- From: Dirk Schulze <dschulze@adobe.com>
- Date: Fri, 1 Jun 2012 15:07:14 -0700
- To: "Dr. Olaf Hoffmann" <Dr.O.Hoffmann@gmx.de>
- CC: "www-svg@w3.org" <www-svg@w3.org>, "public-fx@w3.org" <public-fx@w3.org>

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 Friday, 1 June 2012 22:08:51 UTC