2602-119B-42EB-B3A5-C5D9D401F53B@adobe.com>

On Jun 4, 2012, at 11:58 AM, Cyril Concolato wrote: > 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. I thought it was a typo the last time. But scale(0) is definitely not the identity matrix. Identity transform is: | 1 0 0 | | 0 1 0 | | 0 0 1 | While scale(0) or scale(0,0) is equivalent to: | 0 0 0 | | 0 0 0 | | 0 0 1 | according to SVG 1.1. The identity transform is the neutral element for multiplication, not for addition. For addition it is the zero matrix: | 0 0 0 | | 0 0 0 | | 0 0 0 | But that isn't even the point of Olaf and SMIL. SMIL says that the neutral element for addition according to a scalar is searched. That is why animateTransform just takes scalars as values. So according to SMIL, it should really be 0 for translate, scale, rotate, skweX and skewY. But that does not prevent us from changing it. Would just be one more difference to SMIL :). Greetings, Dirk > > 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, >> Dirk >Received on Monday, 4 June 2012 19:06:56 GMT

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