Lecture_011_Geometric_Queries

Exact Floating Point

Bounding Volume Hierarchy

To know how exactly we should split the scene, we need some assumption:

rays are randomly distributed
rays are not occluded

Theorem: for convex object $A$ inside convex object $B$ , the probability that a random ray that hits $B$ also hits $A$ is given by the ratio of the surface area $S_A$ and $S_B$ of these objects.

$Pr\{\text{hit } A | \text{hit } B\} = \frac{S_A}{S_B}$

Therefore, given a split, we can compute the cost of using this split:

$C_{cost} = C_{travel} + C_{intersect}(\frac{S_A}{S_N} N_A + \frac{S_B}{S_N} N_B)$

Where

$C_{cost}$ is total cost.
$C_{travel}$ is the cost of traversing an interior node (e.g. load data, bbox check).
$C_{intersect}$ is the cost of computing any ray-primitive intersection (where we assume for simplicity that the cost is the same for all primitives).
$S_N$ is total surface area of all primitives in both child A and B.
$S_A$ is the otal surface area of primitives in child node $A$ .
$S_B$ is the otal surface area of primitives in child node $B$ .
$N_A$ is the number of primitives in child node $A$ .
$N_B$ is the number of primitives in child node $B$

The Surface Area Heuristic (https://medium.com/@bromanz/how-to-create-awesome-accelerators-the-surface-area-heuristic-e14b5dec6160)

The original paper by Nvidia is published Here. And pbr-book has a good explanation with code.

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