fogshop: real-time design and rendering of inhomogeneous, single-scattering media

FOGSHOP: Real-time Design and Rendering of Inhomogeneous, Single-Scattering Media Kun Zhou, MSRA Qiming Hou, Tsinghua Univ. Minmin Gong, MSRA John Snyder, MSR Baining Guo, MSRA Heung-Yeung Shum, MSRA

Previous Real-Time Techniques

homogeneous fog no spatial variation

layered fog using textures

vertical variation only immersed lights/objects

volume rendering ignores halos/shadows

from [Sun05]

from DX10 volume fog demo

RBF model supports large fog banks immersed viewer

point lighting effects: media’s appearance and shadows

environmental lighting effects: media’s appearance, approx.

shadowssurface reflectance effects due to immersion in media

noise additioneasy-to-use media design system

Fogshop Features

Modeling Inhomogeneous Media with RBFs

optical density = sum of n 3D Gaussian blobs + constant:

easy-to-control modelcompatible with particle systemsanalytic line integral via erf(x) [Stam93]

01

n

ii xx

22exp iiii bxacx

biai ci

T(a,b) is optical depth between 3D points a and b:

light from ab attenuated by exp(-T(a,b))

viewer, vsurface point, p

point light, s

attenuated by exp(-T(v,p))

Attenuation by Inhomogeneous Fog

ababtatx

dtxbaTab

)()(

,0

integrate density along

path ab

Computing Optical Depth via RBF Splatting

draw bounding box for each RBFintegrate analytically in pixel shaderaccumulate over n blobs using alpha blending

multiple splats integrate optical

depth

single RBF splat

airlight models lighted media’s direct appearancedue to light scatter by fog particlesincludes self-shadowing and haloing

volumetric blending (attenuation only)

fogshop (single

scattering)

Fog scatters, not just attenuates, light!

light scatters once off fog particle at x path consists of two segments exponential attenuation along each segmentaccurate for thin media, plausible for denser

viewer, vsurface point, p

point light, s

x view ray

Single-Scattering Model for Airlight

v p

s

T(v,x)

T(s,x)

x

Single-Scattering Integral dtxsTxvT

sxIxkxL

pv

a ),(),(exp)( 20

0

v p

s

T(v,x)

T(s,x)

x


sxIxkxL

pv

a ),(),(exp)( 20

0

x(t) : scattering location along view ray

v p

s

T(v,x)

T(s,x)

x


sxIxkxL

pv

a ),(),(exp)( 20

0

(x) : optical density at x

v p

s

T(v,x)

T(s,x)

x


sxIxkxL

pv

a ),(),(exp)( 20

0

k() : phase function [constant]

v p

s

T(v,x)

T(s,x)

x


sxIxkxL

pv

a ),(),(exp)( 20

0

I0 : light source intensity

v p

s

T(v,x)

T(s,x)

x


sxIxkxL

pv

a ),(),(exp)( 20

0

radiance reaching x, neglecting attenuation

v p

s

T(v,x)

T(s,x)

x


sxIxkxL

pv

a ),(),(exp)( 20

0

T(v,x), T(s,x) : optical depths

v p

s

T(v,x)

T(s,x)

x


sxIxkxL

pv

a ),(),(exp)( 20

0

total attenuation along path

v

s

view ray samples xi x

i

iii

iia xsxTxvTsx

IxkxL ),(),(exp)( 20

Brute Force Numerical Integration


T(s,xi-2)

v

s

xi-2

T(v,xi-2)

i

iii

iia xsxTxvTsx



iii

iiia xsxTxvT

sxIxkxL ),(),(exp)( 2

0

T(s,xi-1)

v

s

xi-1

T(v,xi-1)


• need many samples xi along every view ray• each needs two optical depth integrals• too expensive for real-time!

i

iii

iia xsxTxvTsx


T(s,xi)

v

s

xi

T(v,xi)

Our Approximation: Decompose by RBFs…

dtsxTxvTsx

IxLpv

a ),(),(exp41)( 2

00


dtsxTxvTsx

Ix

dtsxTxvTsx

IxL

pv n

ii

pv

a

),(),(exp41)(

),(),(exp41)(

20

01

0

20

0


dt

xf

sxTxvTsx

Ix

dtsxTxvTsx

IxL

pv n

ii

pv

a

)(

),(),(exp41)(

),(),(exp41)(

20

01

0

20

0


n

i

pv

i

pv

pv n

ii

pv

a

dtxfxdtxf

dt

xf

sxTxvTsx

Ix

dtsxTxvTsx

IxL

100 0

20

01

0

20

0

)()()(

)(

),(),(exp41)(

),(),(exp41)(


n

ii

n

i

i

pv

i

pv

pv n

ii

pv

a

LL

L

dtxfx

L

dtxf

dt

xf

sxTxvTsx

Ix

dtsxTxvTsx

IxL

10

10

0

0 0

20

01

0

20

0

)()()(

)(

),(),(exp41)(

),(),(exp41)(

… and compute Li with a single sample. i

rib

v

bi

x(t)

dtxbfdtxfxLpv

iri

pv

ii

00

)()()()(

… and compute Li with a single sample.

• projected center is point of max density along view ray

• assumes f (x) smooth wrt blob’s width• i integrated analytically

dtxbfdtxfxLpv

iri

pv

ii

00

)()()()(

rib

i

rib

v

bi

x(t)

use red light path through for blob i [per-ray varying]

use blue light path through bi for other blobs j ≠ i [ray invariant]

ib

rib

v

s

Computing Li : Separate Light Pathsrib

Reuse optical depth integrals over many view rays.

iT

iT

Computing the constant term L0

use similar light path separation trickapply analytic method of [Sun05] see paper for details

Accuracy of Our Approximation

fogshopray traced

),(),(exp41)( 2

0 sxTxvTsx

Ixf

not

smooth

ray traced fogshop

T(x,s) discontinuous(light shafts)

small(looking right at light)

sx

Inaccuracy of Our Approximationwhen

Handling Environmental Airlight

L : environment lighting in SH basisTr : optical depth along view ray r from v∞

PSF : point spread function (for convolving environment)

attenuated & scatteredonly attenuated

PSFLTTLTL rrra *)exp()exp(

* =PSFL

(before scatter)L*PSF

(after scatter)

Environmental Airlight: Results

point airlight environment airlight

surfaces immersed in mediumincident radiance affected by scatteringsubtle yet noticeable effects:

softened shading blurred highlight media’s shadow

can get away with lots of approximation

Standard Slide without subtitleSurface Reflectance: Why?

assume homogeneous medium of average density average varies at each pixel, creating inhomogeneous effects point light: average in single direction sp environment light: average all around puse SH lighting and PSF [Sun05]

Standard Slide without subtitleSurface Reflectance: How?

point light s environment light L

pp

Standard Slide without subtitleSurface Reflectance: Results

point light environment light

break up RBF’s circular shape perturb view rays, indexed by be consistent when camera rotates add noise in world space

Standard Slide without subtitleAdding Noise

without noise with noise

view rayperturbed view ray

v

noise perturbation

rib

rib

preliminary steps render depth maps from camera & lights(immersed) surface renderingairlight rendering

Standard Slide without subtitleRendering Summary

compute T(s,p) for each point light s using RBF splatting to cube mapcompute average optical depth at object centers if using environmental lightingshade per-vertexrender to scene target

Standard Slide without subtitleSurface Rendering

compute T(v,bi), T(s,v), T(s,bi) plane sweep algorithm on CPUaccumulate airlight and screen optical depth T(v,p) perturb view rays if noise enabled computed on GPUattenuate scene target and add airlight

Standard Slide without subtitleAirlight Rendering

+scene target optical depth airlight

result

=

( )

brush/erasercopy/pasteparticle emitterairbrushreal-time light and camera change

Standard Slide without subtitleInteractive Media Design

scripted using a simple languageparabolic path default

Standard Slide without subtitleInteractive Media Design: Particle

Emitter

particles bounce off scene surfacescollision detection using kd-tree ray tracer

Standard Slide without subtitleInteractive Media Design: Airbrush

Performancescene #

vertices#

RBFs # lights fps

gargoyle 78,054 34 3 101box 8,901 3008 1 34terrain 65,047 292 env. map 92city 77,226 353 env. map 162motorcycle 44,430 1223 env. map 31

3.75 Ghz PC, 2GB memory, Nvidia 8800GTX

Contributionsanalytical model of single scattering for spatially-varying mediaenables visually accurate, real-time renderingeasy-to-use tools for interactive media designmain new ideas: decompose scattering integral, one term per RBF sample term at peak of its RBF along view ray optical depth integrals for other RBFs:

• sampled at RBF center• precomputed and reused for multiple view rays

Limitationsinaccurate approximation near lightslight shafts ignoredenvironmental lighting:— low-frequency and distant— very approximate shadows (averages in all directions)— use PRT for self-shadows on scene objects

Future Worklight shaftsmultiple scatteringmixed surface-surface and media-surface shadowing

Thanks!

fogshop: real-time design and rendering of inhomogeneous, single-scattering media

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