This is probably a pretty basic question.
I've avoided interactive graphics for a long time, but now exploring GEM for a class about nine months down the road. (Actually, I've used GEM for some basic webcam analysis, but that project didn't involve any geometry or texture mapping.)
So I created a [gemhead] --> [pix_image] --> [pix_texture] --> [rotate] --> [translateXYZ] --> [sphere] patch (with a bunch of sliders to mess around with the rotation and translation, and a line generator to act as a phasor for rotation angle). With that, I get the image spinning around the sphere and the sphere's position rotating around some axis.
Then I reversed the rotation and translation: [gemhead] --> [pix_image] --> [pix_texture] --> [translateXYZ] --> [rotate] --> [sphere]. In this arrangement, the translation parameters affect the position of the sphere, but the sphere is stationary and the rotation angle affects only the image mapping.
I would have expected: translate first, then rotate, would offset the sphere away from the rotation axis and then the rotation would affect position. Likewise, rotate first, then translate, would rotate the texture mapping and then position the sphere according to translation.
But I get the opposite. So, I'm not understanding something -- either about the order of operations, or the way that the operations are applied.
I have a feeling the answer to this question will take me several steps further -- best to get these concepts right at the beginning.