rayAABB

rayAABB is a common test in computer graphics and computational geometry that determines whether a parametric ray intersects an axis-aligned bounding box (AABB) in 3D space. It is widely used in ray tracing, visibility queries, and broad-phase collision detection to quickly cull objects that do not intersect a ray, improving performance.

An AABB is defined by its minimum and maximum corners (xmin, ymin, zmin) and (xmax, ymax, zmax). A ray is given by origin O and direction D, with the parametric form R(t) = O + tD for t >= 0. The slab method computes intersection intervals along each axis by solving for t where the ray intersects the bounding planes of the box. For each axis, compute t values where the ray meets the slabs: t1 = (min - O_axis) / D_axis and t2 = (max - O_axis) / D_axis. If a component of D is zero, the ray is parallel to that axis; intersection is possible only if the origin coordinate lies within the slab for that axis.

From these, define tmin_axis = min(t1, t2) and tmax_axis = max(t1, t2) for each axis, then overall tmin = max(tmin_x, tmin_y, tmin_z) and tmax = min(tmax_x, tmax_y, tmax_z). The ray intersects the box if tmax >= tmin and tmax >= 0. The entry distance along the ray is tHit = tmin if tmin >= 0, otherwise tHit = tmax if tmax >= 0. If neither condition holds, there is no intersection.

Variations include using the reciprocal of D for faster computation and precomputing sign information to branch-freely select slab intersections. Implementations may return a boolean intersection flag and optionally the near and far intersection distances (tNear and tFar). Common pitfalls include handling rays parallel to an axis and degenerate or inverted boxes.