For various reasons, I was preoccupied with three different thoughts in 2005: the Euler equation (relating vertices, edges and faces), transforming planes with

For various reasons, I was preoccupied with three different thoughts in 2005: the Euler equation (relating vertices, edges and faces), transforming planes with 4x4 matrices, and trying to optimize ray-triangle intersection. On the way to a company meeting, I was sitting on a bus, looking out the window, watching the scenery go by while turning these three topics around in my head. These pieces (which I didn't think were really related) suddenly started fitting together, and I came up with a radically new way of testing ray intersection against an object defined by a mesh of triangles. It ended up being successful beyond my biggest hopes. Eventually got patented by Microsoft, but the patent's now expired. Still my proudest discovery.