[x3d-public] texture transform ordering

[Andreas Plesch]

Mirroring a texture works by scaling S by -1, eg. a texturetransform
with a '-1 1' scale field. This requires repeatS='true' since S
coordinates would be cut off, clamped at 0 otherwise.
To allow repeatS='false' the S coordinates have to be also shifted to
become positive. Since translation is applied _before_ scaling a
translation of '-1 0' is needed. This is unintuitive but clear from
the spec.
Another way would be to have a center of scaling in the middle. This
is accomplished by a '-0.5 -0.5' center field if the matrix
multiplication formula in the spec. is applied literally which is what
x3dom does.
This center value is very hard to understand since the spec. explains
the center point as the point about which scaling and rotation should
be performed. The strange value is probably a result of the inverted
ordering of transformation.
There is a spec. note:
NOTE  This transformation order is the reverse of the Transform node
transformation order since the texture coordinates, not the texture,
are being transformed (i.e., the texture coordinate system).
I do not quite understand the reasoning here. I understand that
scaling by a factor of 2 results in a smaller image since then the
image margin at uv=1,1 is now at the position where uv=0.5,0.5 was. I
also understand that shifting u by plus 0.1 results in the image
shifted to the left since the margin at u=1 is now where u=0.9 was.
But I cannot find an argument why the _ordering_ should be reversed.
Is it an opengl convention somehow ?
The only way I can make sense of the center field is by mentally
applying it as a translation before the scaling/rotation and then
unapplying it afterwards, as the formula demands, not actually as the
center of scaling/rotation. This explains why the center value has to
be inverted from what it is expected (by me).
It gets harder if you want to apply both a scale and a rotation. Since
the rotation is applied before the scale, the scale will then deform
the texture typically then into a sheared shape which is not what is
typically wanted as an outcome.

Any insights or references very welcome,

-Andreas
-- 
Andreas Plesch
Waltham, MA 02453