Efficient GPU Rendering of Subdivision Surfaces. Tim Foley,

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1 Efficient GPU Rendering of Subdivision Surfaces Tim Foley,

2 Collaborators Activision Wade Brainerd Stanford Matthias Nießner NVIDIA Manuel Kraemer Henry Moreton 2

3 Subdivision surfaces are a powerful modelling primitive Smooth surface (+creases) Arbitrary input topology Animation Level of detail 3

4 Subdivision surfaces are a powerful modelling primitive Smooth surface (+creases) Arbitrary input topology Animation Level of detail 4

5 Subdivision surface rendering is not common in games Performance Ease of Integration 5

6 Performance Our method is up to 3x faster than previous non-approximate schemes Ease of Integration Our method can work in a single draw pass (no compute) Can use with existing vertex shaders for animation 6

7 Outline Background Subdivision surfaces GPU tessellation hardware Prior work Overview of our approach Performance evaluation Conclusion 7

8 Outline Background Subdivision surfaces GPU tessellation hardware Prior work Overview of our approach Performance evaluation Conclusion 8

9 Catmull-Clark Subdivision base mesh 9

10 Defined by repeated application of subdivision rules base mesh 10

11 Defined by repeated application of subdivision rules base mesh subdivided once 11

12 Defined by repeated application of subdivision rules base mesh subdivided once limit surface 12

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15 Limit surface for face depends on local neighborhood 15

16 Limit surface for face depends on local neighborhood Connectivity of 1-ring vertices 16

17 Regular faces are easy to evaluate Limit surface equivalent to bicubic B-spline patch 17

18 Irregular Face 18

19 Extraordinary Vertex valence!= 4 19

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25 regular irregular regular regular 25

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27 Outline Background Subdivision surfaces GPU tessellation hardware Prior work Overview of our approach Performance evaluation Conclusion 27

28 GPU Rasterization Pipeline Vertex Fetch Vertex Shader Hull Shader Tessellator Domain Shader Geometry Shader Rasterizer Fragment Shader Blend 28

29 Tessellation Stages Vertex Fetch Vertex Shader Hull Shader Tessellator Domain Shader Geometry Shader Rasterizer Fragment Shader Blend 29

30 Hull Shader Tessellator Domain Shader 30

31 primitive base vertices Hull Shader Tessellator Domain Shader 31

32 primitive base vertices control points Hull Shader Tessellator Domain Shader 32

33 primitive base vertices control points v domain locations u Hull Shader Tessellator Domain Shader 33

34 primitive base vertices control points tessellated primitive post-tessellation vertices v domain locations u Hull Shader Tessellator Domain Shader 34

35 Crux of the Challenge Limit surface of irregular face defined by recursive subdivision Expands to many faces with many control points Variable: depends on subdivision depth Tessellation hardware wants fixed # of control points per face 35

36 Outline Background Subdivision surfaces GPU tessellation hardware Prior work Overview of our approach Performance evaluation Conclusion 36

37 Submit one primitive for each irregular face Use a fixed # of control points Submit many primitives for an irregular face Each of which is simple to evaluate 37

38 Submit one primitive for each irregular face Use a fixed # of control points Submit many primitives for an irregular face Each of which is simple to evaluate 38

39 Exact Evaluation Perform Eigen analysis on subdivision matrix [Stam 1998] Offline process for each topological configuration Project base vertices into Eigen space Yields a fixed # of control points Matrix exponentiation in domain shader Many floating-point operations 39

40 Approximate irregular faces with simpler patch Bicubic Bezier Bicubic Gregory (20 control points) [Loop and Schaefer 2008] [Loop et al. 2009] Fast evaluation No support for semi-sharp features (creases) Approximation affects tangents, parameterization 40

41 Submit one primitive for each irregular face Use a fixed # of control points Submit many primitives for an irregular face Each of which is simple to evaluate 41

42 Subdivide and submit many primitives per face Feature adaptive subdivision (FAS) Generate sub-face control points using compute kernels [Nießner et al. 2012] Many submit many primitives, depending on subdivision level Need to address T-junctions between sub-faces Dynamic feature adaptive subdivision (DFAS) Enables non-uniform subdivision levels Open Subdiv [Schäfer et al. 2012] 42

43 Issues with Feature-Adaptive Subdivision many primitives T-junctions 43

44 Outline Background Subdivision surfaces GPU tessellation hardware Prior work Overview of our approach Performance evaluation Conclusion 44

45 Take recursive subdivision hierarchy many primitives T-junctions 45

46 Summarize using a single primitive one primitive no T-junctions 46

47 Two key ideas Use a quadtree to map domain locations to sub-faces Output a variable # of control points from a Hull Shader 49

48 Two key ideas Use a quadtree to map domain locations to sub-faces Output a variable # of control points from a Hull Shader 50

49 Submit one primitive per base face to tessellator base subdivision face 51

50 Tessellator produces domain locations for evaluation base subdivision face domain locations 52

51 Map domain location to correct sub-face base subdivision face domain locations 53

52 Map domain location to correct sub-face base subdivision face domain locations 54

53 Map domain location to correct sub-face using a quadtree data structure base subdivision face quadtree domain locations 55

54 Map domain location to correct sub-face using a quadtree data structure base subdivision face quadtree domain locations 56

55 Quadtrees can be built ahead of time, and shared 57

56 Quadtrees can be built ahead of time, and shared depend only on 1-ring topology 58

57 Quadtree leaf node tells us which control points to use base subdivision face quadtree 59

58 Quadtree leaf node tells us which control points to use base subdivision face quadtree B-spline control points 60

59 Quadtree leaf node tells us which control points to use base subdivision face B-spline control points 61

60 Evaluate sub-face using its control points base subdivision face B-spline control points tessellated primitive 62

61 Two key ideas Use a quadtree to map domain locations to sub-faces Output a variable # of control points from a Hull Shader 63

62 Hull Shader 64

63 Hull Shader 65

64 Hull Shader Domain Shader 66

65 Hull Shader Domain Shader 67

66 Hull Shader Domain Shader 68

67 Hull Shader Domain Shader control point buffer 69

68 Hull Shader Domain Shader control point buffer 70

69 Hull Shader Domain Shader control points needed for tessellessation factor 3.0 control point buffer 71

70 Hull Shader Domain Shader control point buffer 72

71 More details in paper Collapsing repeated structure in quadtrees Most faces need only one tree traversal step! Sorting control point stencils for efficient evaluation Minimize number of control points needed for given tessellation factors Arrange control points for efficient SIMD computation 73

72 Outline Background Subdivision surfaces GPU tessellation hardware Prior work Overview of our approach Performance evaluation Conclusion 74

76 Up to 3x faster than Adaptive Subdivision *non-exact 78

77 Up to 3x faster than Adaptive Subdivision *non-exact 79

79 Benefit decreases as fraction of regular faces increases 83

80 Only some methods can handle semi-sharp creases 84

81 Benefit decreases as fraction of regular faces increases 85

Big Guy Monster Frog Armor Guy Sterling ( 2014 DigitalFish, Inc.

83 Armor Guy has a greater fraction of irregular faces 88

84 Outline Background Subdivision surfaces GPU tessellation hardware Prior work Overview of our approach Performance evaluation Conclusion 89

85 Conclusion A simpler and faster way to render subdivision surfaces Up to 3x faster than state-of-the-art methods Single draw pass Can use existing shaders for animation Integration in open-source OpenSubdiv library is in progress Interested engine developers should contact NVIDIA 90

86 Thank You 91

Efficient GPU Rendering of Subdivision Surfaces using Adaptive Quadtrees

Efficient GPU Rendering of Subdivision Surfaces using Adaptive Quadtrees Wade Brainerd* Activision Tim Foley* NVIDIA Manuel Kraemer NVIDIA Henry Moreton NVIDIA Matthias Nießner Stanford University Figure