bvh
A crate which exports rays, axis-aligned bounding boxes, and binary bounding volume hierarchies.
About
This crate can be used for applications which contain intersection computations of rays with primitives. For this purpose a binary tree BVH (Bounding Volume Hierarchy) is of great use if the scene which the ray traverses contains a huge number of primitives. With a BVH the intersection test complexity is reduced from O(n) to O(log2(n)) at the cost of building the BVH once in advance. This technique is especially useful in ray/path tracers. For use in a shader this module also exports a flattening procedure, which allows for iterative traversal of the BVH. This library is built on top of nalgebra.
Example
use ;
use BVH;
use ;
use Ray;
let origin = new;
let direction = new;
let ray = new;
let mut spheres = Vec new;
for i in 0..1000u32
let bvh = BVH build;
let hit_sphere_aabbs = bvh.traverse_recursive;
Optimization
This crate provides BVH updating, which is also called optimization. With BVH optimization you can mutate the shapes on which the BVH is built and update the tree accordingly without rebuilding it completely. This method is very useful when there are only very few changes to a huge scene. When the major part of the scene is static, it is faster to update the tree, instead of rebuilding it from scratch.
Drawbacks
First of all, optimizing is not helpful if more than half of the scene is not static. This is due to how optimizing takes place: Given a set of indices of all shapes which have changed, the optimize procedure tries to rotate fixed constellations in search for a better surface area heuristic (SAH) value. This is done recursively from bottom to top while fixing the AABBs in the inner nodes of the BVH. Which is why it is inefficient to update the BVH in comparison to rebuilding, when a lot of shapes have moved.
Another problem with updated BVHs is, that the resulting BVH is not optimal. Assume that the scene is composed of two major groups separated by a large gap. When one shape moves from one group to another, the updating procedure will not be able to find a sequence of bottom-up rotations which inserts the shape deeply into the other branch.
The following benchmarks are run with two different datasets:
- A randomly generated scene with unit sized cubes containing a total of (1200, 12000, and 120000 triangles).
- Sponza, a popular scene for benchmarking graphics engines.
Intersection via traversal of the list of triangles
test ... bench: 1,018,566 ns/iter
test bench_intersect_sponza_list ... bench: 669,474 ns/iter
bench_intersect_120k_triangles_list
This is the most naive approach to intersecting a scene with a ray. It defines the baseline.
Intersection via traversal of the list of triangles with AABB checks
test ... bench: 400,877 ns/iter
test bench_intersect_sponza_list_aabb ... bench: 206,014 ns/iter
bench_intersect_120k_triangles_list_aabb
AABB checks are cheap, compared to triangle-intersection algorithms. Therefore, preceeding AABB checks increase intersection speed by filtering negative results a lot faster.
Build of a BVH from scratch
test ... bench: 1,300,824 ns/iter
test bench_build_12k_triangles_bvh ... bench: 15,327,304 ns/iter
test bench_build_120k_triangles_bvh ... bench: 181,138,173 ns/iter
test bench_build_sponza_bvh ... bench: 120,335,877 ns/iter
bench_build_1200_triangles_bvh
As you can see, building a BVH takes a long time. Building a BVH is only useful if the number of intersections performed on the
scene exceeds the build duration. This is the case in applications such as ray and path tracing, where the minimum
number of intersections is 1280 * 720
for an HD image.
Intersection via BVH traversal
test ... bench: 202 ns/iter
test bench_intersect_120k_triangles_bvh ... bench: 959 ns/iter
test bench_intersect_12k_triangles_bvh ... bench: 461 ns/iter
test bench_intersect_sponza_bvh ... bench: 1,784 ns/iter
bench_intersect_1200_triangles_bvh
These performance measurements show that traversing a BVH is much faster than traversing a list.
Optimization
The benchmarks for how long it takes to update the scene also contain a randomization process which takes some time.
test ... bench: 14,248,069 ns/iter
test bench_optimize_bvh_120k_00p ... bench: 2,338,563 ns/iter
test bench_optimize_bvh_120k_01p ... bench: 12,690,322 ns/iter
test bench_optimize_bvh_120k_10p ... bench: 117,318,325 ns/iter
test bench_optimize_bvh_120k_50p ... bench: 502,788,600 ns/iter
// TODO Sponza benchmarks.
bench_randomize_120k_50p
This is the place where you have to differentiate between rebuilding the tree from scratch or trying to optimize the old one.
These tests show the impact of moving around a particular percentage of shapes (10p
=> 10%
).
It is important to note that the randomization process here moves triangles around indiscriminately.
This will also lead to cases where the BVH would have to be restructured completely.
Intersection after the optimization
These intersection tests are grouped by dataset and by the BVH generation method.
_after_optimize
uses a BVH which was kept up to date with calls tooptimize
, while_with_rebuild
uses the same triangle data as_after_optimize
, but constructs a BVH from scratch.
120K Triangles
test ... bench: 968 ns/iter
test bench_intersect_120k_after_optimize_01p ... bench: 147,160 ns/iter
test bench_intersect_120k_after_optimize_10p ... bench: 1,624,675 ns/iter
test bench_intersect_120k_after_optimize_50p ... bench: 2,775,067 ns/iter
test bench_intersect_120k_with_rebuild_00p ... bench: 964 ns/iter
test bench_intersect_120k_with_rebuild_01p ... bench: 1,016 ns/iter
test bench_intersect_120k_with_rebuild_10p ... bench: 2,025 ns/iter
test bench_intersect_120k_with_rebuild_50p ... bench: 2,373 ns/iter
bench_intersect_120k_after_optimize_00p
Sponza
test ... bench: 1,824 ns/iter
test bench_intersect_sponza_after_optimize_01p ... bench: 3,791 ns/iter
test bench_intersect_sponza_after_optimize_10p ... bench: 4,794 ns/iter
test bench_intersect_sponza_after_optimize_50p ... bench: 7,492 ns/iter
test bench_intersect_sponza_with_rebuild_00p ... bench: 1,823 ns/iter
test bench_intersect_sponza_with_rebuild_01p ... bench: 1,957 ns/iter
test bench_intersect_sponza_with_rebuild_10p ... bench: 2,414 ns/iter
test bench_intersect_sponza_with_rebuild_50p ... bench: 3,135 ns/iter
bench_intersect_sponza_after_optimize_00p
This set of tests shows the impact of randomly moving triangles around and producing degenerated trees. The 120K Triangles dataset has been updated randomly. The Sponza scene was updated using a method which has a maximum offset distance for shapes. This simulates a more realistic scenario.
We also see that the Sponza scene by itself contains some structures which can be tightly wrapped in a BVH. By mowing those structures around we destroy the locality of the triangle groups which leads to more branches in the BVH requiring a check, thus leading to a higher intersection duration.