A technique for classifying a ray tracing intersection with a triangle edge or vertex avoids either rendering holes or multiple hits of the same ray for different triangles. The technique employs a tie-breaking scheme in which certain types of edges are classified as hits and certain types of edges are classified as misses. The test is performed in a coordinate space that comprises a projection into the viewspace of the ray, and thus where the ray direction has a non-zero magnitude in one axis (e.g., z) but a zero magnitude in the two other axes. In this coordinate space, edges are classified as one of top, bottom, left, and right, and an intersection on an edge counts as a hit if the intersection hits a top or left edge, but a miss if the intersection hits a bottom or right edge. Vertices are processed in a related manner.