🚀 go-pugleaf

In article <LAU.93Jan21125414@sunset.ai.sri.com>, lau@sunset.ai.sri.com
(Stephen Lau) writes:
|> ...
|> I would like to call perspective() and lookat() and then somehow get
|> this combined transformation matrix and use it to do my own coordinate
|> transformations and clipping. Is this possible?
|> 
|> I've tried calling perspective() and lookat() and then getmatrix(), but
|> the resulting matrix doesn't transform it to window coordinates, only to
|> local world coordinates. This is part of the way, but I'm missing the final
|> step that then projects this to window coordinates. 
|> 

You must be in mult-matrix mode, that is mmode(MVIEWING). When in this
mode, the
perspective matrix is separated from the modeling-viewing matrix stack.

Try this:
getmatrix(modelViewMat);
mmode(MPROJECTION);
getmatrix(projMat);
mmode(MVIEWING);

Then use your favorite matrix mult routine to get M = Mmv * Mp.

Here's a more detailed explanation that Kurt Akeley posted a while ago:

    1.	Transform your point by the current matrix (if in single matrix mode)
	or by the ModelView matrix followed by the Projection matrix (if in
	multiple matrix mode).  Matrix mode is controlled by the mmode()
	command, which also controls which matrix is returned by getmatrix().
	Set the W component of your point to 1.0 prior to transformation.

    2.	Clip the resulting transformed point against all 6 clipping planes:

		if (x > w OR x < -w OR y > w OR ...)
		then the point does not have a screen coordinate

    3.	Project the transformed point by dividing each of x, y, and z by w.

    4.	Map the point to window coordinates using the equations:

		Xwin = Vsx * X + Vcx
		Ywin = Vsy * Y + Vcy
		Zwin = Vsz * Z + Vcz

		Vsx = (right-left+1)/2
		Vsy = (top-bottom+1)/2
		Vsz = (far-near+1)/2
		Vcx = (right+left)/2
		Vcy = (top+bottom)/2
		Vcz = (far+near)/2

    5.	Add the window offset to Xwin and Ywin to get screen coordinates.
	Z values are not affected by window position.

I've written the Z viewport to be identical to the X and Y viewport operations,
but some SGI machines are off by one on this mapping (no big deal usually).
All computations should be done in floating point.  If screen coordinates are
to be coerced to integers (generally not a good idea) be sure to round toward
nearest.  If truncation is easier, add 0.5 to Vcx, Vcy, and Vcz.