Assignment 2: Lazy K-D Tree
Due: Thursday April 26th, 11:59PM
In this assignment, you will improve pbrt's implementation of the k-d tree accelerator. As described in Chapter 4 of the textbook, before rendering, pbrt constructs a k-d tree containing all geometric primitives in the scene. This approach can be inefficient for several reasons. First, as you will observe in this assignment, building a complete k-d tree for a scene containing many geometric elements can be very costly. Depending on the camera's location and how objects in the scene occlude others from view, it is possible that many k-d tree nodes created in the initial build process may never be hit by any rays. In this case, both computation spent building these nodes and, more importantly, the memory used to store them is wasted. Your objective in this assignment is to modify pbrt's k-d tree accelerator to lazily build the acceleration structure as rays are shot through the scene.
In the images above the same scene rendered from three different camera positions. The scene contains 76 killeroos and each killeroo is a subdivision surface shape with a base mesh consisting of 8316 triangles. Six of these killeroos (the baby killeroos) undergo one level of subdivision, so the resulting meshes contain 33262 triangles. In total, the killeroos constitute 775,692 triangles.
Regardless of the camera position used, pbrt preprocesses the scene into a k-d tree containing 9.7 million nodes. pbrt's statistics for the scene are given below:
Geometry
Total shapes created 781.9k
Triangle Ray Intersections 656.7k:4838.6k (13.57%)
Triangles created 781.7k
Kd-Tree Accelerator
Avg. number of primitives in leaf nodes 12.148M:4.886M (2.49x)
Interior kd-tree nodes made 4.886M
Leaf kd-tree nodes made 4.886M
Maximum number of primitives in leaf node 395
This preprocess can expensive. On my laptop the k-d tree build takes about 30 seconds, while rendering the scene using the k-d tree requires approximately 25 seconds. Additionally, it consumes a large amount of memory. Even with pbrt's compact 8 byte representation of a tree node, the 9.7 million nodes consume 77MB of memory (plus an additional 48MB to store the references to primitives from tree leaf nodes). One solution is to build the tree on demand while tracing rays through the scene. Delayed computation or lazy evaluation is a common technique used in many computer science algorithms. The point of this assignment is to implement a lazy kd-tree to improve pbrt's performance when rendering complex scenes whose geometry extends well beyond the space traversed by the rays generated to render an image, such as in images at center and at right. Your implementation must be lazy in two key ways: (1) kd-tree nodes will be constructed dynamically as needed, and (2) scene objects will be refined into their primitive components only when required.
Step 1: Understanding pbrt's k-d tree
It is critical that you first obtain a detailed understanding of the current k-d tree implementation in pbrt. Read Section 4.4 of the textbook and make sure you can follow the code in kdtree.cpp, located in the accelerator directory of the code base. You should be able to answer the following questions about the current implementation (we do not expect you to hand in answers to these questions).
Describe the memory layout of the k-d tree representation. pbrt takes takes great care to minimize the storage required by a single k-d tree node. Since k-d trees may have millions of nodes, optimizing the memory footprint of nodes is important for both performance and memory utilization. In particular, notice how pbrt saves space by cleverly positioning child nodes in relation to a parent node. This scheme may need to change in your lazy implementation.
- Describe the heuristics of choosing the splitting plane and the implementation of the cost function. You may choose to alter the cost function in this assignment.
What input data is required to build a new k-d tree node? Your implementation will need to be able to access this data dynamically as your lazy k-d tree is generated during the rendering process.
Understand the use of the "badrefines" variable in kdtree.cpp.
Understand how ray traversal through the k-d tree structure works (in the method KdTreeAccel::Intersect). Your lazy imeplementation will need to modify this algorithm to generate new k-d tree nodes while traversing.
Notice that the current k-d tree implementation refines scene objects into their geometric primitives before building the complete k-d tree. What problems does this approach present for lazy evaluation? In particular, look at the implementation of Refine in the loop subdivision shape. What are the benefits of delaying the refine of such objects.
Step 2: Time pbrt's original k-d tree build
Use the ProgressReporter class to measure the amount of time it takes pbrt to create a k-d tree (see the CreateAccelerator function in kdtree.cpp. You'll need to wrap the creation of the KDtreeAccel like this:
ProgressReporter progress(1, "Building KDTree");
KdTreeAccel* accel = new KdTreeAccel(prims, isectCost, travCost,
emptyBonus, maxPrims, maxDepth);
progress.Update();
progress.Done();