vertex's route from scene to screen (and sorry for my bad english)

h!
i have to write simple software 3d renderer and i want to do it in opengl way (without matrix stack so far), so i’ve go two matrices: projection and modelview, opengl keeps matrices in column-major order. all transformations are done (as i think) this way: M’ = M * transform_matrix which is transposed (to be in column-major order)
so, let’s imagine some object in local his coordinates. after multiplying by modelview matrix we’ll have this object with world coordinates (am i right?)
so there is my first problem: how to do it (multiply) correctly (or how it’s done by OpenGL)?
‘v = M * v ? or maybe the are any transpositions/inversions needed (to matrix)?
after that, we have to project vertex on the screen (and i’m afraid it’s more complicated)
and to be honest i don’t understand exactly what to do.
i’ve got projection matrix (exact like after glFrustum or glOtho) and i have to multiply (yeah, same problem, is it the same situation ?)
after that, i have to (as i think) normalize (but how exactly?) these coordinates to screen coordinates (ok, i can do it like glViewport), but somethere i’ve found some dividing by w viewpoint’ and i don’t know what to do with it and where (after which step) to do it

please help

(do i have to add any clipping to triangle fill routine?)

thx for you attention

Get the opengl 1.5 specifications from the front page of opengl.org. You’ll find all those transformations explained there

Originally posted by fuxiulian:

Get the opengl 1.5 specifications from the front page of opengl.org. You’ll find all those transformations explained there

I think this is it.
I’ve missed normalization - this one can explain this dot on the center of the screen

thx a lot