(I want to correct my own post here, because, as this thread has shown, things I
say in the distant past stick around in search engines forever...)
On 9/15/2011 2:33 PM, Paul Martz wrote:
The OpenGL FFP projection matrix transforms from eye coordinates into clip
coordinates. Those two coordinate systems are defined in the spec (see section
2.11 / figure 2.6 in the 2.1 spec). +x = right, +y = up, +z = into the screen,
and eye = origin are already the eye coordinate definition prior to transform
by the projection matrix.
This is wrong on two points.
1. A close read of the spec shows that it doesn't actually define these
coordinate systems, and where the +y = up convention comes from might be a good
topic for discussion in the OpenGL forums. I'm sure I knew the full story back
in 1994, but it's lost in the fog of my memory. Perhaps it stems from simple
Cartesian math: origin in lower-left corner of the window, +x = right, +y = up,
and everything else is inferred from back-transforming.
(Regardless, I still think the getLookAt code is correct, as it is just
performing the inverse of osg::Matrix::lookat.)
2. The projection matrix usually performs a negative scale on z, to support
right-handed world coordinates in conjunction with a +z = into the screen depth
buffer convention. So I was wrong about eye coordinates above. Eye coordinates
generally have -z = into the screen, not +z. The projection performs a negative
scale on z, producing clip coordinates with +z = into the screen. I don't see
where the spec actually prohibits setting up a different convention, though.
Again, it might just be implicit in the math.
-Paul
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