Concept: AABB (Axis-Aligned Bounding Box)

• Parent: PathTracer Learning - Phase 2 - CPU Ray Tracing

Definition

• A box whose faces are aligned with the coordinate axes
• Defined by two points: min = (x_min, y_min, z_min) and max = (x_max, y_max, z_max)
• Every point P inside satisfies: min.x ≤ P.x ≤ max.x (and same for y, z)
• “Axis-aligned” means no rotation — simplifies intersection math enormously

Ray-AABB Intersection (Slab Method)

• Treat the AABB as the intersection of 3 pairs of parallel planes (slabs)
• For each axis, compute entry and exit t values
  • t_x_min = (min.x - ray.origin.x) / ray.direction.x
  • t_x_max = (max.x - ray.origin.x) / ray.direction.x
  • If ray.direction.x < 0, swap min and max
• Combine all 3 axes
  • t_enter = max(t_x_min, t_y_min, t_z_min) — ray enters the box
  • t_exit = min(t_x_max, t_y_max, t_z_max) — ray exits the box
• Hit condition: t_enter <= t_exit && t_exit > t_min
• Implementation

  bool intersectAABB(Ray ray, vec3 boxMin, vec3 boxMax, out float tNear) {
      vec3 invDir = 1.0 / ray.direction;
      vec3 t0 = (boxMin - ray.origin) * invDir;
      vec3 t1 = (boxMax - ray.origin) * invDir;
      vec3 tMin = min(t0, t1);
      vec3 tMax = max(t0, t1);
      float tEnter = max(max(tMin.x, tMin.y), tMin.z);
      float tExit  = min(min(tMax.x, tMax.y), tMax.z);
      tNear = tEnter;
      return tEnter <= tExit && tExit > 0.0;
  }

• Note: invDir = 1.0 / ray.direction precomputed for efficiency
• Handle direction = 0 case: invDir = ±infinity, which works correctly with IEEE 754

AABB Construction

• From a set of points: min = componentwise_min(all_points), max = componentwise_max(all_points)
• From a triangle: min = min(v0, v1, v2), max = max(v0, v1, v2)
• Merging two AABBs: merged.min = min(a.min, b.min), merged.max = max(a.max, b.max)

Surface Area

• SA = 2 * (dx*dy + dy*dz + dz*dx) where dx = max.x - min.x etc.
• Used in SAH (Surface Area Heuristic) for BVH construction
• Intuition: larger surface area → more likely to be hit by a random ray

Why AABB and Not OBB?

• OBB (Oriented Bounding Box) fits tighter but intersection is much more expensive
• AABB intersection: ~6 divisions, ~6 comparisons
• OBB intersection: requires transforming ray to box space (matrix multiply)
• BVH with AABBs is fast enough in practice — hardware RT uses AABBs

Related

• PathTracer Learning - Concept - BVH Construction
• PathTracer Learning - Concept - BVH Traversal