Assignment 2: Lazy KD Tree
Due: Thursday April 13th, 11:59PM
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Description
In this assignment, you will improve pbrt's implementation of the kd-tree accelerator. As described in Chapter 4 of the textbook, before rendering, pbrt constructs a kd-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 kd-tree for a scene containing many geometric elements can be very costly. Depending on the camera's location, or on how large objects in the scene hide others from view, it is possible that many kd-tree nodes created in the initial build process may never be hit by any rays. In this case, both the time spent building these nodes and the memory used to store them is wasted. As an example, the following images show the same scene from three different camera positions.
In all images, the rendered scene contains 4 killeroos, a ground plane, and two walls. In the left image, the camera faces the killeroos and all the objects in the scene are visible. In the center image, the camera is placed such that the killeroos are hidden behind the walls. In the image at right, the camera is zoomed in on one of the killeroo heads, occluding large regions of the scene.
For this scene, pbrt builds the kd-tree consisting of 273.1k tree nodes irregarless of camera position. However, it is clear there is no need to create nodes in the space surrounding the killeroos in the second image, since they are occluded from view and no rays will traverse through that part of the scene. The following segment shows statistics from rendering the left and center scenes in pbrt.
Geometry
Total shapes created 133.1k
Triangle Ray Intersections 1.475M:9.220M (16.00%)
Triangles created 133.1k
Kd-Tree Accelerator
Avg. number of primitives in leaf nodes 865.8k:273.1k (3.17x)
Interior kd-tree nodes made 273.1k
Leaf kd-tree nodes made 273.1k
Maximum number of primitives in leaf node 155
Constructing these extra tree nodes can be expensive. One solution is to dynamically build the tree while tracing rays and only construct nodes when it is necessary. This attempt of delayed computation or lazy evaluation has been commonly applied in computer science.