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Interactive Rendering of Atmospheric Scattering Effects Using Graphics Hardware
Yoshinori Dobashi Hokkaido University Tsuyoshi Yamamoto Hokkaido University 北海道大学の土橋です。 グラフィックスハードウェアを利用したボリュームレンダリング法を用いた光跡の高速表示法について発表させていただきます。 Tomoyuki Nishita Tokyo University
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Overview Introduction Rendering Light Beams
motivation previous work Rendering Light Beams basic Idea problems high quality rendering Rendering the Earth’s Atmosphere rendering sky rendering the earth viewed from space Results Conclusion
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Overview Introduction Introduction Rendering Light Beams
motivation previous work Introduction motivation previous work Rendering Light Beams basic Idea problems high quality rendering Rendering Light Beams basic Idea problems high quality rendering Rendering the Earth’s Atmosphere rendering sky rendering the earth viewed from space Rendering the Earth’s Atmosphere rendering sky rendering the earth viewed from space Results Results Conclusion Conclusion
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Overview Introduction Rendering Light Beams
motivation previous work Rendering Light Beams basic Idea problems high quality rendering Rendering the Earth’s Atmosphere rendering sky rendering the earth viewed from space Results Conclusion
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Motivation Real-time rendering of realistic images
Atmospheric Scattering Effects scattering and absorption of light due to small particles spotlights sunlight through windows earth’s atmosphere requires long computation time Our Goal: Real-time rendering of atmospheric effects
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[e.g. Behrens98, Westermann98]
Previous Work Volume rendering [e.g. Behrens98, Westermann98] use of voxels to store the intensity of light consuming texture memory for volume data difficult to capture the edges of shafts of light edges of spotlight edges of shadows
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Previous Work 2D texture based approach Interleaved sampling
[Dobashi01, Everitt99] use of shadow and projective texture mapping artifacts due to sampling errors Interleaved sampling [Keller01] a general and efficient solution to the sampling problem not optimal for rendering atmospheric scattering Earth’s atmosphere no methods for real-time rendering of realistic images
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Proposed Method Precise and efficient rendering of atmospheric effects
Rendering light beams point/infinite light sources uniform density of atmospheric particles Rendering earth’s atmosphere sky the earth viewed from space density decreases exponentially according to the height from the ground
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Overview Introduction Rendering Light Beams
motivation previous work Rendering Light Beams basic Idea problems high quality rendering Rendering the Earth’s Atmosphere rendering sky rendering the earth viewed from space Results Conclusion
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ò Shading Model for Light Beams Intensity at viewpoint point source
= T l s dt t g H I ) , ( scattered light Ieye viewpoint
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ò Shading Model for Light Beams Intensity at viewpoint t H ) (
point light ò = T l s dt t g H I ) , ( Il :intensity of light l t I ) , ( t H ) ( :visibility function t P :attenuation function t g ) , ( l Is viewpoint
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ò Basic Idea å Intensity at viewpoint = computed at lattices
[Dobashi00] Intensity at viewpoint ò = T l s dt t g H I ) , ( = å n k 1 l t I ) , ( g H screen sampling plane viewpoint point light computed at lattices
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ò Basic Idea å Intensity at viewpoint = light map light map
[Dobashi00] Intensity at viewpoint light map ò = T l s dt t g H I ) , ( n å = l t I ) , ( t H ) ( t g ) , ( l k = 1 light map viewpoint point light texture mapping
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ò Basic Idea å Intensity at viewpoint = object point light shadow
[Dobashi00] Intensity at viewpoint ò = T l s dt t g H I ) , ( n å = l t I ) , ( t H ) ( t g ) , ( l k = 1 object shadow mapping viewpoint point light
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ò Basic Idea å Intensity at viewpoint = object point light shadow
[Dobashi00] Intensity at viewpoint ò = T l s dt t g H I ) , ( n å = l t I ) , ( t H ) ( t g ) , ( l k = 1 object viewpoint point light shadow mapping render sampling planes with additive blending
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Problems number of planes Accuracy µ number of lattice points
Many planes/lattices for high quality image artifacts due to quantization errors sampling errors pseudo-contours quantization with 8 bit precision in most hardware accumulation of errors in proportion to number of sampling planes increase in rendering time 次に、適用例の説明に入る前に、提案手法での表示精度について議論させていただきます。 提案手法では、こちらの図のように、視点の正面にサンプルプレーンを複数枚配置し、さらにこれをメッシュ状に分割してレンダリングを行なっております。 そのため、提案手法の表示制度はこのサンプルプレーンの枚数とメッシュの分割数に依存することになります。 サンプルプレーンの枚数は、レイトレーシングでの、奥ゆき方向のサンプル数に対応し、また、メッシュ数は画面上でのサンプル数に対応します。 これらのサンプリング数が少ないといわゆるエイリアシング問題が生じます。 rendering time number of planes number of lattice points
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ò ò High Quality Rendering å Intensity at viewpoint point light = P Dt
Is t point light P Il Intensity at viewpoint ò = T l s dt t g H I ) , ( = å n k 1 s t DI ) , ( l Dt ò D + = t l k s dt g H I ) , (
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ò ò High Quality Rendering å Intensity at viewpoint point light = P Dt
) , ( Il = å n k 1 s t DI ) , ( l t P ò D + = t l k s dt g H I ) , ( Dt Is changes severely changes smoothly const. in Dt
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ò ò ò High Quality Rendering å Intensity at viewpoint fh fl
point light Intensity at viewpoint ò = T l s dt t g H I ) , ( Il = å n k 1 s t DI ) , ( l t P ò D + = t l k s dt g H I ) , ( Dt Is fh fl ò D + t l k dt H I ) ( , g x
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ò ò ò High Quality Rendering å Intensity at viewpoint = 1.0 fh fl
point light Intensity at viewpoint ò = T l s dt t g H I ) , ( Il = 1.0 = å n k 1 s t DI ) , ( l scattered light ò D + = t l k s dt g H I ) , ( Is fh fl ò D + t l k dt H I ) ( , g x scattering component
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ò ò ò High Quality Rendering å Intensity at viewpoint fh fl
point light Intensity at viewpoint ò = T l s dt t g H I ) , ( object Il = å n k 1 s t DI ) , ( l ratio of reached light ò D + = t l k s dt g H I ) , ( Is fh fl ò D + t l k dt H I ) ( , g x Illumination component scattering component
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High Quality Rendering
Scattering component fl: ò D + t k dt g ) , ( l changes smoothly can be sampled at a large interval use of texture to store pre-integrated values Illumination component fh: ò D + t l k dt H I ) ( , includes visibility H and intensity distribution Il must be sampled at a short interval sub-planes for accurate sampling
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High Quality Rendering
Scattering component fl: ò D + t k dt g ) , ( l changes smoothly can be sampled at a large interval use of texture to store pre-integrated values Illumination component fh: ò D + t l k dt H I ) ( , includes visibility H and intensity distribution Il must be sampled at a short interval sub-planes for accurate sampling
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Textures for Scattering Component
ò D + - = t c k l dt s F f 2 )) ( exp( ) , br a r (point light) viewpoint point light :phase function ) ( a, l F rc :density b :attenuation ratio a :phase angle s :distance between light and P’ t :distance between viewpoint and P’ tk :distance between viewpoint and P s sampling plane k plane k+1 t P’ tk P a Dt
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Textures for Scattering Component
ò D + - = t c k l dt s F f 2 )) ( exp( ) , br a r (point light) U V point light local coordinate UV k t u + - = ' s / cos a 2 v sampling plane k+1 sampling plane k s Q t a tk viewpoint P’(u’, v) P’ P(u, v) P Dt
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Textures for Scattering Component
) , ( l v u q c f k = U ) exp( k c t br - = ' )) ( ), / (cos , 2 1 du v u F q + ò D l r x point light sampling plane k+1 sampling plane k s k c : constant for each sampling plane Q t v u q ) , ( l : 2D texture a V fl is evaluated precisely since texture stores integrated values tk reducing quantization errors viewpoint P’(u’, v) P(u, v) Dt
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High Quality Rendering
Scattering component fl: ò D + t k dt g ) , ( l changes smoothly can be sampled at a large interval use of texture to store pre-integrated values Illumination component fh: ò D + t l k dt H I ) ( , includes visibility H and intensity distribution Il must be sampled at a short interval sub-planes for accurate sampling
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Computation of Illumination Component
ò D + = t l k h dt H I f ) ( , light mk sub-planes between sampling planes k and k+1 å - = 1 ) ( , k m j l h r H I t f rj : distance between viewpoint and sub-plane j sub-plane viewpoint sampling plane mk is determined adaptively strong intensity many sub-planes
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Intensity of scattered light
Computation of Illumination Component Determining number of sub-planes, mk light 1. shoot a ray 2. compute intensity of scattered light sub-plane use textures for scattering component 3. generate sub-planes in proportion to intensity viewpoint sampling plane same contribution of each sub-plane to pixel intensity Intensity of scattered light mk e :user-specified threshold e
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Overview Introduction Rendering Light Beams
motivation previous work Rendering Light Beams basic Idea problems high quality rendering Rendering the Earth’s Atmosphere rendering sky rendering the earth viewed from space Results Conclusion
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Rendering Earth’s Atmosphere
No shadows of objects earth viewpoint atmosphere Rendering Sky extending method for light beams Rendering the earth viewed from space
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Rendering Earth’s Atmosphere
No shadows of objects Rendering Sky extending method for light beams viewpoint atmosphere Rendering the earth viewed from space atmosphere is very thin layer covering the earth earth
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Rendering Earth’s Atmosphere
No shadows of objects Rendering Sky extending method for light beams viewpoint Rendering the earth viewed from space atmosphere sampling spheres atmosphere is very thin layer covering the earth earth use of sampling spheres instead of sampling plane
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Rendering Earth’s Atmosphere
No shadows of objects Rendering Sky extending method for light beams atmosphere viewpoint earth sampling spheres Rendering the earth viewed from space atmosphere is very thin layer covering the earth use of sampling spheres instead of sampling plane
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Rendering Sky ò Intensity at viewpoint Ps : intensity of sunlight
earth Ps atmosphere Pv sun I ò = T v l sun dt t g s r F I ) , ( a sun I ) ( l : intensity of sunlight s g , : attenuation ratio between Ps and P v t : attenuation ratio between P and Pv F a : phase function : density of particles r
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Rendering Sky ò Intensity at viewpoint : intensity of sunlight
earth viewpoint atmosphere Pv ò = T v l sun dt t g s r F I ) , ( a sun I ) ( l : intensity of sunlight F ) , ( l a : phase function : density of particles t r ) , ( l v t g ) , ( l : attenuation ratio between Ps and P l s g ) , ( : attenuation ratio between P and Pv
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Rendering Sky å Õ Intensity at viewpoint Ps k+1
earth viewpoint atmosphere Pv å Õ = - D n k j v l sun t g s F I 1 ) , ( R a sun I Ps k k+1 sun I ) ( l : intensity of sunlight l s g ) , ( : attenuation ratio between Ps and P P F ) , ( l a : phase function ) , ( l k v t g D : attenuation between sampling planes k and k+1 t ) ( R : cumulative density of particles between sampling planes k and k+1
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Rendering Sky å Õ Intensity at viewpoint Algorithm
= - D n k j v l sun t g s F I 1 ) , ( R a Algorithm create textures of gl , Dgv , R Pv for k = n to 1, repeat: viewpoint map gl , Dgv , R textures onto sampling plane k earth
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Rendering Sky å Õ Intensity at viewpoint Algorithm
= - D n k j v l sun t g s F I 1 ) , ( R a Algorithm create textures of gl , Dgv , R Pv for k = n to 1, repeat: viewpoint map gl , Dgv , R textures onto sampling plane k earth compute IsunF at lattice points
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Rendering Sky å Õ Intensity at viewpoint Algorithm
= - D n k j v l sun t g s F I 1 ) , ( R a Algorithm create textures of gl , Dgv , R Pv for k = n to 1, repeat: viewpoint map gl , Dgv , R textures onto sampling plane k earth compute IsunF at lattice points draw plane with blending: FB = FB x Dgv + F x R x gl (FB: frame buffer) attenuation intensity of scattered light
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Rendering Sky å Õ Intensity at viewpoint Algorithm
= - D n k j v l sun t g s F I 1 ) , ( R a Algorithm create textures of gl , Dgv , R Pv for k = n to 1, repeat: viewpoint map gl , Dgv , R textures onto sampling plane k earth compute IsunF at lattice points draw plane with blending: FB = FB x Dgv + F x R x gl (FB: frame buffer) attenuation intensity of scattered light
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Rendering Sky ò Textures of gl, Dgv , R Ps b
- = s PP dl l ) ( exp( r b s l PP g ) , ( sun I Ps : extinction coefficient (constant) b atmosphere s : density of particles r Pv ) exp( ( ah h - = r (a: const) viewpoint P h earth
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Rendering Sky ò Textures of gl, Dgv , R Ps b
: extinction coefficient (constant) b : density of particles r ) exp( ( ah h - = (a: const) ò s PP dl l g , sun I Ps atmosphere ql s Pv viewpoint P h earth ) , ( l q s h g PP Û
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Rendering Sky ò Textures of gl, Dgv , R store as 2D textures Ps b
: extinction coefficient (constant) b : density of particles r ) exp( ( ah h - = (a: const) ò s PP dl l g , sun I Ps atmosphere qv Pv viewpoint P h store as 2D textures earth ) , ( l q s h g PP Û ) , ( l q v h g PP D Û ) , ( l q v h R PP Û
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Overview Introduction Rendering Light Beams
motivation previous work Rendering Light Beams basic Idea problems high quality rendering Rendering the Earth’s Atmosphere rendering sky rendering the earth viewed from space Results Conclusion
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Experimental Results previous method previous method proposed method
#planes: 40 mesh: 60x60 #planes: 160 mesh: 60x60 #planes: 30 #sub-planes: 120 (ave.) mesh: 10x10 computer: Athlon 1.7GHz, GeForce3
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Experimental Results # of planes (sub-planes) time result method 40
0.13 [sec.] previous ray-tracing 29 [sec.] - interleaved [Keller01] 0.12 [sec.] 160 mesh 60x90 10x15 23 (174) 0.08 [sec.] proposed Image size: 300x450 computer: Athlon 1.7GHz, GeForce3
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Experimental Results interleaved [Keller01] method previous proposed
ray-tracing result # of planes (sub-planes) 40 160 23 (174) - mesh 60x90 10x15 10x15 - time 0.13 [sec.] 0.12 [sec.] 0.08 [sec.] 29 [sec.] Image size: 300x450 computer: Athlon 1.7GHz, GeForce3
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Results sampling plane: 9 sub-plane:309 sampling plane: 30
time: 0.32 [sec.] time: 0.12 [sec.] Image size: 720x480 computer: Athlon 1.7GHz, GeForce3
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Results sampling plane: 100(sky) sampling sphere: 10 30(shaft)
sub-plane:135 sampling sphere: 10 time: 0.06 [sec.] time: 0.16 [sec.] Image size: 720x480 computer: Athlon 1.7GHz, GeForce3
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DEMO Real-time Animation Using Note PC Pentium III (1.2 GHz)
Nvidia GeForce 2 Go
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Conclusion Fast rendering of atmospheric effects
Rendering of light beams 2D textures to store intensities of scattered light sub-planes for precise sampling of shadows Extension to rendering earth’s atmosphere rendering of sky rendering of earth viewed from space
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