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

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 19:06:54 UTC