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Acceleration

Explore bounding volume hierarchy and space subdivision approaches to accelerate digital image synthesis. Learn about techniques such as BVH traversal, uniform grid, kd-trees, and BSP trees.

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Acceleration

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

  2. Acceleration techniques

  3. Bounding volume hierarchy

  4. Find bounding box of objects Bounding volume hierarchy

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

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

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

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

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

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

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

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

  13. Bounding volume hierarchy

  14. Bounding volume hierarchy

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

  16. KD tree Space subdivisionapproaches BSP tree

  17. Uniform grid

  18. Preprocess scene Find bounding box Uniform grid

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

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

  21. 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

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

  23. octree Octree

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

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

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

  27. K-d tree A C B B A

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

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

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

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

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

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

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

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

  36. 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

  37. 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

  38. 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

  39. 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

  40. 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

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

  42. Hierarchy Primitive Transformed Primitive Aggregate Geometric Primitive T Material Shape Support both Instancing and animation Store intersectable primitives, call Refine If necessary

  43. Primitive class Primitive : public ReferenceCounted { <Primitive interface> const int primitiveId; static int nextprimitiveId; } class TransformedPrimitive: public Primitive { … Reference<Primitive> instance; }

  44. 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, Transform &WorldToObject); BSSRDF *GetBSSRDF(DifferentialGeometry &dg, Transform &WorldToObject); geometry // updatemaxt material

  45. Intersection struct Intersection { <Intersection interface> DifferentialGeometry dg; const Primitive *primitive; Transform WorldToObject, ObjectToWorld; int shapeId, primitiveId; float rayEpsilon; }; adaptively estimated primitive stores the actual intersecting primitive, hence Primitive->GetAreaLight and GetBSDF can only be called for GeometricPrimitive

  46. 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

  47. GeometricPrimitive bool Intersect(Ray &r,Intersection *isect) { float thit, rayEpsilon; if (!shape->Intersect(r, &thit, &rayEpsilon, &isect->dg)) return false; isect->primitive = this; isect->WorldToObject = *shape->WorldToObject; isect->ObjectToWorld = *shape->ObjectToWorld; isect->shapeId = shape->shapeId; isect->primitiveId = primitiveId; isect->rayEpsilon = rayEpsilon; r.maxt = thit; return true; }

  48. Object instancing 61 unique plants, 4000 individual plants, 19.5M triangles With instancing, store only 1.1M triangles, 11GB->600MB

  49. TransformedPrimitive Reference<Primitive> primitive; AnimatedTransform WorldToPrimitive; Ray ray = WorldToPrimitive(r); if (!instance->Intersect(ray, isect)) return false; r.maxt = ray.maxt; isect->WorldToObject = isect->WorldToObject *WorldToInstance; for instancing and animation

  50. TransformedPrimitive bool Intersect(Ray &r, Intersection *isect){ Transform w2p; WorldToPrimitive.Interpolate(r.time,&w2p); Ray ray = w2p(r); if (!primitive->Intersect(ray, isect)) return false; r.maxt = ray.maxt; isect->primitiveId = primitiveId; if (!w2p.IsIdentity()) { // Compute world-to-object transformation for instance isect->WorldToObject=isect->WorldToObject*w2p; isect->ObjectToWorld=Inverse( isect->WorldToObject); // Transform instance's differential geometry to world space Transform PrimitiveToWorld = Inverse(w2p); isect->dg.p = PrimitiveToWorld(isect->dg.p); isect->dg.nn = Normalize(PrimitiveToWorld(isect->dg.nn)); isect->dg.dpdu = PrimitiveToWorld(isect->dg.dpdu); isect->dg.dpdv = PrimitiveToWorld(isect->dg.dpdv); isect->dg.dndu = PrimitiveToWorld(isect->dg.dndu); isect->dg.dndv = PrimitiveToWorld(isect->dg.dndv); } return true; }

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