You need to traverse the quad-tree as follows:

1. start at root node.

2. intersect your ray with the root node's bounding box.

3. does it intersect it? if not, return (to the calling function) with no intersection (if you can't express "no intersection" in your algorithm, just use infinite distance)

4. if this is a leaf node:

- intersect the ray with all the triangles in the node, and return (to the calling function) the closest intersection

else:

- find out which children nodes the ray intersects, and sort them according to closest intersection (this is the trickiest part in my experience)

- recurse to step 2 for each child node, in order of intersection, until the closest triangle found is closer than the distance to a child's bounding box (in which case any triangle inside that child will be further away than the one you've already found, so there's no need to traverse it)

- return (to the calling function) the closest intersection you found

This is a recursive process, and will find the closest triangle intersecting the ray with complexity O(log(n)) where n is the number of triangles in your quadtree. You probably want to implement this with a stack instead of using recursion (at least once everything is working) for performance's sake. The really annoying part is getting the bounding box collisions right, I highly recommend you overlay your quadtree on top of your triangles using wireframe rectangles to debug any issues.

**Edited by Bacterius, 22 August 2013 - 03:47 PM.**

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

- *Pessimal Algorithms and Simplexity Analysis*