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

From: Cyril Concolato <cyril.concolato@telecom-paristech.fr>
Date: Fri, 01 Jun 2012 11:16:09 +0200
Message-ID: <4FC88859.3060007@telecom-paristech.fr>
To: www-svg@w3.org
Hi Olaf,

Le 6/1/2012 10:51 AM, Dr. Olaf Hoffmann a écrit :
> 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),
Yes, sorry for the confusion. See my second post.
> 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.
> 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.
Right, I think we should think of addition as composition.


> 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.
> Olaf
Received on Friday, 1 June 2012 09:19:07 UTC

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