(L) [2014/04/23] [tby svinoosha] [SAH probability question.] Wayback!Hi everyone,
my apologies ahead if this was covered, i searched!
I am trying to figure out the Surface Area Heuristic [SMILEY :oops:] , specifically what the authors meant by the probability of ray hitting a child node given that it hit the parent node. The authors define it as:
P_left = SurfaceArea(left_child)/SurfaceArea(parent)
I don't understand what the definition of child's surface area is. I've seen (most) code implement it as the volume of the left box when the parent box is split by plane. I've found at least two implementations that computed the "clipped" bounding box of left child and the objects contained in the left child. That may produce a smaller bounding volume then the first case. Or should the SurfaceArea(node) be (at least given simple geometry, like spheres, triangles) the combined area of the actual contained object geometry of a node?
I tried these variations in my code (kd-tree). Obviously each interpretation biases the cost function which leads to different trees. But at least in the few data sets i tried, i could not see one being obviously better then the others. Any input?
Thanks!
(L) [2014/04/24] [tby tarlack] [SAH probability question.] Wayback!The surface area of your child is the area of the surface of the bounding volume. For instance for a bounding box, it is the sum of the area of the six faces of the box. The area of the primitives contained in the child can not be the probability : think about duplicated triangles : increasing the number of duplications does not increase the probability to hit one of the triangles : the probability is equal to the probability of hitting one of the duplicated triangles.
(L) [2014/04/24] [tby svinoosha] [SAH probability question.] Wayback!Ah, good point about overlapping geometry. That makes sense, thanks! But what about clipped bounds (geometry and sub-voxel). Wouldn't that be a better approximation of the "traceble" space?
(L) [2014/04/25] [tby tarlack] [SAH probability question.] Wayback!If I understand correctly what you mean, I agree with you. Intuitively, I would say that the most accurate probability to hit the child geometry should be obtained with the surface area of the convex hull of the geometry contained in the child, so the closer to this convex hull, the more accurate you will be [SMILEY :)]