Surface Area Heuristic

chhenning 101 Nov 10, 2009 at 22:08

Hi there, I have a question regarding the surface area heuristic ( SAH ) mentioned here:

It says that the surface area is calculated as:

area = 2 * width * height * depth

But when I look at the provided source code it much different. Although, probably not incorrect. Here it’s:

real SAV = 0.5f / (a_Box.w() * a_Box.d() + a_Box.w() * a_Box.h() + a_Box.d() * a_Box.h());

Did Jacco forgot to update is article or is the change based on some optimization?


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poita 101 Nov 11, 2009 at 00:23

Well the first calculation for surface area is obviously false as that’s clearly calculating the volume and doubling it.

The second formula appears to be calculating the inverse surface area.

w=width, h=height, d=depth

Surface area
= 2 * (wh + wd + hd)

Inv. surface area
= 1 / (2 * (wh + wd + hd))
= 0.5 / (wh + wd + hd)

The inverse surface area is more useful as you can just multiply by it to divide by the surface area. As you should know, dividing is quite significantly more expensive than multiplying, so you’ll often see people storing inverses for performance reasons.

chhenning 101 Nov 11, 2009 at 16:57

Thanks guys that cleared it up for me.

gloVA10 101 Jan 21, 2010 at 16:24

Hello, im a bit confused about what are
Ctraversal and Cintersect in the article that you speak of. Any hints??

Reedbeta 167 Jan 21, 2010 at 17:15

They are heuristic “cost” values that you can tune to get the best performing tree. Ctraversal is the cost of splitting a node into child nodes and Cintersect is the cost of computing a ray-triangle intersection. The ratio of the two controls how deep the tree gets. The idea is to stop splitting nodes when it would be more expensive to do so than just to intersect all the triangles in that node.