1. 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

2. 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

3. 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

4. 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

5. 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

6. [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

7. 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

8. 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

9. 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

10. ò Shading Model for Light Beams Intensity at viewpoint point source= T l s dt t g H I ) , (
scattered light
Ieye
viewpoint

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. ò ò High Quality Rendering å Intensity at viewpoint point light = P DtIs 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 ) , (

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. Textures for Scattering Componentò 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

25. Textures for Scattering Componentò 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

26. 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

27. 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

28. Computation of Illumination Componentò 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

29. 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

30. 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

31. Rendering Earth’s Atmosphere
No shadows of objects
earth
viewpoint
atmosphere
Rendering Sky
extending method for light beams
Rendering the earth viewed from space

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. 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

49. 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

50. 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

51. DEMO Real-time Animation Using Note PC Pentium III (1.2 GHz)
Nvidia GeForce 2 Go

52. 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