- From: Jeff Rafter <lists@jeffrafter.com>
- Date: Mon, 07 Feb 2005 13:06:32 -0800
- To: www-svg@w3.org
I have been having trouble understanding some of the basic matrix
operations in the SVG 1.1 specification. As an example I will use the
operation:
matrix.Scale(scaleFactor)
According to the specification, it says "Post-multiplies a uniform scale
transformation on the current matrix and returns the resulting matrix."
[1] Without any doubt the uniform scale matrix will look like:
[ scale 0 0 ]
[ 0 scale 0 ]
[ 0 0 1 ]
We will call this matrix "scaleMatrix." My area of confusion comes when
you talk about postmultiply versus premultiply. Clearly there are only
two options for the operation matrix.Scale(scaleFactor):
resultMatrix = scaleMatrix * matrix
or
resultMatrix = matrix * scaleMatrix
According to Chris Liley's document[2], "Premultiply corresponds to
postconcatenate and postmultiply corresponds to preconcatenate.". Then
in his example he shows the following:
"Alternatively, M2 may be preconcatenated with M1. This will cause M2
to be applied first:
p' = M1 • M2 • p
So, if "M2 is preconcatenated with M1" and in the example the places M1
to the left (pre) side of the multiplication operator, I assume this
means that when a uniform scale is post-multiplied onto an existing
matrix that the operation would look like:
resultMatrix = scaleMatrix * matrix
Or in matrices:
[ scale 0 0 ] [ matrix.a matrix.c matrix.e ]
[ 0 scale 0 ] * [ matrix.b matrix.d matrix.f ]
[ 0 0 1 ] [ 0 0 1 ]
Which results in:
[ (scale * matrix.a) (scale * matrix.c) (scale * matrix.e) ]
[ (scale * matrix.b) (scale * matrix.d) (scale * matrix.f) ]
[ 0 0 1 ]
But ASV6 and Batik do not agree with this interpretation. Clearly I must
be wrong, so am I simply misunderstanding pre versus post multiply-- or
is my matrix math wacky?
[1] http://www.w3.org/TR/SVG/coords.html#DOMInterfaces
[2] http://www.ii.uib.no/undervisning/kurs/v01/i291/i291/geom_sn.pdf
Thanks,
Jeff Rafter
Received on Monday, 7 February 2005 21:07:03 UTC