Re: [css3-transforms] neutral element for addition - by animation

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.


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]
> [2]
> [3]
>> 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 18:59:16 UTC