# (Task 3) Bounding Volume Hierarchy

## Walkthrough

In this task you will implement a bounding volume hierarchy that accelerates ray-scene intersection. Most of this work will be in student/bvh.inl. Note that this file has an unusual extension (.inl = inline) because it is an implementation file for a template class. This means bvh.h must #include it, so all code that sees bvh.h will also see bvh.inl. Note that this means when you try rebuilding, it will have to rebuild a bunch of files which may take some time.

First, take a look at the definition for our BVH in rays/bvh.h. We represent our BVH as nodes (a vector of Nodes) as an implicit tree data structure in the same fashion as heaps that you probably have seen in some other courses. A Node has the following fields:

• BBox bbox: the bounding box of the node (bounds all primitives in the subtree rooted by this node)
• size_t start: start index of primitives in the BVH’s primitive array
• size_t size: range of index in the primitive list (# of primitives in the subtree rooted by the node)
• size_t l: the index of the left child node
• size_t r: the index of the right child node

The BVH class also maintains a vector of all primitives in the BVH. The fields start and size in the BVH Node refer to the range of contained primitives in this array. The primitives in this array are not initially in any particular order, and you will need to rearrange the order as you build the BVH so that your BVH can accurately represent the spacial hierarchy.

The starter code constructs a valid BVH, but it is a trivial BVH with a single node containing all scene primitives. Once you are done with this task, you can check the box for BVH in the left bar under “Visualize” when you start render to visualize your BVH and see each levels.

Finally, note that the BVH visualizer will start drawing from BVH::root_idx, so be sure to set this to the proper index (probably $$0$$ or nodes.size() - 1, depending on your implementation) when you build the BVH.

## Step 0: Bounding Box Calculation & Intersection

Implement BBox::hit in student/bbox.cpp and Triangle::bbox in student/tri_mesh.cpp (if you haven’t already from Task 2).

We recommend checking out this Scratchapixel article for implementing bounding box intersections.

## Step 1: BVH Construction

Your job is to construct a BVH in void BVH<Primitive>::build in student/bvh.inl using the Surface Area Heuristic discussed in class. Tree construction would occur when the BVH object is constructed. Below is the pseudocode from class by which your BVH construction procedure should generally follow:

If you find it easier to think of looping over partitions rather than buckets, here is another outline of pseudocode that you may use:

Notes:

• The $$B$$ referenced in the first pseudocode is the bucket that the primitive’s centroid would lie in along the axis we are currently on.
• For the centroid referenced in the pseudocode, we can simply take the center of the primitive’s bbox to be a good approximation.
• A helpful C++ function to use for partitioning primitives is std::partition. This function divides the original group of elements into two sub-groups, where the first group contains elements that return true for the execution policy and the second group contains the elements that return false. Note that the elements are not sorted within the subgroups themselves. You may want to use std::sort to sort them.
• You may find that this task is one of the most time consuming parts of A3, especially since this part of the documentation is intentionally sparse.

## Step 2: Ray-BVH Intersection

Implement the ray-BVH intersection routine Trace BVH<Primitive>::hit(const Ray& ray) in student/bvh.inl. You may wish to consider the node visit order optimizations we discussed in class. Once complete, your renderer should be able to render all of the test scenes in a reasonable amount of time. Below is the pseudocode that we went over in class:

Note:

• Implementing BVH will make your renderer much faster, but it is not required to finish the assignment. When you go to Render mode and click Open Render Window, there is a checkbox to not use BVH. Simply uncheck that and you will be able to test the rest of the tasks.

## Reference Results

In Render mode, simply check the box for “BVH” and then render your image. You should be able to see the BVH you generated in task 3 once it starts rendering. You can click on the horizontal bar to see each level of your BVH.

The BVH constructed for Spot the Cow on the 10th level.

The BVH constructed for a scene composed of several cubes and spheres on the 0th and 1st levels.

The BVH constructed for the Stanford Bunny on the 10th level.