Triangle setup

Hi all,

I was wondering what exactly the triangle setup stage comprises, and how it's implemented on a modern GPU.

If I understand correctly, it's main task is to compute gradients of interpolants. When graphics cards specify a setup rate of one triangle per clock cycle, does this include all interpolants (including up to 8x4 texture coordinates)? Or is the triangle rate dependent on the number of interpolants?

Do they derive the gradients from the 'plane equation approach' or is there a faster method? With 'plane equation approach' I mean for example for the z interpolant (could be any other interpolant) we compute the plane equation Ax+By+Cz+D=0 so the gradients are dz/dx=-A/C, etc. Since (A, B, C) is the plane normal it can be computed with a cross product. C can be reused for all interpolants, but it still looks like a lot of work. And since every interpolant requires perspective correction this adds three divisions and a whole lot of multiplications.

Any thoughts?

 

Thanks! I just managed to get the same result with the plane equation approach:

dz/dx = -A/C = ((y1/w1 - y0/w0)*(z2/w2 - z0/w0)-(y2/w2 - y0/w0)*(z1/w1 - z0/w0)) / ((x1/w1 - x0/w0)*(y2/w2 - y0/w0)-(x2/w2 - x0/w0)*(y1/w1 - y0/w0))

= z0 * (y1*w2-y2*w1) / (-x1*w0*y2+x1*y0*w2+x0*w1*y2+x2*w0*y1-x2*y0*w1-x0*w2*y1)
+ z1 * (y2*w0-y0*w2) / (-x1*w0*y2+x1*y0*w2+x0*w1*y2+x2*w0*y1-x2*y0*w1-x0*w2*y1)
+ z2 * (y0*w1-y1*w0) / (-x1*w0*y2+x1*y0*w2+x0*w1*y2+x2*w0*y1-x2*y0*w1-x0*w2*y1)

Which is exactly the product of (z0, z1, z2) with (the first column of) the inverse of the matrix formed by the (x, y, w) coordinates, as shown in the paper you refer to.

So is the setup engine's task limited to computing this matrix inverse as efficiently as possible?

 

How is this possible exactly? Couldn't it create division by zero? Thanks!

 

darkblu, that's exactly the plane equation approach. The C component is exactly the area of the triangle (actually, twice the area). The other componets also correspond with areas.

The method with the inverse matrix appears to be faster when computing multiple gradients.

 

Sorry, I'm not with you here. Perspective requires division by w, so when it's zero things go wrong. Triangle area can only be computed after assembly (not in the vertex engine like Jawed said). Or am I confusing a couple things here?

 

No problem. I still wonder what part of the triangle setup or perspective can be done in the vertex pipeline though. Obviously doing things per triangle is triple the work of doing it per vertex. So anything that can be done in the vertex pipeline should be well worth it.

 

Ah, I see. The slide shows that backface culling and clipping is done after the vertex pipelines, then perspective divide, which makes sense. It doesn't seem like the vertex pipelines are doing any actual perspective work, although it would make sense to compute 1/w there already for later use (ignoring division by zero). For triangles crossing the near clip plane 1/w would have to be recomputed for the new vertices. After that the perspective divide is safe and efficient.