# [css3-transforms] Relation between mathematical description and effect of a transformation

From: Dr. Olaf Hoffmann <Dr.O.Hoffmann@gmx.de>
Date: Sat, 21 Apr 2012 14:40:34 +0100

Message-Id: <201204211540.35418.Dr.O.Hoffmann@gmx.de>
```Hello,

http://www.w3.org/TR/2012/WD-css3-transforms-20120403/#mathematical-description

The draft shows some examples, what can be assumed as the effect of several
types of transformations and in this chapter 17. it provides a 'Mathematical
Description of Transform Functions' - well, better it provides only matrices,
no direct relation to the effect of such a matrix on the presentation.

For 2D-Transforms it is sufficiently described in SVG already what the
effect for a point r = (x, y, 1) for a matrix M is, r_p representation in the
previous coordinate system, r_c in the current coordinate system
(respectively r=(x, y, z, ?) for three dimensions?):

r_p = M r_c

I think this should be noted in this draft as well - and this is even more
important for the matrices related to 3D-transformations, because it is not
obvious, what the relation is.
The old SVG transform draft http://www.w3.org/TR/SVG-Transforms/
has slightly more advanced descriptions. Well, even with these formulas
I do not get something similar to for example 5 of the current draft.

Due to my experience with perspective transforms, for a central projection,
what seems to be intended here in examples like 4,5, one needs an
additional transformation like (index _p here for projected)

(x_p, y_p) = (x_c, y_c) * l/z_c with l a length.

Obviously the fourth dimension of the matrices is intended for this,
but the relation to such a transformation is not decribed.

The parallel projection as intended in example 3 is simpler,
one just has to use a simple 3x2 (respectively 4x2) matrix, to
extract only the x and y components.

I suggest to decribe/define the effect of such matrices
in detail as a functional relation between the representation of an arbitrary
point r_c in the current coordinate system to the representation of
this projected point r_p.
Other solutions for the problem are possible as well of course, but
without a precise description at least the effect of the 3D transforms
are undefined and those of the 2D transforms are applicable only for SVG,
that has already a precise description for 2D.

Best wishes

Olaf

PS: Is it really useful to change the preferred mailing list for this draft
to the www-style list instead of the public-fx, as for the previous draft?
Because the draft applies still to SVG as well, I added the public-fx...
```
Received on Saturday, 21 April 2012 13:41:05 UTC

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