In part II of this series, we looked at hierarchical tree traversal as a means of quickly identifying pairs of potentially colliding 3D objects and we demonstrated how optimizing for low divergence can result in substantial performance gains on massively parallel processors. Having a fast traversal algorithm is not very useful, though, unless we also have a tree to go with it. In this part, we will close the circle by looking at tree building; specifically, parallel bounding volume hierarchy (BVH) construction. We will also see an example of an algorithmic optimization that would be completely pointless on a single-core processor, but leads to substantial gains in a parallel setting.

There are many use cases for BVHs, and also many ways of constructing them. In our case, construction speed is of the essence. In a physics simulation, objects keep moving from one time step to the next, so we will need a different BVH for each step. Furthermore, we know that we are going to spend only about 0.25 milliseconds in traversing the BVH, so it makes little sense to spend much more on constructing it. One well-known approach for handling dynamic scenes is to essentially recycle the same BVH over and over. The basic idea is to only recalculate the bounding boxes of the nodes according to the new object locations while keeping the hierarchical structure of nodes the same. It is also possible to make small incremental modifications to improve the node structure around objects that have moved the most. However, the main problem plaguing these algorithms is that the tree can deteriorate in unpredictable ways over time, which can result in arbitrarily bad traversal performance in the worst case. To ensure predictable worst-case behavior, we instead choose to build a new tree from scratch every time step. Let’s look at how.

## Exploiting the Z-Order Curve

The most promising current parallel BVH construction approach is to use a so-called linear BVH (LBVH). The idea is to simplify the problem by first choosing the order in which the leaf nodes (each corresponding to one object) appear in the tree, and then generating the internal nodes in a way that respects this order. We generally want objects that located close to each other in 3D space to also reside nearby in the hierarchy, so a reasonable choice is to sort them along a space-filling curve. We will use the Z-order curve for simplicity. Continue reading