Nearest neighbour search is a very natural problem: given a target point and a set of candidates, find the closest candidate to the target. For points in the standard k-dimensional Euclidean space, k-d trees and related data structures offer a good solution. But we're not always so lucky.
In part 1, I outlined an algorithm for computing intersections between rays and axis-aligned bounding boxes. The idea to eliminate branches by relying on IEEE 754 floating point properties goes back to Brian Smits in , and the implementation was fleshed out by Amy Williams. et al. in .
It's surprisingly difficult to find a good code snippet for this on Google, so here's an efficient computation of integer powers in C, using binary exponentiation:
Clang is known for its great error messages, but I did manage to horribly confuse it:
The visitor pattern is tremendously useful when working with certain kinds of information like abstract syntax trees. It's basically a poor man's version of sum types for languages that don't natively support them. Unfortunately, they take advantage of function overloading, something which duck-typed languages like Python lack.
Finding the tightest axis-aligned bounding box for a sphere is trivial: the box extends from the center by the radius in all dimensions. But once the sphere is transformed, finding the minimal bounding box becomes trickier. Rotating a sphere, for example, shouldn't change its bounding box, but naïvely rotating the bounding box will expand it unnecessarily. Luckily there's a trick to computing minimal bounding boxes by representing the transformed sphere as a quadric surface.
In my last post, I talked about a beautiful method for computing ray/triangle intersections. In this post, I will extend it to computing intersections with triangle fans. Since meshes are often stored in a corner table, which is simply an array of triangle fans, this gives an efficient algorithm for ray tracing triangle meshes.
3D ray/triangle intersections are obviously an important part of much of computer graphics. The Möller–Trumbore algorithm, for example, computes these intersections very quickly. But there is another method that I believe is more elegant, and in some cases allows you to compute the intersection for “free.”