- From: Cyril Concolato <cyril.concolato@telecom-paristech.fr>
- Date: Mon, 04 Jun 2012 21:21:04 +0200
- 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 Dirk, Le 6/4/2012 9:06 PM, Dirk Schulze a écrit : > 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. Up to this point, I agree with you. > > The identity transform is the neutral element for multiplication, not for addition. That's where I differ. The neutral element for addition of a scale transform is 'e' such that for all X: scale(X+e)=scale(X) So yes e=0 but this does not mean a matrix of zeros. If you decompose scale(X+e) with a product of scales: scale(X+e)=scale(X)scale(e')=scale(X) for all X, then e'=1. Applying a by animation of scale is post-multiplying with a scale transform and the neutral element is the identity. > 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's not really contradictory with what I said above. > 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. Yes, 0 as in scale(X+0)=scale(X). > > But that does not prevent us from changing it. Would just be one more difference to SMIL :). I don't think this would be the case. Cyril > > 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 19:21:38 UTC