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Understanding post-multiplication in the SVG 1.1 Sepecification: msg#00041

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Subject: Understanding post-multiplication in the SVG 1.1 Sepecification


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





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