RTNN: Accelerating Neighbor Search Using Hardware Ray Tracing

A long talk for the PPoPP 2022 paper with the same title. The code is at: https://github.com/horizon-research/rtnn.

Transcript

1. Yuhao Zhu
   https://github.com/horizon-research/rtnn
   University of Rochester
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2. 2
   (BNF1MBO
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   • What is ray tracing?
   

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3. 3
   (BNF1MBO
   "DDFMFSBUJOH
   /FJHICPS4FBSDI
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   • What is ray tracing?
   
   
   • How does hardware
   support ray tracing?
   

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4. (BNF1MBO
   4
   "DDFMFSBUJOH
   /FJHICPS4FBSDI
   6TJOH)BSEXBSF
   3BZ5SBDJOH
   • What is ray tracing?
   
   
   • How does hardware
   support ray tracing?
   
   
   • What is neighbor search?
   

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5. 5
   • What is ray tracing?
   
   
   • How does hardware
   support ray tracing?
   
   
   • What is neighbor search?
   
   
   • How to use hardware ray
   tracing to accelerate
   neighbor search?
   (BNF1MBO
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6. 6
   (BNF1MBO
   "DDFMFSBUJOH
   /FJHICPS4FBSDI
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   • What is ray tracing?
   

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7. View Slide

8. 8
   2D image
   cgarena.com
   

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9. 8
   Modeling
   3D mesh 2D image
   cgarena.com
   

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10. .FTI JF )PX4DFOFJT3FQSFTFOUFE
    
    9
    Very informally: 3D piece-wide linear
    approximation of arbitrary 3D surfaces
    free3d.com
    

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11. .FTI JF )PX4DFOFJT3FQSFTFOUFE
    
    9
    Very informally: 3D piece-wide linear
    approximation of arbitrary 3D surfaces
    Quadrilateral mesh
    free3d.com
    

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12. TABLE I
    PROCESSING TIMES AND QUALITY MEASURES FOR THE PROCESSED MESHES. THE COLUMNS ARE RESPECTIVELY THE NUMBER OF VERTICES OF THE
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    .FTI JF )PX4DFOFJT3FQSFTFOUFE
    
    9
    Very informally: 3D piece-wide linear
    approximation of arbitrary 3D surfaces
    Quadrilateral mesh Triangular mesh
    Valette, et al. [TVCG’08]
    free3d.com
    

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13. 10
    Modeling Rendering
    Lighting, camera,
    material, etc.
    3D mesh 2D image
    cgarena.com
    

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14. 10
    Modeling Rendering
    Lighting, camera,
    material, etc.
    Visibility Shading
    3D mesh 2D image
    cgarena.com
    

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15. 10
    Modeling Rendering
    Lighting, camera,
    material, etc.
    Visibility Shading
    3D mesh 2D image
    cgarena.com
    Visibility Problem
    
    
    For each pixel in the image (to be
    rendered), which point in the scene
    (i.e., on the mesh) corresponds to it?
    

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16. 10
    Modeling Rendering
    Lighting, camera,
    material, etc.
    Visibility Shading
    3D mesh 2D image
    cgarena.com
    

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17. 10
    Modeling Rendering
    Lighting, camera,
    material, etc.
    Visibility Shading
    3D mesh 2D image
    cgarena.com
    * Usually cast multiple rays for each pixel
    

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18. Shading Problem
    
    
    What’s the color of an
    intersecting scene point
    along the ray direction?
    10
    Modeling Rendering
    Lighting, camera,
    material, etc.
    Visibility Shading
    3D mesh 2D image
    cgarena.com
    * Usually cast multiple rays for each pixel
    

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19. "TJEF0UIFS(FPNFUSZ1SJNJUJWFT
    11
    Hair and furs are usually modeled using
    curves (e.g., Catmull–Rom spline).
    https://developer.nvidia.com/blog/optix-sdk-7-1/
    Points and spheres.
    https://www.sciencefocus.com/future-technology/notre-dame-how-faithfully-can-we-rebuild-the-cathedral-with-modern-tech/
    

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20. 3BZ4DFOF*OUFSTFDUJPO
    12
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • Goal: calculate the [x, y, z]
    coordinates of the closest hit
    between the ray and the mesh.
    
    
    • Why closest hit?
    [x, y, z]
    Valette, et al. [TVCG’08]
    x
    y
    z
    

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21. 3BZ4DFOF*OUFSTFDUJPO
    12
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • Goal: calculate the [x, y, z]
    coordinates of the closest hit
    between the ray and the mesh.
    
    
    • Why closest hit?
    [x, y, z]
    Valette, et al. [TVCG’08]
    x
    y
    z
    

    View Slide

22. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

23. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    • iterate all triangles
    [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

24. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    • iterate all triangles
    • test intersection for each triangle [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

25. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    • iterate all triangles
    • test intersection for each triangle
    • return the closest hit, if any
    [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

26. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    • iterate all triangles
    • test intersection for each triangle
    • return the closest hit, if any
    • Complexity:
    [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

27. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    • iterate all triangles
    • test intersection for each triangle
    • return the closest hit, if any
    • Complexity:
    • O(# of rays x # of triangles)
    [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

28. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    • iterate all triangles
    • test intersection for each triangle
    • return the closest hit, if any
    • Complexity:
    • O(# of rays x # of triangles)
    • Slow:
    [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

29. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    • iterate all triangles
    • test intersection for each triangle
    • return the closest hit, if any
    • Complexity:
    • O(# of rays x # of triangles)
    • Slow:
    • lots of triangles and lots of rays
    [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

30. &YIBVTUJWF4FBSDI
    13
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric)
    • The simplest solution:
    • iterate all triangles
    • test intersection for each triangle
    • return the closest hit, if any
    • Complexity:
    • O(# of rays x # of triangles)
    • Slow:
    • lots of triangles and lots of rays
    • …and it’s recursive
    [x, y, z]
    Valette, et al. [TVCG’08]
    

    View Slide

31. "TJEF8IZ3FDVSTJWF3BZ5SBDJOH
    14
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric) Valette, et al. [TVCG’08]
    • To implement realistic shading.
    Color?
    

    View Slide

32. "TJEF8IZ3FDVSTJWF3BZ5SBDJOH
    14
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric) Valette, et al. [TVCG’08]
    • To implement realistic shading.
    • The color* of an exiting ray depends
    on the colors* of all incident rays.
    Color?
    Color?
    Color?
    Color?
    

    View Slide

33. "TJEF8IZ3FDVSTJWF3BZ5SBDJOH
    14
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric) Valette, et al. [TVCG’08]
    • To implement realistic shading.
    • The color* of an exiting ray depends
    on the colors* of all incident rays.
    • color* should technically be radiance; not
    important for our discussion here.
    Color?
    Color?
    Color?
    Color?
    

    View Slide

34. "TJEF8IZ3FDVSTJWF3BZ5SBDJOH
    14
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric) Valette, et al. [TVCG’08]
    • To implement realistic shading.
    • The color* of an exiting ray depends
    on the colors* of all incident rays.
    • color* should technically be radiance; not
    important for our discussion here.
    • also depends on the surface material (diffuse vs.
    specular vs. …); not important for our discussion here.
    Color?
    Color?
    Color?
    Color?
    

    View Slide

35. "TJEF8IZ3FDVSTJWF3BZ5SBDJOH
    14
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric) Valette, et al. [TVCG’08]
    • To implement realistic shading.
    • The color* of an exiting ray depends
    on the colors* of all incident rays.
    • color* should technically be radiance; not
    important for our discussion here.
    • also depends on the surface material (diffuse vs.
    specular vs. …); not important for our discussion here.
    • How do we know the color of an
    incident ray? Cast more rays!
    Color?
    Color?
    Color?
    Color?
    

    View Slide

36. "TJEF8IZ3FDVSTJWF3BZ5SBDJOH
    15
    INPUT AND OUTPUT MESHES, THE METRIC USED FOR THE CLUSTERING, THE TIME SPENT ON THE CURVATURE MEASURE COMPUTATION AND ON THE
    CLUSTERING, THE PERCENTAGE OF MINIMAL INTERNAL ANGLES BELLOW 30o AND THE AVERAGE TRIANGLE ASPECT RATIO.
    Fig. 12. Coarsened versions of the rockerarm model (1000 vertices) and the
    buddha model (20k vertices).
    models (left : AQ metric; right: IQ metric). The anisotropic
    behavior of the AQ metric is clearly visible in elongated
    Fig. 13. Closeup view of the David model remeshed to 500k vertices
    (Isotropic metric) Valette, et al. [TVCG’08]
    • To implement realistic shading.
    
    
    • The color* of an exiting ray depends
    on the colors* of all incident rays.
    
    
    • color* should technically be radiance; not
    important for our discussion here.
    
    
    • also depends on the surface material (diffuse vs.
    specular vs. …); not important for our discussion here.
    
    
    • How do we know the color of an
    incident ray? Cast more rays!
    Secondary Ray
    Secondary Ray
    Secondary Ray
    

    View Slide

37. "TJEF3FOEFSJOH&RVBUJPO
    16
    https://en.wikipedia.org/wiki/Rendering_equation
    Lo
    (x, ωo
    ) =
    ∫
    Ω
    fr
    (x, ωo
    , ωi
    ) Li
    (x, ωi
    ) cos θ dωi
    “Color” of
    exiting ray wo
    “Color” of
    incident ray wi
    Integrate incident rays over the hemisphere
    “Transfer
    function”
    

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38. 4QFFEJOH6Q3BZ5SJBOHMF*OUFSTFDUJPO5FTU
    17
    • Prune the search space.
    • Only search part of the scene that does intersect the ray.
    intersect(space, ray) {
    
    
    if ray doesn’t intersect space boundary:
    
    
    return
    
    
    else:
    
    
    foreach subspace in space
    
    
    if (subspace != empty)
    
    
    intersect(subspace, ray)
    
    
    }
    

    View Slide

39. 4QFFEJOH6Q3BZ5SJBOHMF*OUFSTFDUJPO5FTU
    17
    • Prune the search space.
    • Only search part of the scene that does intersect the ray.
    intersect(space, ray) {
    
    
    if ray doesn’t intersect space boundary:
    
    
    return
    
    
    else:
    
    
    foreach subspace in space
    
    
    if (subspace != empty)
    
    
    intersect(subspace, ray)
    
    
    }
    

    View Slide

40. 4QFFEJOH6Q3BZ5SJBOHMF*OUFSTFDUJPO5FTU
    17
    • Prune the search space.
    • Only search part of the scene that does intersect the ray.
    intersect(space, ray) {
    
    
    if ray doesn’t intersect space boundary:
    
    
    return
    
    
    else:
    
    
    foreach subspace in space
    
    
    if (subspace != empty)
    
    
    intersect(subspace, ray)
    
    
    }
    

    View Slide

41. 4QFFEJOH6Q3BZ5SJBOHMF*OUFSTFDUJPO5FTU
    17
    • Prune the search space.
    • Only search part of the scene that does intersect the ray.
    • Key: how to partition the space?
    intersect(space, ray) {
    
    
    if ray doesn’t intersect space boundary:
    
    
    return
    
    
    else:
    
    
    foreach subspace in space
    
    
    if (subspace != empty)
    
    
    intersect(subspace, ray)
    
    
    }
    

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42. 4QBDF1BSUJUJPOWT0CKFDU1BSUJUJPO
    18
    Space partition: one object could
    be in different partitions
    Object partition: different
    partitions could overlap in space
    

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43. 4QBDF1BSUJUJPOJOH%BUB4USVDUVSFT
    19
    Uniform Grid Quadtree (or Octree in 3D)
    

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44. 4QBDF1BSUJUJPOJOH%BUB4USVDUVSFT
    20
    K-d Tree Binary Space Partitioning Tree
    

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45. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
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46. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
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47. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
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48. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
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    C
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    3
    C
    1
    

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49. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
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    1
    4
    C
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    3
    C
    1
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    2 3
    

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50. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
    2
    1
    4
    B
    C
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    3
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    1
    D
    2 3
    

    View Slide

51. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
    2
    1
    4
    B
    C
    D
    3
    B
    C
    1
    D
    2 3
    

    View Slide

52. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
    2
    1
    4
    B
    C
    D E
    3
    B
    C
    1
    D
    2 3
    

    View Slide

53. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
    2
    1
    4
    B
    C
    D E
    3
    B
    C
    1
    D
    2 3
    E
    4
    

    View Slide

54. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
    2
    1
    4
    A
    B
    C
    D E
    3
    B
    C
    1
    D
    2 3
    E
    4
    

    View Slide

55. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
    2
    1
    4
    A
    B
    C
    D E
    3
    A
    B
    C
    1
    D
    2 3
    E
    4
    

    View Slide

56. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    Scene
    BVH Tree
    21
    2
    1
    4
    A
    B
    C
    D E
    3
    A
    B
    C
    1
    D
    2 3
    E
    4
    Interior
    node
    Leaf
    node
    Root
    Primitive
    

    View Slide

57. #PVOEJOH7PMVNF)JFSBSDIZ 0CKFDU1BSUJUJPO
    
    2
    1
    4
    22
    A
    B
    C
    D E
    3
    • A, B, C, D, E are the bounding volumes, which are Axis-Aligned Bounding
    Boxes (AABBs) here. Other (irregular) bounding volumes are possible.
    A
    B
    C
    1
    D
    2 3
    E
    4
    Interior
    node
    Leaf
    node
    Root
    Primitive
    

    View Slide

58. *OUFSTFDUJPO5FTU6TJOH#7)
    23
    2
    1
    4
    A
    B
    C
    D E
    A
    B E
    C D
    2 3
    4
    3
    1
    Current
    Stack
    A
    Ray
    Ray-AABB Intersection Test
    ClosestHit = NA
    

    View Slide

59. *OUFSTFDUJPO5FTU6TJOH#7)
    24
    2
    1
    4
    A
    B
    C
    D E
    A
    B E
    C D
    2 3
    4
    3
    1
    Current
    Stack
    B
    E
    Ray-AABB Intersection Test
    Ray
    ClosestHit = NA
    

    View Slide

60. *OUFSTFDUJPO5FTU6TJOH#7)
    25
    2
    1
    4
    A
    B
    C
    D E
    A
    B E
    C D
    2 3
    4
    3
    1
    Current
    Stack
    C
    E D
    Ray-AABB Intersection Test
    Ray
    ClosestHit = NA
    

    View Slide

61. *OUFSTFDUJPO5FTU6TJOH#7)
    26
    2
    1
    4
    A
    B
    C
    D E
    A
    B E
    C D
    2 3
    4
    3
    1
    Current
    Stack
    D
    E
    Ray-AABB Intersection Test
    Ray
    ClosestHit = NA
    

    View Slide

62. *OUFSTFDUJPO5FTU6TJOH#7)
    27
    2
    1
    4
    A
    B
    C
    D E
    A
    B E
    C D
    2 3
    4
    3
    1
    Current
    Stack E
    2
    Ray-Triangle Intersection Test
    Ray
    3
    ClosestHit = NA
    

    View Slide

63. *OUFSTFDUJPO5FTU6TJOH#7)
    28
    2
    1
    4
    A
    B
    C
    D E
    A
    B E
    C D
    2 3
    4
    3
    1
    Current
    Stack
    Ray
    Ray-AABB Intersection Test
    E
    ClosestHit = 2
    

    View Slide

64. *OUFSTFDUJPO5FTU6TJOH#7)
    28
    2
    1
    4
    A
    B
    C
    D E
    A
    B E
    C D
    2 3
    4
    3
    1
    Current
    Stack
    Ray
    Ray-AABB Intersection Test
    E
    ClosestHit = 2
    Distance to E > Distance to 2; Stop!
    

    View Slide

65. 3BZ""##*OUFSTFDUJPO
    29
    Ray: O + tD, tmin
    <= t <= tmax
    O
    D
    thit
    tmin
    tmax
    

    View Slide

66. "4VCUMFCVU$SJUJDBM$BTF
    30
    Ray: O + tD, tmin
    <= t <= tmax
    O
    D
    thit
    tmin
    tmax
    

    View Slide

67. "4VCUMFCVU$SJUJDBM$BTF
    30
    Ray: O + tD, tmin
    <= t <= tmax
    O
    D
    thit
    tmin
    tmax
    Should this be counted as a hit?
    tmin
    tmax
    

    View Slide

68. "4VCUMFCVU$SJUJDBM$BTF
    30
    Ray: O + tD, tmin
    <= t <= tmax
    O
    D
    thit
    tmin
    tmax
    Should this be counted as a hit?
    tmin
    tmax
    

    View Slide

69. "4VCUMFCVU$SJUJDBM$BTF
    30
    Ray: O + tD, tmin
    <= t <= tmax
    O
    D
    thit
    Yes; any ray segment that’s completely inside
    an AABB must be treated as intersecting.
    tmin
    tmax
    Should this be counted as a hit?
    tmin
    tmax
    

    View Slide

70. "TJEF5XP5FSNJOPMPHZ$POGVTJPOT
    31
    • Ray casting vs. ray tracing
    
    
    • Technically, finding the intersection of one ray and the scene is called ray casting.
    
    
    • Ray tracing referes to recursive ray casting.
    
    
    • Acceleration structures
    
    
    • Data structures that help speed up ray tracing is called “acceleration structures” (e.g., BVH),
    not to be confused with hardware accelerators.
    

    View Slide

71. 32
    (BNF1MBO
    "DDFMFSBUJOH
    /FJHICPS4FBSDI
    6TJOH)BSEXBSF
    3BZ5SBDJOH
    • What is ray tracing?
    
    
    • How does hardware
    support ray tracing?
    

    View Slide

72. 3BZ5SBDJOHPO(16T6TJOH#7)
    33
    2
    1
    4
    A
    B
    C
    D E
    3
    Ray
    Ray
    Ray
    

    View Slide

73. 3BZ5SBDJOHPO(16T6TJOH#7)
    33
    2
    1
    4
    A
    B
    C
    D E
    3
    Ray
    Ray
    Ray
    • Build the BVH.
    

    View Slide

74. 3BZ5SBDJOHPO(16T6TJOH#7)
    33
    2
    1
    4
    A
    B
    C
    D E
    3
    Ray
    Ray
    Ray
    • Build the BVH.
    • For each ray (thread):
    
    
    • Traverse the BVH (manage local stack)
    
    
    • Ray-AABB intersection test
    
    
    • Ray-primitive intersection test
    
    
    • Executes a shading algorithm
    

    View Slide

75. 3BZ5SBDJOHPO(16T6TJOH#7)
    33
    2
    1
    4
    A
    B
    C
    D E
    3
    Ray
    Ray
    Ray
    • Build the BVH.
    • For each ray (thread):
    
    
    • Traverse the BVH (manage local stack)
    
    
    • Ray-AABB intersection test
    
    
    • Ray-primitive intersection test
    
    
    • Executes a shading algorithm
    • Prior to OptiX (2010)
    
    
    • Manually implement in CUDA.
    

    View Slide

76. 3BZ5SBDJOHPO(16T6TJOH#7)
    33
    2
    1
    4
    A
    B
    C
    D E
    3
    Ray
    Ray
    Ray
    • Build the BVH.
    • For each ray (thread):
    
    
    • Traverse the BVH (manage local stack)
    
    
    • Ray-AABB intersection test
    
    
    • Ray-primitive intersection test
    
    
    • Executes a shading algorithm
    • Prior to OptiX (2010)
    
    
    • Manually implement in CUDA.
    Fixed-function
    ~Fixed-function
    

    View Slide

77. 3BZ5SBDJOHJO0QUJ9BOE5VSJOH(16
    34
    • OptiX (2010): a ray tracing-specific
    programming model.
    
    
    • Provides a generic ray tracing pipeline.
    
    
    • Some pipeline stages are programmable; others
    are fixed functions.
    ACM Reference Format
    Parker, S., Bigler, J., Dietrich, A., Friedrich, H., Hoberock, J., Luebke, D., McAllister, D., McGuire, M., Morley,
    K., Robison, A., Stich, M. 2010. OptiX™: A General Purpose Ray Tracing Engine.
    ACM Trans. Graph. 29, 4, Article 66 (July 2010), 13 pages. DOI = 10.1145/1778765.1778803
    http://doi.acm.org/10.1145/1778765.1778803.
    Copyright Notice
    Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted
    without fee provided that copies are not made or distributed for profi t or direct commercial advantage
    and that copies show this notice on the fi rst page or initial screen of a display along with the full citation.
    Copyrights for components of this work owned by others than ACM must be honored. Abstracting with
    credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any
    component of this work in other works requires prior specifi c permission and/or a fee. Permissions may be
    requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701, fax +1
    (212) 869-0481, or permissions@acm.org.
    © 2010 ACM 0730-0301/2010/07-ART66 $10.00 DOI 10.1145/1778765.1778803
    http://doi.acm.org/10.1145/1778765.1778803
    OptiX: A General Purpose Ray Tracing Engine
    Steven G. Parker1⇤ James Bigler1 Andreas Dietrich1 Heiko Friedrich1 Jared Hoberock1 David Luebke1
    David McAllister1 Morgan McGuire1,2 Keith Morley1 Austin Robison1 Martin Stich1
    NVIDIA1 Williams College2
    Figure 1: Images from various applications built with OptiX. Top: Physically based light transport through path tracing. Bottom: Ray tracing
    of a procedural Julia set, photon mapping, large-scale line of sight and collision detection, Whitted-style ray tracing of dynamic geometry,
    and ray traced ambient occlusion. All applications are interactive.
    Abstract
    The NVIDIA® OptiX™ ray tracing engine is a programmable sys-
    tem designed for NVIDIA GPUs and other highly parallel archi-
    tectures. The OptiX engine builds on the key observation that
    most ray tracing algorithms can be implemented using a small set
    of programmable operations. Consequently, the core of OptiX
    is a domain-specific just-in-time compiler that generates custom
    ray tracing kernels by combining user-supplied programs for ray
    generation, material shading, object intersection, and scene traver-
    sal. This enables the implementation of a highly diverse set of
    ray tracing-based algorithms and applications, including interactive
    rendering, offline rendering, collision detection systems, artificial
    intelligence queries, and scientific simulations such as sound prop-
    agation. OptiX achieves high performance through a compact ob-
    ject model and application of several ray tracing-specific compiler
    optimizations. For ease of use it exposes a single-ray programming
    model with full support for recursion and a dynamic dispatch mech-
    anism similar to virtual function calls.
    CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional
    Graphics and Realism; D.2.11 [Software Architectures]: Domain-
    specific architectures; I.3.1 [Computer Graphics]: Hardware
    Architectures—;
    Keywords: ray tracing, graphics systems, graphics hardware
    ⇤e-mail: sparker@nvidia.com
    1 Introduction
    To address the problem of creating an accessible, flexible, and effi-
    cient ray tracing system for many-core architectures, we introduce
    OptiX, a general purpose ray tracing engine. This engine combines
    a programmable ray tracing pipeline with a lightweight scene rep-
    resentation. A general programming interface enables the imple-
    mentation of a variety of ray tracing-based algorithms in graphics
    and non-graphics domains, such as rendering, sound propagation,
    collision detection and artificial intelligence.
    In this paper, we discuss the design goals of the OptiX engine as
    well as an implementation for NVIDIA Quadro®, GeForce®, and
    Tesla® GPUs. In our implementation, we compose domain-specific
    compilation with a flexible set of controls over scene hierarchy, ac-
    celeration structure creation and traversal, on-the-fly scene update,
    and a dynamically load-balanced GPU execution model. Although
    OptiX currently targets highly parallel architectures, it is applica-
    ble to a wide range of special- and general-purpose hardware and
    multiple execution models.
    To create a system for a broad range of ray tracing tasks, several
    ACM Transactions on Graphics, Vol. 29, No. 4, Article 66, Publication date: July 2010.
    

    View Slide

78. 3BZ5SBDJOHJO0QUJ9BOE5VSJOH(16
    34
    • OptiX (2010): a ray tracing-specific
    programming model.
    
    
    • Provides a generic ray tracing pipeline.
    
    
    • Some pipeline stages are programmable; others
    are fixed functions.
    • Prior to Turing architecture (2018):
    
    
    • Everything runs on CUDA cores.
    ACM Reference Format
    Parker, S., Bigler, J., Dietrich, A., Friedrich, H., Hoberock, J., Luebke, D., McAllister, D., McGuire, M., Morley,
    K., Robison, A., Stich, M. 2010. OptiX™: A General Purpose Ray Tracing Engine.
    ACM Trans. Graph. 29, 4, Article 66 (July 2010), 13 pages. DOI = 10.1145/1778765.1778803
    http://doi.acm.org/10.1145/1778765.1778803.
    Copyright Notice
    Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted
    without fee provided that copies are not made or distributed for profi t or direct commercial advantage
    and that copies show this notice on the fi rst page or initial screen of a display along with the full citation.
    Copyrights for components of this work owned by others than ACM must be honored. Abstracting with
    credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any
    component of this work in other works requires prior specifi c permission and/or a fee. Permissions may be
    requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701, fax +1
    (212) 869-0481, or permissions@acm.org.
    © 2010 ACM 0730-0301/2010/07-ART66 $10.00 DOI 10.1145/1778765.1778803
    http://doi.acm.org/10.1145/1778765.1778803
    OptiX: A General Purpose Ray Tracing Engine
    Steven G. Parker1⇤ James Bigler1 Andreas Dietrich1 Heiko Friedrich1 Jared Hoberock1 David Luebke1
    David McAllister1 Morgan McGuire1,2 Keith Morley1 Austin Robison1 Martin Stich1
    NVIDIA1 Williams College2
    Figure 1: Images from various applications built with OptiX. Top: Physically based light transport through path tracing. Bottom: Ray tracing
    of a procedural Julia set, photon mapping, large-scale line of sight and collision detection, Whitted-style ray tracing of dynamic geometry,
    and ray traced ambient occlusion. All applications are interactive.
    Abstract
    The NVIDIA® OptiX™ ray tracing engine is a programmable sys-
    tem designed for NVIDIA GPUs and other highly parallel archi-
    tectures. The OptiX engine builds on the key observation that
    most ray tracing algorithms can be implemented using a small set
    of programmable operations. Consequently, the core of OptiX
    is a domain-specific just-in-time compiler that generates custom
    ray tracing kernels by combining user-supplied programs for ray
    generation, material shading, object intersection, and scene traver-
    sal. This enables the implementation of a highly diverse set of
    ray tracing-based algorithms and applications, including interactive
    rendering, offline rendering, collision detection systems, artificial
    intelligence queries, and scientific simulations such as sound prop-
    agation. OptiX achieves high performance through a compact ob-
    ject model and application of several ray tracing-specific compiler
    optimizations. For ease of use it exposes a single-ray programming
    model with full support for recursion and a dynamic dispatch mech-
    anism similar to virtual function calls.
    CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional
    Graphics and Realism; D.2.11 [Software Architectures]: Domain-
    specific architectures; I.3.1 [Computer Graphics]: Hardware
    Architectures—;
    Keywords: ray tracing, graphics systems, graphics hardware
    ⇤e-mail: sparker@nvidia.com
    1 Introduction
    To address the problem of creating an accessible, flexible, and effi-
    cient ray tracing system for many-core architectures, we introduce
    OptiX, a general purpose ray tracing engine. This engine combines
    a programmable ray tracing pipeline with a lightweight scene rep-
    resentation. A general programming interface enables the imple-
    mentation of a variety of ray tracing-based algorithms in graphics
    and non-graphics domains, such as rendering, sound propagation,
    collision detection and artificial intelligence.
    In this paper, we discuss the design goals of the OptiX engine as
    well as an implementation for NVIDIA Quadro®, GeForce®, and
    Tesla® GPUs. In our implementation, we compose domain-specific
    compilation with a flexible set of controls over scene hierarchy, ac-
    celeration structure creation and traversal, on-the-fly scene update,
    and a dynamically load-balanced GPU execution model. Although
    OptiX currently targets highly parallel architectures, it is applica-
    ble to a wide range of special- and general-purpose hardware and
    multiple execution models.
    To create a system for a broad range of ray tracing tasks, several
    ACM Transactions on Graphics, Vol. 29, No. 4, Article 66, Publication date: July 2010.
    

    View Slide

79. 3BZ5SBDJOHJO0QUJ9BOE5VSJOH(16
    34
    • OptiX (2010): a ray tracing-specific
    programming model.
    
    
    • Provides a generic ray tracing pipeline.
    
    
    • Some pipeline stages are programmable; others
    are fixed functions.
    • Prior to Turing architecture (2018):
    
    
    • Everything runs on CUDA cores.
    • Turing architecture:
    
    
    • RT Cores accelerate fixed-function stages.
    
    
    • Programmable stages on the CUDA cores.
    ACM Reference Format
    Parker, S., Bigler, J., Dietrich, A., Friedrich, H., Hoberock, J., Luebke, D., McAllister, D., McGuire, M., Morley,
    K., Robison, A., Stich, M. 2010. OptiX™: A General Purpose Ray Tracing Engine.
    ACM Trans. Graph. 29, 4, Article 66 (July 2010), 13 pages. DOI = 10.1145/1778765.1778803
    http://doi.acm.org/10.1145/1778765.1778803.
    Copyright Notice
    Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted
    without fee provided that copies are not made or distributed for profi t or direct commercial advantage
    and that copies show this notice on the fi rst page or initial screen of a display along with the full citation.
    Copyrights for components of this work owned by others than ACM must be honored. Abstracting with
    credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any
    component of this work in other works requires prior specifi c permission and/or a fee. Permissions may be
    requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701, fax +1
    (212) 869-0481, or permissions@acm.org.
    © 2010 ACM 0730-0301/2010/07-ART66 $10.00 DOI 10.1145/1778765.1778803
    http://doi.acm.org/10.1145/1778765.1778803
    OptiX: A General Purpose Ray Tracing Engine
    Steven G. Parker1⇤ James Bigler1 Andreas Dietrich1 Heiko Friedrich1 Jared Hoberock1 David Luebke1
    David McAllister1 Morgan McGuire1,2 Keith Morley1 Austin Robison1 Martin Stich1
    NVIDIA1 Williams College2
    Figure 1: Images from various applications built with OptiX. Top: Physically based light transport through path tracing. Bottom: Ray tracing
    of a procedural Julia set, photon mapping, large-scale line of sight and collision detection, Whitted-style ray tracing of dynamic geometry,
    and ray traced ambient occlusion. All applications are interactive.
    Abstract
    The NVIDIA® OptiX™ ray tracing engine is a programmable sys-
    tem designed for NVIDIA GPUs and other highly parallel archi-
    tectures. The OptiX engine builds on the key observation that
    most ray tracing algorithms can be implemented using a small set
    of programmable operations. Consequently, the core of OptiX
    is a domain-specific just-in-time compiler that generates custom
    ray tracing kernels by combining user-supplied programs for ray
    generation, material shading, object intersection, and scene traver-
    sal. This enables the implementation of a highly diverse set of
    ray tracing-based algorithms and applications, including interactive
    rendering, offline rendering, collision detection systems, artificial
    intelligence queries, and scientific simulations such as sound prop-
    agation. OptiX achieves high performance through a compact ob-
    ject model and application of several ray tracing-specific compiler
    optimizations. For ease of use it exposes a single-ray programming
    model with full support for recursion and a dynamic dispatch mech-
    anism similar to virtual function calls.
    CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional
    Graphics and Realism; D.2.11 [Software Architectures]: Domain-
    specific architectures; I.3.1 [Computer Graphics]: Hardware
    Architectures—;
    Keywords: ray tracing, graphics systems, graphics hardware
    ⇤e-mail: sparker@nvidia.com
    1 Introduction
    To address the problem of creating an accessible, flexible, and effi-
    cient ray tracing system for many-core architectures, we introduce
    OptiX, a general purpose ray tracing engine. This engine combines
    a programmable ray tracing pipeline with a lightweight scene rep-
    resentation. A general programming interface enables the imple-
    mentation of a variety of ray tracing-based algorithms in graphics
    and non-graphics domains, such as rendering, sound propagation,
    collision detection and artificial intelligence.
    In this paper, we discuss the design goals of the OptiX engine as
    well as an implementation for NVIDIA Quadro®, GeForce®, and
    Tesla® GPUs. In our implementation, we compose domain-specific
    compilation with a flexible set of controls over scene hierarchy, ac-
    celeration structure creation and traversal, on-the-fly scene update,
    and a dynamically load-balanced GPU execution model. Although
    OptiX currently targets highly parallel architectures, it is applica-
    ble to a wide range of special- and general-purpose hardware and
    multiple execution models.
    To create a system for a broad range of ray tracing tasks, several
    ACM Transactions on Graphics, Vol. 29, No. 4, Article 66, Publication date: July 2010.
    

    View Slide

80. "O4.JO5VSJOH(16
    35
    https://wccftech.com/nvidia-turing-gpu-architecture-geforce-rtx-graphics-cards-detailed/
    

    View Slide

81. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    • “Shaders” are user-defined functions executing on CUDA cores.
    

    View Slide

82. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    • “Shaders” are user-defined functions executing on CUDA cores.
    

    View Slide

83. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    BVH Traversal +
    Ray-AABB Test
    (TL)
    • “Shaders” are user-defined functions executing on CUDA cores.
    

    View Slide

84. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    BVH Traversal +
    Ray-AABB Test
    (TL)
    • “Shaders” are user-defined functions executing on CUDA cores.
    A
    B E
    C D
    2 3
    4
    1
    

    View Slide

85. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    Intersection (IS)
    Shader
    Enter leaf node
    BVH Traversal +
    Ray-AABB Test
    (TL)
    • “Shaders” are user-defined functions executing on CUDA cores.
    A
    B E
    C D
    2 3
    4
    1
    

    View Slide

86. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    Intersection (IS)
    Shader
    Enter leaf node
    BVH Traversal +
    Ray-AABB Test
    (TL)
    • “Shaders” are user-defined functions executing on CUDA cores.
    • Allows custom primitives (not just triangles).
    A
    B E
    C D
    2 3
    4
    1
    

    View Slide

87. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    Intersection (IS)
    Shader
    Enter leaf node
    BVH Traversal +
    Ray-AABB Test
    (TL)
    No
    Any-Hit (AH)
    Shader
    Ray primitive
    intersect?
    Yes
    • “Shaders” are user-defined functions executing on CUDA cores.
    • Allows custom primitives (not just triangles).
    

    View Slide

88. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    Intersection (IS)
    Shader
    Enter leaf node
    BVH Traversal +
    Ray-AABB Test
    (TL)
    No
    Any-Hit (AH)
    Shader
    Ray primitive
    intersect?
    Yes
    Found
    a hit?
    Traversal
    completes
    • “Shaders” are user-defined functions executing on CUDA cores.
    • Allows custom primitives (not just triangles).
    

    View Slide

89. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    Intersection (IS)
    Shader
    Enter leaf node
    BVH Traversal +
    Ray-AABB Test
    (TL)
    No
    Any-Hit (AH)
    Shader
    Ray primitive
    intersect?
    Yes
    Closest-Hit
    (CH) Shader
    Miss Shader
    Found
    a hit?
    Traversal
    completes
    • “Shaders” are user-defined functions executing on CUDA cores.
    • Allows custom primitives (not just triangles).
    

    View Slide

90. 0QUJ91SPHSBNNJOH.PEFM
    36
    Construct
    BVH
    Ray Generation
    (RG) Shader
    Intersection (IS)
    Shader
    Enter leaf node
    BVH Traversal +
    Ray-AABB Test
    (TL)
    No
    Any-Hit (AH)
    Shader
    Ray primitive
    intersect?
    Yes
    Closest-Hit
    (CH) Shader
    Miss Shader
    Found
    a hit?
    Traversal
    completes
    • “Shaders” are user-defined functions executing on CUDA cores.
    • Allows custom primitives (not just triangles).
    Fixed functions executed
    on the RT cores.
    

    View Slide

91. 0QUJ91SPHSBNNJOH.PEFM
    37
    Ray Generation
    (RG) Shader
    Construct
    BVH
    … …
    … …
    … …
    BVH Traversal +
    Ray-AABB Test
    (TL)
    Found
    a hit?
    Closest-Hit
    (CH) Shader
    Miss Shader
    Any-Hit (AH)
    Shader
    Intersection (IS)
    Shader
    Ray primitive
    intersect?
    Enter leaf node
    Yes
    No
    Traversal
    completes
    One Single CUDA Kernel
    CUDA Threads
    OptiX Rays
    

    View Slide

92. -JGFPGBO0QUJ93BZ
    38
    2
    1
    4
    A
    B
    C
    D E
    3
    CUDA
    Cores
    RT Cores
    RG
    TL (A, B, D)
    IS (2, 3)
    TL (C, E)
    CH
    Think of RT cores as special function units for BVH traversal.
    

    View Slide

93. "TJEF0UIFS/PUBCMF3BZ5SBDJOH&OHJOFT
    39
    • Intel OSPRay
    
    
    • Won 2020 Oscar for Scientific and Technical
    Achievement.
    
    
    • Built on Intel Embree, a collection of ray
    tracing kernels, which uses Intel Implicit
    SPMD Program Compiler (ISPC) for explicit
    vectorization.
    
    
    • PBRT
    
    
    • Pedagogical engine.
    
    
    • The book won 2014 Oscar for Scientific and
    Technical Achievement.
    

    View Slide

94. (BNF1MBO
    40
    "DDFMFSBUJOH
    /FJHICPS4FBSDI
    6TJOH)BSEXBSF
    3BZ5SBDJOH
    • What is ray tracing?
    
    
    • How does hardware
    support ray tracing?
    
    
    • What is neighbor search
    
    
    • How does it relate to ray tracing?
    

    View Slide

95. /FJHICPS4FBSDI
    41
    r
    Range Search
    query
    search points
    

    View Slide

96. /FJHICPS4FBSDI
    42
    Range Search
    usually also limits the total # of neighbors:
    
    
    • practical memory constraint,
    
    
    • downstream algorithms expect a fixed # of neighbors.
    

    View Slide

97. /FJHICPS4FBSDI
    42
    Range Search
    usually also limits the total # of neighbors:
    
    
    • practical memory constraint,
    
    
    • downstream algorithms expect a fixed # of neighbors.
    rangeSearch(query, points, range, K)
    Return any K points that are
    within range of query
    

    View Slide

98. /FJHICPS4FBSDI
    43
    Range Search KNN Search
    2 nearest neighbors
    usually also limits the total # of neighbors:
    
    
    • practical memory constraint,
    
    
    • downstream algorithms expect a fixed # of neighbors.
    rangeSearch(query, points, range, K)
    Return any K points that are
    within range of query
    

    View Slide

99. /FJHICPS4FBSDI
    44
    Range Search KNN Search
    usually also limits the total # of neighbors:
    
    
    • practical memory constraint,
    
    
    • downstream algorithms expect a fixed # of neighbors.
    usually also limits ranges of neighbors:
    
    
    • neighbors too far away are of no significance
    (e.g., force from a remote particle).
    rangeSearch(query, points, range, K)
    Return any K points that are
    within range of query
    

    View Slide

100. /FJHICPS4FBSDI
     44
     Range Search KNN Search
     usually also limits the total # of neighbors:
     
     
     • practical memory constraint,
     
     
     • downstream algorithms expect a fixed # of neighbors.
     usually also limits ranges of neighbors:
     
     
     • neighbors too far away are of no significance
     (e.g., force from a remote particle).
     rangeSearch(query, points, range, K)
     Return any K points that are
     within range of query
     KNN(query, points, range, K)
     Return K nearest points that
     are within range of query
     

     View Slide

101. 0VS'PDVT-PX%JNFOTJPOBM4FBSDI
     45
     • Low dimension: <= 3D.
     
     
     • Prevalent in science and engineering fields (e.g., computational
     fluid dynamics, graphics, vision).
     
     
     • They deal with physical data (e.g., particles, surface samples) that are inherent 2D/3D.
     
     
     • High-dimensional search is a completely different game.
     
     
     • “Curse of dimensionality” means we need different algorithms and distance metric.
     

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102. 5VSOUIF1SPCMFN"SPVOE
     46
     r
     Q
     Find all points within r from Q
     

     View Slide

103. 5VSOUIF1SPCMFN"SPVOE
     47
     Find all points within r from Q
     Find whether Q is within r from other points
     Q
     r
     

     View Slide

104. 1PJOUJO4QIFSF5FTU
     48
     Q
     

     View Slide

105. 1PJOUJO4QIFSF5FTU
     48
     Q
     Is Q in the AABB?
     
     
     (Prunes remote points)
     

     View Slide

106. 1PJOUJO4QIFSF5FTU
     48
     Q
     Is Q in the AABB?
     
     
     (Prunes remote points)
     

     View Slide

107. 1PJOUJO4QIFSF5FTU
     48
     Q
     Is Q in the AABB?
     
     
     (Prunes remote points)
     If so, is Q in the sphere?
     

     View Slide

108. • Recall: any ray that’s within an
     AABB must be treated as
     intersecting.
     1PJOUJO""##5FTU
     49
     Q
     2r
     

     View Slide

109. • Recall: any ray that’s within an
     AABB must be treated as
     intersecting.
     • Idea: generate a short ray from
     Q and (ask the RT cores to)
     perform the ray-AABB test.
     1PJOUJO""##5FTU
     49
     Q
     2r
     

     View Slide

110. • Recall: any ray that’s within an
     AABB must be treated as
     intersecting.
     • Idea: generate a short ray from
     Q and (ask the RT cores to)
     perform the ray-AABB test.
     • The ray has an arbitrary direction and a
     very small length.
     1PJOUJO""##5FTU
     49
     Q
     2r
     

     View Slide

111. • Recall: any ray that’s within an
     AABB must be treated as
     intersecting.
     • Idea: generate a short ray from
     Q and (ask the RT cores to)
     perform the ray-AABB test.
     • The ray has an arbitrary direction and a
     very small length.
     • Why a very small ray length?
     1PJOUJO""##5FTU
     49
     Q
     2r
     

     View Slide

112. • Recall: any ray that’s within an
     AABB must be treated as
     intersecting.
     • Idea: generate a short ray from
     Q and (ask the RT cores to)
     perform the ray-AABB test.
     • The ray has an arbitrary direction and a
     very small length.
     • Why a very small ray length?
     1PJOUJO""##5FTU
     49
     Q
     2r
     Q’
     

     View Slide

113. 50
     • What is ray tracing?
     
     
     • How does hardware
     support ray tracing?
     
     
     • What is neighbor search?
     
     
     • How to use hardware ray
     tracing to accelerate
     neighbor search?
     (BNF1MBO
     "DDFMFSBUJOH
     /FJHICPS4FBSDI
     6TJOH)BSEXBSF
     3BZ5SBDJOH
     

     View Slide

114. 0WFSBMM*EFB
     51
     rangeSearch(query, points, r, K)
     

     View Slide

115. 0WFSBMM*EFB
     52
     Create an AABB of width 2r for every point
     rangeSearch(query, points, r, K)
     https://forums.developer.nvidia.com/t/bvh-building-algorithm-and-primitive-order/182231/8
     

     View Slide

116. 0WFSBMM*EFB
     52
     Create an AABB of width 2r for every point
     rangeSearch(query, points, r, K)
     https://forums.developer.nvidia.com/t/bvh-building-algorithm-and-primitive-order/182231/8
     Construct a BVH from the AABBs
     
     
     (No control; hidden behind the OptiX APIs and most
     likely done in hardware)
     

     View Slide

117. 0WFSBMM*EFB
     52
     Create an AABB of width 2r for every point
     rangeSearch(query, points, r, K)
     https://forums.developer.nvidia.com/t/bvh-building-algorithm-and-primitive-order/182231/8
     Construct a BVH from the AABBs
     
     
     (No control; hidden behind the OptiX APIs and most
     likely done in hardware)
     

     View Slide

118. 0WFSBMM*EFB
     52
     Create an AABB of width 2r for every point
     rangeSearch(query, points, r, K)
     https://forums.developer.nvidia.com/t/bvh-building-algorithm-and-primitive-order/182231/8
     Construct a BVH from the AABBs
     
     
     (No control; hidden behind the OptiX APIs and most
     likely done in hardware)
     Use spheres as primitives,
     not triangles.
     

     View Slide

119. 0WFSBMM*EFB
     52
     Create an AABB of width 2r for every point
     rangeSearch(query, points, r, K)
     https://forums.developer.nvidia.com/t/bvh-building-algorithm-and-primitive-order/182231/8
     Generate a ray for each query
     
     
     (RG Shader)
     Construct a BVH from the AABBs
     
     
     (No control; hidden behind the OptiX APIs and most
     likely done in hardware)
     

     View Slide

120. 0WFSBMM*EFB
     52
     Create an AABB of width 2r for every point
     rangeSearch(query, points, r, K)
     https://forums.developer.nvidia.com/t/bvh-building-algorithm-and-primitive-order/182231/8
     Generate a ray for each query
     
     
     (RG Shader)
     Construct a BVH from the AABBs
     
     
     (No control; hidden behind the OptiX APIs and most
     likely done in hardware)
     Traverse BVH; skip non-circumscribing AABBs
     
     
     (No control; done in hardware)
     

     View Slide

121. 0WFSBMM*EFB
     52
     Create an AABB of width 2r for every point
     rangeSearch(query, points, r, K)
     https://forums.developer.nvidia.com/t/bvh-building-algorithm-and-primitive-order/182231/8
     Generate a ray for each query
     
     
     (RG Shader)
     Construct a BVH from the AABBs
     
     
     (No control; hidden behind the OptiX APIs and most
     likely done in hardware)
     Traverse BVH; skip non-circumscribing AABBs
     
     
     (No control; done in hardware)
     At leaf nodes: calc dist, collect neighbors
     
     
     (IS Shader)
     

     View Slide

122. 0WFSBMM*EFB
     52
     Create an AABB of width 2r for every point
     rangeSearch(query, points, r, K)
     https://forums.developer.nvidia.com/t/bvh-building-algorithm-and-primitive-order/182231/8
     Generate a ray for each query
     
     
     (RG Shader)
     Construct a BVH from the AABBs
     
     
     (No control; hidden behind the OptiX APIs and most
     likely done in hardware)
     Traverse BVH; skip non-circumscribing AABBs
     
     
     (No control; done in hardware)
     At leaf nodes: calc dist, collect neighbors
     
     
     (IS Shader)
     

     View Slide

123. "OPUIFS1FSTQFDUJWF1PJOUJO4QIFSF5FTU
     53
     Ray Generation
     (RG) Shader
     Construct
     BVH
     BVH Traversal +
     Ray-AABB Test
     (TL)
     Found
     a hit?
     Closest-Hit
     (CH) Shader
     Miss Shader
     Any-Hit (AH)
     Shader
     Intersection (IS)
     Shader
     Ray primitive
     intersect?
     Enter leaf node
     Yes
     No
     Traversal
     completes
     Is Q in the AABB?
     
     
     (Prunes remote points)
     If so, is Q in the sphere?
     

     View Slide

124. 1SPCMFN$POUSPM'MPX%JWFSHFODF
     54
     X
     OptiX groups every 32 adjacent rays into a warp.
     

     View Slide

125. 1SPCMFN$POUSPM'MPX%JWFSHFODF
     54
     X
     OptiX groups every 32 adjacent rays into a warp.
     

     View Slide

126. 1SPCMFN$POUSPM'MPX%JWFSHFODF
     55
     Y
     OptiX groups every 32 adjacent rays into a warp.
     

     View Slide

127. 1SPCMFN$POUSPM'MPX%JWFSHFODF
     55
     Y
     OptiX groups every 32 adjacent rays into a warp.
     

     View Slide

128. *EFB0SEFS2VFSJFT4QBUJBMMZ
     56
     • Intuition: group spatially close
     queries together so that their rays
     follow similar traversal paths.
     

     View Slide

129. *EFB0SEFS2VFSJFT4QBUJBMMZ
     56
     • Intuition: group spatially close
     queries together so that their rays
     follow similar traversal paths.
     • Improving ray coherence in graphics parlance.
     

     View Slide

130. *EFB0SEFS2VFSJFT4QBUJBMMZ
     56
     • Intuition: group spatially close
     queries together so that their rays
     follow similar traversal paths.
     • Improving ray coherence in graphics parlance.
     • How? A simple heuristic: queries
     enclosed by the same AABB are
     spatially close.
     

     View Slide

131. *EFB0SEFS2VFSJFT4QBUJBMMZ
     57
     1
     2
     3
     4
     7
     6
     5
     8
     

     View Slide

132. *EFB0SEFS2VFSJFT4QBUJBMMZ
     57
     • A query might be enclosed by many
     AABBs, but any AABB will do.
     1
     2
     3
     4
     7
     6
     5
     8
     

     View Slide

133. *EFB0SEFS2VFSJFT4QBUJBMMZ
     57
     • A query might be enclosed by many
     AABBs, but any AABB will do.
     • How to find one? Cast a ray and
     immediately terminate the ray once
     the first IS shader is called.
     1
     2
     3
     4
     7
     6
     5
     8
     

     View Slide

134. *EFB0SEFS2VFSJFT4QBUJBMMZ
     57
     • A query might be enclosed by many
     AABBs, but any AABB will do.
     • How to find one? Cast a ray and
     immediately terminate the ray once
     the first IS shader is called.
     • optixTerminateRay()
     1
     2
     3
     4
     7
     6
     5
     8
     

     View Slide

135. *EFB0SEFS2VFSJFT4QBUJBMMZ
     57
     • A query might be enclosed by many
     AABBs, but any AABB will do.
     • How to find one? Cast a ray and
     immediately terminate the ray once
     the first IS shader is called.
     • optixTerminateRay()
     • Effectively returning ID (key) of the
     first enclosing leaf AABB.
     1
     2
     3
     4
     7
     6
     5
     8
     

     View Slide

136. *EFB0SEFS2VFSJFT4QBUJBMMZ
     57
     • A query might be enclosed by many
     AABBs, but any AABB will do.
     • How to find one? Cast a ray and
     immediately terminate the ray once
     the first IS shader is called.
     • optixTerminateRay()
     • Effectively returning ID (key) of the
     first enclosing leaf AABB.
     • Then sort by key.
     1
     2
     3
     4
     7
     6
     5
     8
     

     View Slide

137. 4FBSDI"MHPSJUIN 4P'BS
     
     58
     1
     2
     3
     4
     7
     6
     5
     8
     bvh ← buildBVH(points, r);
     
     
     firstHitAABBs ← traceRays(bvh, queries);
     
     
     reorderQueries(queries, firstHitAABBs);
     
     
     traceRays(bvh, queries);
     

     View Slide

138. 1SPCMFN-BSHF""##T
     59
     Q
     2r
     rangeSearch(query, points, r, K)
     • Strictly speaking, the AABB width
     must be 2r.
     
     
     • What if we can find K neighbors
     in a smaller range? We can use a
     smaller AABB.
     
     
     • What’s the benefit?
     

     View Slide

139. #FOF
     fi
     UTPG4NBMMFS""##T
     60
     35
     30
     25
     20
     15
     10
     5
     0
     Time (s)
     30
     25
     20
     15
     10
     5
     0
     AABB Width
     • Using smaller AABBs drastically
     reduces the search time.
     

     View Slide

140. #FOF
     fi
     UTPG4NBMMFS""##T
     60
     35
     30
     25
     20
     15
     10
     5
     0
     Time (s)
     30
     25
     20
     15
     10
     5
     0
     AABB Width
     • Using smaller AABBs drastically
     reduces the search time.
     • Smaller AABB means a query is
     enclosed by fewer AABBs.
     

     View Slide

141. #FOF
     fi
     UTPG4NBMMFS""##T
     60
     35
     30
     25
     20
     15
     10
     5
     0
     Time (s)
     30
     25
     20
     15
     10
     5
     0
     AABB Width
     • Using smaller AABBs drastically
     reduces the search time.
     • Smaller AABB means a query is
     enclosed by fewer AABBs.
     • …which leads to fewer
     traversals and IS shader calls.
     

     View Slide

142. #FOF
     fi
     UTPG4NBMMFS""##T
     60
     35
     30
     25
     20
     15
     10
     5
     0
     Time (s)
     30
     25
     20
     15
     10
     5
     0
     AABB Width
     • Using smaller AABBs drastically
     reduces the search time.
     • Smaller AABB means a query is
     enclosed by fewer AABBs.
     • …which leads to fewer
     traversals and IS shader calls.
     • Particularly important for KNN search,
     where the IS shader manipulates a priority
     queue.
     

     View Slide

143. *EFB2VFSZ1BSUJUJPOJOH
     61
     • For each query, find an AABB size
     that’s just large enough to ensure
     correctness.
     2r
     

     View Slide

144. *EFB2VFSZ1BSUJUJPOJOH
     61
     • For each query, find an AABB size
     that’s just large enough to ensure
     correctness.
     2r
     d
     

     View Slide

145. *EFB2VFSZ1BSUJUJPOJOH
     62
     • For each query, find an AABB size
     that’s just large enough to ensure
     correctness.
     • Group queries such that queries in
     each partition share the same AABB.
     q0
     q1
     q2
     q3
     Calc. Smallest AABB Size
     q1 .. .. .. BVH 0
     Partitions
     … ……
     Queries
     ……
     q0 .. BVH 1
     .. BVH n-1
     q2 BVH n
     q3 ..
     

     View Slide

146. *EFB2VFSZ1BSUJUJPOJOH
     62
     • For each query, find an AABB size
     that’s just large enough to ensure
     correctness.
     • Group queries such that queries in
     each partition share the same AABB.
     • Build a different BVH for each
     partition.
     q0
     q1
     q2
     q3
     Calc. Smallest AABB Size
     q1 .. .. .. BVH 0
     Partitions
     … ……
     Queries
     ……
     q0 .. BVH 1
     .. BVH n-1
     q2 BVH n
     q3 ..
     

     View Slide

147. *EFB2VFSZ1BSUJUJPOJOH
     62
     • For each query, find an AABB size
     that’s just large enough to ensure
     correctness.
     • Group queries such that queries in
     each partition share the same AABB.
     • Build a different BVH for each
     partition.
     • Essentially trades BVH construction
     overhead for faster search.
     q0
     q1
     q2
     q3
     Calc. Smallest AABB Size
     q1 .. .. .. BVH 0
     Partitions
     … ……
     Queries
     ……
     q0 .. BVH 1
     .. BVH n-1
     q2 BVH n
     q3 ..
     

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148. %FUFSNJOJOH""##4J[FGPS3BOHF4FBSDI
     63
     d
     

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149. %FUFSNJOJOH""##4J[FGPS3BOHF4FBSDI
     63
     • Build a uniform grid.
     d
     

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150. %FUFSNJOJOH""##4J[FGPS3BOHF4FBSDI
     63
     • Build a uniform grid.
     • Start from the cell that contains the
     query, and iteratively grow along all
     four (2D) or six (3D) directions.
     d
     

     View Slide

151. %FUFSNJOJOH""##4J[FGPS3BOHF4FBSDI
     63
     • Build a uniform grid.
     • Start from the cell that contains the
     query, and iteratively grow along all
     four (2D) or six (3D) directions.
     • Stop when K neighbors are found (or
     the sphere boundary is reached).
     d
     

     View Slide

152. %FUFSNJOJOH""##4J[FGPS3BOHF4FBSDI
     63
     • Build a uniform grid.
     • Start from the cell that contains the
     query, and iteratively grow along all
     four (2D) or six (3D) directions.
     • Stop when K neighbors are found (or
     the sphere boundary is reached).
     • We call the final collection of cells
     the megacell, with a width d.
     d
     

     View Slide

153. %FUFSNJOJOH""##4J[FGPS3BOHF4FBSDI
     63
     • Build a uniform grid.
     • Start from the cell that contains the
     query, and iteratively grow along all
     four (2D) or six (3D) directions.
     • Stop when K neighbors are found (or
     the sphere boundary is reached).
     • We call the final collection of cells
     the megacell, with a width d.
     • d is the AABB size.
     d
     

     View Slide

154. %FUFSNJOJOH""##4J[FGPS,//4FBSDI
     64
     • Find the megacell (width d), just like
     in range search.
     
     
     • Can we use d as the AABB size?
     d
     

     View Slide

155. %FUFSNJOJOH""##4J[FGPS,//4FBSDI
     65
     • Find the megacell (width d), just like
     in range search.
     
     
     • Can we use d as the AABB size?
     
     
     • No! Some of the nearest K neighbors
     might be outside of the megacell.
     d
     p2
     q
     qp1
     > qp2
     p1
     

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156. "$POTFSWBUJWF""##4J[FGPS,//
     66
     d
     p2
     q
     p1
     

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157. "$POTFSWBUJWF""##4J[FGPS,//
     66
     d
     p2
     q
     p1
     

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158. "$POTFSWBUJWF""##4J[FGPS,//
     66
     • The circumscribing circle/sphere of
     the megacall is guaranteed to have
     the K nearest neighbors.
     d
     p2
     q
     p1
     

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159. "$POTFSWBUJWF""##4J[FGPS,//
     66
     • The circumscribing circle/sphere of
     the megacall is guaranteed to have
     the K nearest neighbors.
     • Why? Given a circle with N neighbors, those N
     neighbors are by definition the N nearest
     neighbors; N is guaranteed to be >= K.
     d
     p2
     q
     p1
     

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160. "$POTFSWBUJWF""##4J[FGPS,//
     66
     • The circumscribing circle/sphere of
     the megacall is guaranteed to have
     the K nearest neighbors.
     • Why? Given a circle with N neighbors, those N
     neighbors are by definition the N nearest
     neighbors; N is guaranteed to be >= K.
     • AABB must be the circumscribing
     square/cube of that circle/sphere.
     d
     p2
     q
     p1
     

     View Slide

161. "$POTFSWBUJWF""##4J[FGPS,//
     66
     • The circumscribing circle/sphere of
     the megacall is guaranteed to have
     the K nearest neighbors.
     • Why? Given a circle with N neighbors, those N
     neighbors are by definition the N nearest
     neighbors; N is guaranteed to be >= K.
     • AABB must be the circumscribing
     square/cube of that circle/sphere.
     • Width is for 2D and for 3D.
     2d 3d
     d
     p2
     q
     p1
     

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162. $BO8F%P#FUUFS
     67
     d
     p2
     q
     p1
     A
     B
     

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163. $BO8F%P#FUUFS
     67
     • What we really want to find is sphere
     C, which is smallest sphere that
     contains K nearest neighbors.
     d
     p2
     q
     p1
     A
     B
     C
     

     View Slide

164. $BO8F%P#FUUFS
     67
     • What we really want to find is sphere
     C, which is smallest sphere that
     contains K nearest neighbors.
     • How? We know cube A has at least K
     neighbors.
     d
     p2
     q
     p1
     A
     B
     C
     

     View Slide

165. "#FUUFS""##4J[FGPS,//
     68
     • Assumption: point density is locally
     uniform within and around a
     megacell.
     d
     p2
     q
     p1
     A
     B
     C
     

     View Slide

166. "#FUUFS""##4J[FGPS,//
     68
     • Assumption: point density is locally
     uniform within and around a
     megacell.
     • A sphere C that has the same
     volume as cube A will contain K
     neighbors, which are guaranteed to
     be the K nearest neighbors.
     d
     p2
     q
     p1
     A
     B
     C
     

     View Slide

167. "#FUUFS""##4J[FGPS,//
     68
     • Assumption: point density is locally
     uniform within and around a
     megacell.
     • A sphere C that has the same
     volume as cube A will contain K
     neighbors, which are guaranteed to
     be the K nearest neighbors.
     • AABB size is for 3D.
     2 3
     3
     4π
     d
     d
     p2
     q
     p1
     A
     B
     C
     

     View Slide

168. 4FBSDI"MHPSJUIN 4P'BS
     
     69
     bvh ← buildBVH(points, r);
     
     
     firstHitAABBs ← traceRays(bvh, queries);
     
     
     reorderQueries(queries, firstHitAABBs);
     
     
     traceRays(bvh, queries);
     

     View Slide

169. 4FBSDI"MHPSJUIN 4P'BS
     
     69
     bvh ← buildBVH(points, r);
     
     
     firstHitAABBs ← traceRays(bvh, queries);
     
     
     reorderQueries(queries, firstHitAABBs);
     
     
     traceRays(bvh, queries);
     foreach q in queries:
     
     
     AABBSize ← findSmallestAABBSize(q);
     
     
     partitions.add(AABBSize, q); // assuming a hash table
     
     
     foreach p in partitions:
     
     
     queries ← all queries in p;
     
     
     r ← AABBSize of p;
     

     View Slide

170. #VOEMF1BSUJUJPOT
     70
     • Problem: too many partitions leads
     to high BVH construction overhead.
     

     View Slide

171. #VOEMF1BSUJUJPOT
     70
     • Problem: too many partitions leads
     to high BVH construction overhead.
     • Especially bad when point density is globally
     non-uniform (e.g., astrophysics simulation).
     

     View Slide

172. #VOEMF1BSUJUJPOT
     70
     • Problem: too many partitions leads
     to high BVH construction overhead.
     • Especially bad when point density is globally
     non-uniform (e.g., astrophysics simulation).
     • Bundle partitions to minimize overall
     search time. Bundling two partitions:
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     

     View Slide

173. #VOEMF1BSUJUJPOT
     70
     • Problem: too many partitions leads
     to high BVH construction overhead.
     • Especially bad when point density is globally
     non-uniform (e.g., astrophysics simulation).
     • Bundle partitions to minimize overall
     search time. Bundling two partitions:
     • eliminates one BVH construction cost.
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     

     View Slide

174. #VOEMF1BSUJUJPOT
     70
     • Problem: too many partitions leads
     to high BVH construction overhead.
     • Especially bad when point density is globally
     non-uniform (e.g., astrophysics simulation).
     • Bundle partitions to minimize overall
     search time. Bundling two partitions:
     • eliminates one BVH construction cost.
     • but also increases the search cost. Why?
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     

     View Slide

175. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     

     View Slide

176. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     

     View Slide

177. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     • …is equivalent to the number of points inside an AABB, which
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     

     View Slide

178. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     • …is equivalent to the number of points inside an AABB, which
     • …is density x volume (r3), assuming locally-uniform density
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     

     View Slide

179. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     • …is equivalent to the number of points inside an AABB, which
     • …is density x volume (r3), assuming locally-uniform density
     • Search cost ∝ r3
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     

     View Slide

180. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     • …is equivalent to the number of points inside an AABB, which
     • …is density x volume (r3), assuming locally-uniform density
     • Search cost ∝ r3
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     Tsearch
     = kNρS3
     

     View Slide

181. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     • …is equivalent to the number of points inside an AABB, which
     • …is density x volume (r3), assuming locally-uniform density
     • Search cost ∝ r3
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     Tsearch
     = kNρS3
     # of queries in
     a partition
     

     View Slide

182. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     • …is equivalent to the number of points inside an AABB, which
     • …is density x volume (r3), assuming locally-uniform density
     • Search cost ∝ r3
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     Tsearch
     = kNρS3
     # of queries in
     a partition
     Point density in
     a partition
     

     View Slide

183. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     • …is equivalent to the number of points inside an AABB, which
     • …is density x volume (r3), assuming locally-uniform density
     • Search cost ∝ r3
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     Tsearch
     = kNρS3
     # of queries in
     a partition
     Point density in
     a partition
     AABB size of
     the partition
     

     View Slide

184. $PTU.PEFM
     71
     • Search cost is dictated by the number of IS shader calls, which
     • …is dictated by the number of AABBs a query resides in, which
     • …is equivalent to the number of points inside an AABB, which
     • …is density x volume (r3), assuming locally-uniform density
     • Search cost ∝ r3
     35
     28
     21
     14
     7
     0
     Execution Time (s)
     0.9
     0.6
     0.3
     0.0
     # of IS Shader Calls (millions)
     Tsearch
     = kNρS3
     # of queries in
     a partition
     Point density in
     a partition
     AABB size of
     the partition
     A constant
     regressed offline
     

     View Slide

185. $PTU.PEFM
     72
     • When combining two partitions, the AABB size of the new partition
     must be the max of the two.
     k(N1
     ρ1
     + N2
     ρ2
     )[max(S1
     , S2
     )]3 k(N1
     ρ1
     S3
     1
     + N2
     ρ2
     S3
     2
     )
     >
     

     View Slide

186. 0QUJNBM#VOEMJOH
     73
     • Bundling increases search cost, but
     reduces BVH construction cost.
     What’s the optimal bundling?
     

     View Slide

187. 0QUJNBM#VOEMJOH
     73
     • Bundling increases search cost, but
     reduces BVH construction cost.
     What’s the optimal bundling?
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     

     View Slide

188. 0QUJNBM#VOEMJOH
     73
     • Bundling increases search cost, but
     reduces BVH construction cost.
     What’s the optimal bundling?
     • Combinatorial optimization, but we
     have to solve it at run-time.
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     

     View Slide

189. 0QUJNBM#VOEMJOH
     73
     • Bundling increases search cost, but
     reduces BVH construction cost.
     What’s the optimal bundling?
     • Combinatorial optimization, but we
     have to solve it at run-time.
     • We leverage an empirical
     observation to simplify the problem
     structure, which yields an efficient
     linear-time solution.
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     

     View Slide

190. &NQJSJDBM0CTFSWBUJPO
     74
     • Empirically: AABB size and # of
     queries are inversely correlated.
     

     View Slide

191. &NQJSJDBM0CTFSWBUJPO
     74
     • Empirically: AABB size and # of
     queries are inversely correlated.
     104
     105
     106
     107
     Number of Queries
     2.3
     1.9
     1.5
     1.1
     0.7
     0.3
     AABB Size
     

     View Slide

192. &NQJSJDBM0CTFSWBUJPO
     74
     • Empirically: AABB size and # of
     queries are inversely correlated.
     104
     105
     106
     107
     Number of Queries
     2.3
     1.9
     1.5
     1.1
     0.7
     0.3
     AABB Size
     Intuitively, only a handful of
     sparsely located queries need a
     large AABB to find K neighbors.
     

     View Slide

193. &NQJSJDBM0CTFSWBUJPO
     74
     • Empirically: AABB size and # of
     queries are inversely correlated.
     • Given this empirical observation, we
     can derive the optimal bundling in
     linear time.
     
     
     • Proof omitted; see paper.
     104
     105
     106
     107
     Number of Queries
     2.3
     1.9
     1.5
     1.1
     0.7
     0.3
     AABB Size
     Intuitively, only a handful of
     sparsely located queries need a
     large AABB to find K neighbors.
     

     View Slide

194. 0QUJNBM#VOEMJOH"MHPSJUIN
     75
     • Algorithm:
     
     
     • Sort partitions according to the ascending order
     of their AABB sizes.
     
     
     • Start from the last partition and scan backward;
     at each step, bundle all partitions that have been
     scanned, leave the rest unbundled.
     
     
     • Pick the one with the lowest search cost.
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     Larger AABBs, fewer queries.
     

     View Slide

195. 0QUJNBM#VOEMJOH"MHPSJUIN
     75
     • Algorithm:
     
     
     • Sort partitions according to the ascending order
     of their AABB sizes.
     
     
     • Start from the last partition and scan backward;
     at each step, bundle all partitions that have been
     scanned, leave the rest unbundled.
     
     
     • Pick the one with the lowest search cost.
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     Larger AABBs, fewer queries.
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     

     View Slide

196. 0QUJNBM#VOEMJOH"MHPSJUIN
     75
     • Algorithm:
     
     
     • Sort partitions according to the ascending order
     of their AABB sizes.
     
     
     • Start from the last partition and scan backward;
     at each step, bundle all partitions that have been
     scanned, leave the rest unbundled.
     
     
     • Pick the one with the lowest search cost.
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     Larger AABBs, fewer queries.
     p1 p2 p3 p4
     b1 b2 b3
     Partitions
     Bundles
     

     View Slide

197. 'JOBM4FBSDI"MHPSJUIN
     76
     foreach q in queries:
     
     
     AABBSize ← findSmallestAABBSize(q);
     
     
     partitions.add(AABBSize, q); // assuming a hash table
     foreach p in partitions:
     
     
     queries ← all queries in p;
     
     
     r ← AABBSize of p;
     
     
     bvh ← buildBVH(points, r);
     
     
     firstHitAABBs ← traceRays(bvh, queries);
     
     
     reorderQueries(queries, firstHitAABBs);
     
     
     traceRays(bvh, queries);
     

     View Slide

198. 'JOBM4FBSDI"MHPSJUIN
     76
     foreach q in queries:
     
     
     AABBSize ← findSmallestAABBSize(q);
     
     
     partitions.add(AABBSize, q); // assuming a hash table
     foreach p in partitions:
     
     
     queries ← all queries in p;
     
     
     r ← AABBSize of p;
     
     
     bvh ← buildBVH(points, r);
     
     
     firstHitAABBs ← traceRays(bvh, queries);
     
     
     reorderQueries(queries, firstHitAABBs);
     
     
     traceRays(bvh, queries);
     bundle(partitions);
     

     View Slide

199. 77
     Results
     

     View Slide

200. &YQFSJNFOUBM4FUVQ
     • OptiX 7.1, CUDA 11; RTX 2080.
     
     
     • Baselines:
     
     
     • cuNSearch: grid search in CUDA; used in SPlisHSPlasH fluid simulator.
     
     
     • FRNN: grid search in CUDA.
     
     
     • PCLOctree: octree-search in CUDA (i.e., use octree, as opposed to BVH, to prune search).
     
     
     • FastRNN: KNN search in RT cores without our optimizations.
     
     
     • Datasets:
     
     
     • KITTI: self-driving car datasets; points are surface samples; mostly confined in 2D (ground)
     
     
     • Stanford 3D Scanning Repo: Bunny, Dragon, Buddha.
     
     
     • N-body simulation: non-uniform distribution in 3D.
     78
     

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201. 4QFFEVQTPWFS#BTFMJOFT
     79
     10-1
     100
     101
     102
     103
     Speedup (log)
     KITTI-1M
     KITTI-6M
     KITTI-12M
     KITTI-25M
     NBody-9M
     NBody-10M
     Bunny-360K
     Dragon-3.6M
     Buddha-4.6M
     OOM
     DNF
     Range Search PCLOctree cuNSearch
     KNN Search FRNN FastRNN
     10-1
     100
     101
     102
     103
     Speedup (log)
     1M 6M 12M 25M
     KITTI
     9M 10M
     N-body 3D scans
     360K 3.6M 4.6M
     Range search speedup: 2.2X — 44.0X
     
     
     KNN search speedup: 3.5X — 65.0X
     1. higher speedups on larger inputs.
     
     
     2. higher speedups on KNN search.
     

     View Slide

202. 5JNF%JTUSJCVUJPO
     80
     100
     80
     60
     40
     20
     0
     Time (%)
     KITTI-1M
     KITTI-6M
     KITTI-12M
     KITTI-25M
     NBody-9M
     NBody-10M
     Bunny-360K
     Dragon3.6M
     Buddha-4.6M
     Data Opt BVH FS Search
     100
     80
     60
     40
     20
     0
     Time (%)
     KITTI-1M
     KITTI-6M
     KITTI-12M
     KITTI-25M
     NBody-9M
     NBody-10M
     Bunny-360K
     Dragon3.6M
     Buddha-4.6M
     Data Opt BVH FS Search
     Range search: much of the time is
     spent on optimization, data transfer,
     BVH construction.
     KNN search: time is mostly
     dominated by the actual search.
     KITTI N-body 3D scan KITTI N-body 3D scan
     0 0
     

     View Slide

203. 5JNF%JTUSJCVUJPO
     81
     100
     80
     60
     40
     20
     0
     Time (%)
     KITTI-1M
     KITTI-6M
     KITTI-12M
     KITTI-25M
     NBody-9M
     NBody-10M
     Bunny-360K
     Dragon3.6M
     Buddha-4.6M
     Data Opt BVH FS Search
     100
     80
     60
     40
     20
     0
     Time (%)
     KITTI-1M
     KITTI-6M
     KITTI-12M
     KITTI-25M
     NBody-9M
     NBody-10M
     Bunny-360K
     Dragon3.6M
     Buddha-4.6M
     Data Opt BVH FS Search
     N-body N-body
     Galaxy (point) distribution in universe is very non-
     uniform; so a lot of time spent on partitioning.
     0 0
     

     View Slide

204. 0QUJNJ[BUJPO&
     ff
     FDUT
     82
     10-2
     100
     102
     Log-Scale Time (s)
     KNN Range
     18.6%
     161.3
     NoOpt Sched. Oracle
     Sched. + Partition
     Sched. + Partition + Bundle
     N-body (9M)
     10-2
     100
     102
     104
     Log-Scale Time (s)
     KNN Range
     18.8%
     NoOpt Sched. Oracle
     Sched. + Partition
     Sched. + Partition + Bundle
     KITTI (12M)
     

     View Slide

205. 83
     Concluding Remarks
     

     View Slide

206. (FOFSBM1VSQPTF*SSFHVMBS1SPDFTTPS
     • Conventional GPUs evolved to support general-purpose regular
     applications; will the same happen to RT cores?
     
     
     • A few examples of using RT cores for non-graphics workloads.
     
     
     • Key: formulate your problem as a BVH search.
     
     
     • But very limited, because RT cores are built to support only BVH
     search, which has a very specific branching logic (ray-AABB test).
     
     
     • Relax the hardware? Does it make sense? Will Nvidia do it?
     84
     

     View Slide

207. "QQSPYJNBUF/FJHICPS4FBSDI
     • Most often applications don’t need precise search.
     
     
     • Many natural opportunities for approximation in our algorithm.
     
     
     • Use a smaller-than-necessary AABB to build the BVH.
     
     
     • Elide ray-sphere test (skip IS shader calls); provides an error bound.
     
     
     • Even better: many applications that use neighbor search are
     differentiable (e.g., neural network). We could integrate
     approximate neighbor search into the training process to tolerate
     end-to-end accuracy loss.
     
     
     • See Yu Feng’s ISCA 2022 paper.
     85
     

     View Slide