Clipless Dual-Space Bounds for Faster Stochastic Rasterization Samuli Laine Timo Aila Tero Karras Jaakko Lehtinen NVIDIA Research

(x,y)

(x,y,u,v,t)

Motion Blur

t=0t=1

Motion Blur

t Accumulation Buffer [Haeberli ‘90]

t InterleaveUVT [Fatahalian ‘09]

t

t

t

4 samples/pixel (16 UVT triples)16 samples/pixel (64 UVT triples) Scene: Assassin’s Creed, courtesy of Ubisoft InterleaveUVT [Fatahalian ‘09]

Unique UVTs 4 samples/pixel, unique UVTs16 samples/pixel, unique UVTs Scene: Assassin’s Creed, courtesy of Ubisoft

5D Rasterization t=0t=1 t

5D Rasterization t=0t=1 t

5D Rasterization t=0t=1 t

5D Rasterization t

t=0t=1 t ?

5D Rasterization t=0t=1 t

5D Rasterization t=0t=1 t ?

5D Rasterization t=0t=1 t ?

Pixar Algorithm t=0t=1 t t=.5

Pixar Algorithm t=0t=1 t t=.5 XX

Pixar Algorithm t=0t=1 t t=.5 XX

Our Method t=0t=1 t

Our Method t=0t=1 t

Our Method t=0t=1 t XXX t range computed for pixel

Our Method  Determine pixels potentially covered by triangle  For each pixel  Compute time bounds t min,t max  Enumerate samples where t min ≤ t ≤ t max  For each such sample, perform 5D coverage test  Same for lens bounds u min,u max and v min,v max

Bound Computation  Lens bounds computed in screen space  Time bounds computed in dual space

Lens Bounds x y u=0u= –1u= +1 film lens focal plane u screen-space x is linear with u

Lens Bounds x y u= –1u= +1 screen-space x is linear with u

Lens Bounds x y u=au=b screen-space x is linear with u u a b

Time Bounds  World-space affine motion  Not affine in screen space, but affine in clip space  Perspective causes singularities in screen space  Operate in dual space

Clip Space and Dual Space x w t=0 t=1

Clip Space and Dual Space x w γ δ γ= –1 γ= +1

Clip Space and Dual Space x w γ δ δ { γ= –0.5

Clip Space and Dual Space x w γ δ

x w γ δ

x w γ δ

x w γ δ δ is linear in x and w δ = x – wγ x and w are linear in t δ is linear in t t=0 t=1 t=0 t=1

Clip Space and Dual Space x w γ δ t=0 t=1 t=0 t=1

Clip Space and Dual Space x w γ δ t=0 t=1 t=0 t=1

Clip Space and Dual Space x w γ δ t=0 t=1 t=0 t=1 t=a t

Clip Space and Dual Space x w γ δ t=0 t=1 t=0 t=1 t=a t a

Time Bounds  Compute separately for x and y  Intersect resulting spans  If intersection is empty, skip pixel

Recap  For each triangle  For each pixel  Compute t, u, v bounds  Cull samples outside bounds  Profit

Results  Measure sample test efficiency (STE)  Compare against methods that allow arbitrary sampling patterns # samples tested with full 5D test # samples hit STE =

Results Scene: Age of Conan PC MMO, courtesy of Funcom Bbox scan Pixar Our method static23.6 motion motion x defocus defocus x both both x STE in %, scene Conan

Results Scene: Assassin’s Creed, courtesy of Ubisoft Bbox scan Pixar Our method static23.2 motion motion x defocus defocus x both both x STE in %, scene Assassin

Results Bbox scan Pixar Our method static motion motion x defocus defocus x both both x STE in %, scene Cars

Conclusions  Each triangle processed once  Arbitrary sampling patterns  High STE  Future work  Combined motion + defocus case

Thank You