Acceleration

1. Acceleration Digital Image Synthesis Yung-Yu Chuang 10/8/2009 with slides by Mario Costa Sousa, Gordon Stoll and Pat Hanrahan

2. Classes • Primitive (in core/primitive.*) • GeometricPrimitive • InstancePrimitive • Aggregate • Two types of accelerators are provided (in accelerators/*.cpp) • GridAccel • KdTreeAccel

3. Hierarchy Primitive Instance Primitive Aggregate Geometric Primitive T Material Shape

4. Primitive class Primitive : public ReferenceCounted { <Primitive interface> } class InstancePrimitive : public Primitive { … Reference<Primitive> instance; }

5. Interface BBox WorldBound(); bool CanIntersect(); bool Intersect(const Ray &r, Intersection *in); bool IntersectP(const Ray &r); void Refine(vector<Reference<Primitive>> &refined); void FullyRefine(vector<Reference<Primitive>> &refined); AreaLight *GetAreaLight(); BSDF *GetBSDF(const DifferentialGeometry &dg, const Transform &WorldToObject); geometry // updatemaxt material

6. Intersection • primitive stores the actual intersecting primitive, hence Primitive->GetAreaLight and GetBSDF can only be called for GeometricPrimitive struct Intersection { <Intersection interface> DifferentialGeometry dg; const Primitive *primitive; Transform WorldToObject; }; More information than DifferentialGeometry; also contains material information

7. GeometricPrimitive • represents a single shape • holds a reference to a Shape and its Material,and a pointer to an AreaLight Reference<Shape> shape; Reference<Material> material; // BRDF AreaLight *areaLight; // emittance • Most operations are forwarded to shape

8. Object instancing 61 unique plant models, 1.1M triangles, 300MB 4000 individual plants, 19.5M triangles

9. InstancePrimitive Reference<Primitive> instance; Transform InstanceToWorld, WorldToInstance; Ray ray = WorldToInstance(r); if (!instance->Intersect(ray, isect)) return false; r.maxt = ray.maxt; isect->WorldToObject = isect->WorldToObject *WorldToInstance;

10. Aggregates • Acceleration is a heart component of a ray tracer because ray/scene intersection accounts for the majority of execution time • Goal: reduce the number of ray/primitive intersections by quick simultaneous rejection of groups of primitives and the fact that nearby intersections are likely to be found first • Two main approaches: spatial subdivision, object subdivision • No clear winner

11. Acceleration techniques

12. Bounding volume hierarchy

13. Find bounding box of objects Bounding volume hierarchy

14. Find bounding box of objects Split objects into two groups Bounding volume hierarchy

15. Find bounding box of objects Split objects into two groups Recurse Bounding volume hierarchy

16. Find bounding box of objects Split objects into two groups Recurse Bounding volume hierarchy

17. Find bounding box of objects Split objects into two groups Recurse Bounding volume hierarchy

18. Find bounding box of objects Split objects into two groups Recurse Bounding volume hierarchy

19. At midpoint Sort, and put half of the objects on each side Use modeling hierarchy Where to split?

20. If hit parent, then check all children BVH traversal

21. Don't return intersection immediately because the other subvolumes may have a closer intersection BVH traversal

22. Bounding volume hierarchy

23. Bounding volume hierarchy

24. Quadtree (2D) Octree (3D) Space subdivisionapproaches Unifrom grid

25. KD tree Space subdivisionapproaches BSP tree

26. Uniform grid

27. Preprocess scene Find bounding box Uniform grid

28. Preprocess scene Find bounding box Determine grid resolution Uniform grid

29. Preprocess scene Find bounding box Determine grid resolution Place object in cell if its bounding box overlaps the cell Uniform grid

30. Preprocess scene Find bounding box Determine grid resolution Place object in cell if its bounding box overlaps the cell Check that object overlaps cell (expensive!) Uniform grid

31. Preprocess scene Traverse grid 3D line = 3D-DDA (Digital Differential Analyzer) Uniform grid traversal naive DDA

32. octree Octree

33. K-d tree A A Leaf nodes correspond to unique regions in space

34. K-d tree A B A Leaf nodes correspond to unique regions in space

35. K-d tree A B B A Leaf nodes correspond to unique regions in space

36. K-d tree A C B B A

37. K-d tree A C B C B A

38. K-d tree A C D B C B A

39. K-d tree A C D B C B D A

40. K-d tree A D B B C C D A Leaf nodes correspond to unique regions in space

41. K-d tree traversal A D B B C C D A Leaf nodes correspond to unique regions in space

42. BSP tree 6 5 9 7 10 8 1 11 2 4 3

43. BSP tree 6 5 1 outside ones inside ones 9 7 10 8 1 11 2 4 3

44. BSP tree 6 5 1 5 6 7 8 9 10 11 2 3 4 9 7 10 8 1 11 2 4 3

45. BSP tree 6 1 5 5 9b 9 6 7 9a 10 11a 8 9b 11b 7 10 11b 8 9a 1 11 11a 2 4 3

46. BSP tree 6 5 1 9b 9 5 2 7 10 11b 8 8 3 6 9a 1 11 9b 7 4 11a 2 4 9a 11b 3 10 11a

47. BSP tree traversal 6 5 1 9b 9 5 2 7 11b 10 11b 8 8 3 6 9a 9a 1 11 9b 7 4 11a 2 4 9a 11b point 3 10 11a

48. BSP tree traversal 6 5 1 9b 9 5 2 7 11b 10 11b 8 8 3 6 9a 9a 1 11 9b 7 4 11a 2 4 9a 11b point 3 10 11a

49. BSP tree traversal 6 5 1 9b 9 5 2 7 11b 10 11b 8 8 3 6 9a 9a 1 11 9b 7 4 11a 2 4 9a 11b point 3 10 11a

50. Ray-Box intersections • Both GridAccel and KdTreeAccel require it • Quick rejection, use enter and exit point to traverse the hierarchy • AABB is the intersection of three slabs