[osg-users] Correction of wikipage Support/Maths/MatrixTransformations
Matthias Bindernagel
matthias.bindernagel at gmx.de
Wed Sep 3 11:19:47 PDT 2008
Hello,
on the page
http://www.openscenegraph.org/projects/osg/wiki/Support/Maths/MatrixTransformations
is stated that one should
>pass this matrix
>
>GLfloat ZrotateMatrix[][4] = {
> { cosA, -sinA, 0, 0 },
> { sinA, cosA, 0, 0 },
> { 0, 0, 1, 0 },
> { 0, 0, 0, 1 }
>};
>
>to glLoadMatrixf(): and see what happens (g'ahead try it, don't take my word
for it).
>Your rotations will be the opposite of what you expect.
Well, the correctness of the result depends on what you expect: OpenGL's
glLoadMatrixf() and its variants expect a column-major-matrix as parameter
(see http://www.opengl.org/sdk/docs/man/xhtml/glLoadMatrix.xml); passing a
row-major-matrix (like done in this example) to glLoadMatrixf() results in a
transformation described by the transposed matrix-argument. Same holds true
for the translation described later on the wiki page.
So the results of the allegedly erroneous examples are actually correct,
regarding the OpenGL documentation and standard maths.
Another point I want to mention here is my surprise about the argumentation of
the matrix-vector-product in OSG:
Almost every book or website I've read about computer graphics in general and
some DSL's in particular uses
V' = M * V
on a broad basis, where V' is the transformed vector, V is the original vector
and M descibes the trafo.
One could - like the documentation did - replace this commonly used matrix
product with W' = W * N, but (at least in my opinion) _must_ mention that:
1. W' and W are transposed vectors (that is, they are row vectors, instead of
widely used column vectors)
2. N must not be a common transformation matrix (like the ones mentioned on
wikipedia or mathworld.wolfram.com), but the transpose of such a matrix.
IMHO, the documentation found on that wiki page does need some slight
corrections, but also a lot of additions to clearly state when to use
original or transposed transformation matrices.
Regards, Matthias Bindernagel
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