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### Transcript of Ian Mallett (me), Cem Yuksel · PDF file Ian Mallett (me), Cem Yuksel University of Utah, USA....

• Parameterization of Tabulated BRDFs Ian Mallett (me), Cem Yuksel

University of Utah, USA

• Background / Motivation

● BRDFs describe light scattering

● Extremely important to realism

● Measured data is realistic – e.g. Matusik et al. 2003

• Background / Motivation

BRDF Data Table BRDF

Parameterization

● What parameterization (mapping of data to BRDF's angle space) should we use?

θin

φin

θout

• Background / Motivation

● Literature lacks general methods to compare and generate parameterizations!

• Contributions

1. Framework to generate and evaluate parameterizations

2. Provide example parameterization and analysis

3. Discuss related technical and theoretical issues

• Mathematical Framework

● Want parameterization to importance-sample BRDF:

γ is angle state vector (θin,φin,θout,φout) s is parameter vector (s inθ ,s inφ ,s outθ ,s outφ )

● We describe how to formulate this in the paper

d γ d s

∝BRDF (γ)

d γ d s

∝ BRDF (γ)

• Example Parameterization

● Fit a quadratic Bézier curve for each table axis

P1 P0

P2

Effect on BRDF data spacing: Higher density near specular plane (green/blue axes)

• Example Parameterization

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

ch ro

m e-

st ee

l tu

ng st

en -c

ar bi

de ss

44 0

st ee

l ch

ro m

e bl

ac k-

ob si

di an

al um

in iu

m br

as s

bl ue

-m et

al lic

-p ai

nt 2

sp ec

ul ar

-b la

ck -p

he no

lic he

m at

ite si

lic on

-n itr

re d-

m et

al lic

-p ai

nt go

ld -m

et al

lic -p

ai nt

3 co

lo r-

ch an

gi ng

-p ai

nt 3

bl ac

k- ph

en ol

ic gr

ea se

-c ov

er ed

-s te

el ni

ck el

gr ee

n- m

et al

lic -p

ai nt

2 co

lo r-

ch an

gi ng

-p ai

nt 1

fr ui

tw oo

d- 24

1 pv

c sp

ec ia

l-w al

nu t-2

24 bl

ac k-

ox id

iz ed

-s te

el co

lo r-

ch an

gi ng

-p ai

nt 2

na tu

ra l-2

09 da

rk -s

pe cu

la r-f

ab ric

ip sw

ic h-

pi ne

-2 21

ch er

ry -2

35 sp

ec ul

ar -b

lu e-

ph en

ol ic

sp ec

ul ar

-g re

en -p

he no

lic go

ld -m

et al

lic -p

ai nt

2 co

lo ni

al -m

ap le

-2 23

bl ac

k- so

ft- pl

as tic

gr ee

n- m

et al

lic -p

ai nt

al um

-b ro

nz e

vi ol

et -a

cr yl

ic tw

o- la

ye r-

go ld

da rk

-b lu

e- pa

in t

tw o-

la ye

r- si

lv er

pu rp

le -p

ai nt

sp ec

ul ar

-v io

le t-p

he no

lic si

lv er

-m et

al lic

-p ai

nt bl

ue -m

et al

lic -p

ai nt

gr ee

n- ac

ry lic

bl ue

-r ub

be r

gr ee

n- fa

br ic

ye llo

w -m

at te

-p la

st ic

go ld

-m et

al lic

-p ai

nt re

d- ph

en ol

ic sp

ec ul

ar -m

ar oo

n- ph

en ol

ic lig

ht -b

ro w

n- fa

br ic

bl ac

k- fa

br ic

bl ue

-a cr

yl ic

bl ue

-f ab

ric go

ld -p

ai nt

si lv

er -m

et al

lic -p

ai nt

2 re

d- pl

as tic

pi ck

le d-

oa k-

26 0

gr ee

n- pl

as tic

da rk

-r ed

-p ai

nt si

lv er

-p ai

nt ny

lo n

po ly

ur et

ha ne

-f oa

m m

ar oo

n- pl

as tic

re d-

sp ec

ul ar

-p la

st ic

re d-

fa br

ic 2

gr ay

-p la

st ic

sp ec

ul ar

-r ed

-p he

no lic

av en

tu rn

in e

sp ec

ul ar

-w hi

te -p

he no

lic lig

ht -r

ed -p

ai nt

pe ar

l-p ai

nt w

hi te

-p ai

nt pi

nk -ja

sp er

w hi

te -d

iff us

e- bb

al l

ye llo

w -p

la st

ic de

lri n

sp ec

ul ar

-y el

lo w

-p he

no lic

vi ol

et -r

ub be

r al

um in

a- ox

id e

sp ec

ul ar

-o ra

ng e-

ph en

ol ic

w hi

te -m

ar bl

e te

flo n

gr ee

n- la

te x

ne op

re ne

-r ub

be r

ye llo

w -p

ai nt

or an

ge -p

ai nt

pi nk

-f ab

ric 2

pi nk

-fe lt

ye llo

w -p

he no

lic pi

nk -p

la st

ic re

d- fa

br ic

po ly

et hy

le ne

w hi

te -f

ab ric

2 pu

re -r

ub be

r be

ig e-

fa br

ic w

hi te

-a cr

yl ic

pi nk

-fa br

ic w

hi te

-f ab

ric

Bezier Uniform Identity

• Example Parameterization

● More examples in paper . . .

• Higher-Order Reconstruction Filtering

● Important for measured data

● We suggest cubic B-spline – Good results

– Efficient GPU implementation (Sigg and Hadwiger 2005)

• Higher-Order Reconstruction Filtering

Linear Filter Higher-Order Filter (Cubic B-spline)

• Conclusion

● Propose new mathematical framework to generate and analyze parameterizations

● Validate our approach by generating and analyzing an example parameterization

● Discuss higher-order filtering for measured BRDFs

• Questions

• External Image Sources

● BRDF picture: Derived from https://en.wikipedia.org/wiki/Bidirectional_scattering _distribution_function#/media/File:BSDF05_800.png

● BRDF diagram: remade from http://cybertron.cg.tu-berlin.de/rapid_prototyping_1 1ws/rp_brdf/img/reflection_t.png

● University of Utah and CGI images adapted from respective websites

http://cybertron.cg.tu-berlin.de/rapid_prototyping_11ws/rp_brdf/img/reflection_t.png http://cybertron.cg.tu-berlin.de/rapid_prototyping_11ws/rp_brdf/img/reflection_t.png

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