I feel like a complete idiot here, but I'm trying and trying to understand the whole point of matrix stacks and I just don't get it.

I ran this code:

void setup()
{
 size(640, 480,P3D);
 noStroke();
 smooth();
translate(50,50);
printMatrix();
}

and got this:

001.0000  000.0000  000.0000 -270.0000
000.0000  001.0000  000.0000 -190.0000
000.0000  000.0000  001.0000 -415.6922
000.0000  000.0000  000.0000  001.0000


WTF? Where are those numbers coming from? What's with the random decimal points? "-415.6922"? Huh?

I don't get this at all. And Googling doesn't help; no sites seem to give me a useful or adequate explanation of what matrices are in this context, or why they'd be useful to me.

Please help, as I suspect that a lot of what I want to do in Processing requires these bastard things, and this is driving me mad.

[Update] it just occurred to me that -270 - 50 = -320, which is half my sketch's width, and -190 - 50 = -240, which is the height. But I still don't understand anything beyond that.

If you care about how matrices actually work, find a book about 3D graphics programming, and look for topics related to perspective, projection, and the camera.

But it's very rare that you need to worry about the exact numbers found in the matrix, so perhaps you have a different question about something you're trying to do and cannot?

The matrix stack allows you to 'stack' transformations of the graphic space, literally adding (well, technically I think the matrices are multiplied) one transformation on top of another. Instead of printing the matrix after translating, rotating, and scaling the drawing context, try drawing something. That should help tremendously with your understanding.

Pushing the matrix is like sticking your hand on top of the stack before adding new transformations. Popping is picking your hand up, and knocking off all the transformations on top of it.

So, instead of printing the matrix, draw something on screen:

Code:

translate( width/4, height/4 );
rect(0,0,50,50);
pushMatrix();
rotate(45);
fill(127);
rect(0,0,50,50);
scale(0.5);
fill(55);
rect(0,0,50,50);
popMatrix();
fill(0);
rect(0,0,10,10);
 

If you haven't already quit in frustration, I hope this helps.

Okay, when I switch to OpenGL mode, it does something different...but I'm still not understanding what.

I feel very stupid.

So using push and pop basically resets the transformations? I think I understand now. It keeps the transformation local within a function or class, and then after that function or class does its thing it resets it to the original values.

Okay, that makes more sense now.

not sure if it's (still) relevant, but this is a really nice book to browse through:

http://www.opengl.org/documentation/red_book/ ->
http://www.glprogramming.com/red/

Also some 'tutor' programs where you can fiddle with some settings:
http://www.xmission.com/~nate/tutors.html

And the slides we got for the course computer graphics at our university about the Mathstuffs:
http://www.cs.vu.nl/~graphics/slides/lecture4-2up.pdf

HTH