PixelPie: Maximal Poisson-disk Sampling with Rasterization. M. A. Yalçin D. Luebke A. Varshney

Transcription

1 PixelPie: Maximal Poisson-disk Sampling with Rasterization C. Y. Ip M. A. Yalçin D. Luebke A. Varshney

2 Poisson-Disk Distribution

3 Poisson-Disk Distribution Random samples that are at

4 Applications Antialiasing Dithering Object Placement [Dippe & Wald SIGGRAPH 1985] [

5 Dart Throwing [Cook SIGGRAPH 1986]

6 Dart Throwing [Cook SIGGRAPH 1986]

7 Dart Throwing [Cook SIGGRAPH 1986]

8 Dart Throwing [Cook SIGGRAPH 1986]

9 Dart Throwing [Cook SIGGRAPH 1986]

10 Dart Throwing [Cook SIGGRAPH 1986]

11 Dart Throwing [Cook SIGGRAPH 1986]

12 Dart Throwing [Cook SIGGRAPH 1986]

13 Related Work Spatial Data Structure Approaches: Trees [Dunbar & Humphreys ToG 2006, Gamito & Maddock ToG 2009] Grid [Jones et al. JGT 2006, 2011] Approximate Approaches: Tiles [Lagae & Dutre CGF 2005, 2006, Kopf et al. ToG 2006, Ostromoukhov et al. ToG 2004, 2007] Farthest Point Optimization [Balzer ToG 2009, Chen & Gotsman CGF 2012, de Goes et al. ToG 2012] Parallel Approaches: GPGPU [Wei ToG 2008] CUDA [Bower et al. ToG 2010, Xiang et al. SIGGRAPH 2011, Ebeida et al. ToG 2011, CGF 2012] Survey [Lagae & Dutre CGF 2006]

14 Concept

15 When There is a Conflict

16 Draw Solid Disks The conflicted dart center

17 In Parallel

18 Empty Domain

19 Random Darts

20 Draw Solid Disks around the Darts

21 Remove Darts with Occluded Center

22 Iteratively Fill in the Empty Regions

23 Poisson-disk Distribution

24 Rasterization Implementation

25 Rasterize Disks on Textures Render solid disks by Rasterization Target Domain: Discrete depth texture Reject conflicts by Occlusion Queries

26 Related Work Voronoi Diagrams and Distance Transform by Rasterization GPU Rasterization [Hoff et al. SIGGRAPH 1999 ] 3D Distance transform [Sigg et al. Vis 2003, Sud et al. I3D 2004] High order Voronoi Diagrams [Fischer & Gostman JGT 2006] Jump Flooding Approach [Rong et al. I3D 2006, TVCG 2011] [Hoff et al. SIGGRAPH 1999 ] [Sigg et al. Vis 2003]

27 Graphics Pipeline: 2-Step Iterative Procedure Input Primitive s Draw and Reject Occluded Framebuffe Disks Vertex Geometr y Rasteriz er Step 1: Throw Random Darts Emit Triangles Fragmen t r Operations (Depth Test) Trim Triangles to Disks on a Depth Map Reject Conflicts w/ Trim Triangles to Step 2: Re-throw Darts Occlusion Queries Disks on a Coverage Map Post-processing: Find empty regions (CUDA stream compaction) Iteratively Fill the empty regions

28 How about using CUDA? Input Primitive s Vertex Geometr y Rasteriz er Fragmen t Framebuffe r Operations (Depth Test)

29 How about using CUDA? Input Primitive s Vertex Geometr y Rasteriz er Fragmen t Framebuffe r Operations (Depth Test) Hardware rasterizer and depth test not currently available in CUDA CUDA software rasterization is slower than the hardware [Laine & Karras HPG 2011] Use GPU hardware to accelerate geometry computing

30 Step 1: Input Inp ut Vertex Geometry Rasterize r Fragment Outp ut

31 Step 1: Input Inp ut Vertex Geometry Rasterize r Fragment Outp ut

32 Step 1: Geometry Inp ut Vertex Geometry Rasterize r Fragment Outp ut

33 Step 1: Geometry Inp ut Vertex Geometry Rasterize r Fragment Outp ut Emits a triangle Unique depth by with

34 Step 1: Rasterizer Inp ut Vertex Geometry Rasterize r Fragment Outp ut The Rasterizer rasterizes

35 Step 1: Fragment Inp ut Vertex Geometry Rasterize r Fragment Outp ut Trims the triangle to

36 Step 1: Output Inp ut Vertex Geometry Rasterize r Fragment Outp ut Depth Test ensures proper

37 Step 2: Input Inp ut Vertex Geometry Rasterize r Fragment Outp ut Re-throw Darts

38 Step 2: Input Inp ut Vertex Geometry Rasterize r Fragment Outp ut Re-throw Darts

39 Step 2: Geometry Inp ut Vertex Geometry Rasterize r Fragment Outp ut Query the depth map for

40 Step 2: Geometry Inp ut Vertex Geometry Rasterize r Fragment Outp ut Occluded Dart Center: Depth-map depth <

41 Step 2: Geometry Inp ut Vertex Geometry Rasterize r Fragment Outp ut

42 Step 2: Geometry Inp ut Vertex Geometry Rasterize r Fragment Outp ut Unoccluded Dart Center: Depth-map depth =

43 Step 2: Geometry Inp ut Vertex Geometry Emits a triangle Rasterize r Fragment Outp ut Results buffer

44 Step 2: Fragment Inp ut Vertex Geometry Rasterize r Fragment Outp ut Trims the triangle to

45 Step 2: Output Inp ut Vertex Geometry Rasterize r Fragment Outp ut

46 Post Processing

47 Stream Compaction (CUDA Thrust)

48 Keep Iterating

49 Keep Iterating

50 No Empty Pixel: Complete Guarantee Maximal!

51 Quality

52 Spectrum Quality Comparison Samples Power Spectrum Periodogram

53 Spectrum Quality Comparison Samples Power Spectrum Periodogram

54 Spectrum Quality Comparison Samples Power Spectrum Periodogram

55 Angular Bias of Rasterized Disks Figure 8: parison of pixel-centered and subpixel-centered Figure 8: Comparison of pixel-centered and Com subpixel-centered disks: (a) shows the shape of a discretized pixel-centered disk, (b) disks: (a) shows the shape of a discretized pixel-centered disk, (b) shows of disks centered at 2 2 subpixel locations, and shows variations of disks centered at 2 2variations subpixel locations, and (c) shows the average (c) shows the average of the subpixel-centered disks at 2 of2the andsubpixel-centered disks at 2 2 and 4 of 4 subpixel subpixel sam locations. The average of subpixel sampling effec4 4 subpixel locations. The average pling effectively generates anti-aliased disks. tively generates anti-aliased disks. (a) Figure 8: Com parison of pixel-centered and Com parison of pixel-centered and subpixel-cente 8: Comparison of pixel-centered and subpixel-centere disks: (a) shows the shape of a discretized pixel shows the shape of a discretized pixel-centered disk(b a) shows the shape of a discretized pixel-centered(c)disk, shows variations ofat disks centered atlocations, 2 2 subp (a) (b) Subpixel-centered ations of disks centered 2 2 subpixel locations, (a) (b) ariations of disks centered 2 subpixel an Pixel-centered Subpixel-centered variation Figure 10: 1024 subpixel-cente Anti-aliased average (c) shows the average of the subpixel-centered 2

56 Spectrum Quality Comparison Samples Power Spectrum Periodogram

57 Spectrum Quality Comparison Samples Power Spectrum Periodogram

58 Performance

59 Uniform Sampling

60 Importance Sampling

61 Random Darts Sampling according to an importance m

62 Vary the Disk Radii

63 Importance Sampling

64 Importance Sampling: Geometry

65 Importance Sampling: Geometry

66 Results 0.053s on GTX58024s on Core i7 [Kalantari & Sen CGF 2011]

67 Results 0.031s on GTX58025s on Core i7 [Kalantari & Sen CGF 2011]

68 Conclusions Poisson-disk sampling with programmable graphics functions and hardware Rasterization and Occlusion Queries to reject conflicts Subpixel-centered disks to reduce bias Importance sampling by varying disk radii 6.8 M samples / sec on GTX 580

69 Acknowledgements Anonymous reviewers for the constructive comments National Science Foundation: CCF , CMMI , CNS NVIDIA CUDA Center of Excellence Program Thank you!

70 Cheuk Yiu Ip 1 M. Adil Yalcin 1 David Luebke 2 Amitabh Varshney 1 Cheuk Yiu Ip M. Adil Yalcin David 1Luebke Amitabh Varshney 2 University of Maryland, CollegePark 1 NVIDIA Research 2 University of Maryland, CollegePark NVIDIA Research Questions?and ing with ling withrasterization Rasterization andprogrammable Programmables s Adil Yalcin 1 David Luebke 2 Amitabh Varshney 1. Adil Yalcin David 1Luebke Amitabh Varshney 2 1 NVIDIA Research 2 Maryland, CollegePark Maryland, CollegePark NVIDIA Research Please see our websites for the paper and software: Software sf.net/p/pixelpie Cheuk(b)Yiu Ip (c) (c) (b) (d) (d) (e) (e) erformmaxim alalpoisson-disk pling performm axim Poisson-disksam sam plingby byrasterization rasterizationand andocclusion occlusionculling. culling.first, First,we werasterize rasteriz GVIL Research Highlights ose, blue is far) in (a). Second, wecull the occluded disks to rem oveconflicting sam ples in (b). close, blueis far) in (a). Second, wecull the occluded disks to removeconflicting samples in (b).thi Th gions to obtain a m axim al Poisson-disk distribution in (c). (e) and (f) show uniformand im portance egions to obtain a maximal Poisson-disk distribution in (c). (e) and (f) show uniformand importanc (c) (d) (e) (f)