Eolas Technologies Incorporated v. Adobe Systems Incorporated et al

Filing 1136

SUR-REPLY to Reply to Response to Motion re 1118 Opposed MOTION for Discovery Motion for Leave to Serve Discovery on Apple, Inc., Patrick Heynen and Los Alamos National Laboratory filed by Eolas Technologies Incorporated, The Regents of the University of California. (Attachments: # 1 Exhibit 4)(McKool, Mike)

EXHIBIT 4

Computer Graphics. 26.2, July 1992

A Fast and Accurate Light Reftection Model
Xiao D. He

Pmrick 0, Heyne/!

Ke""l'fh E. Torrance

Ridwrd L P/riJ/i/ls"

Dm'ill H Sa/esi"

Donald p, Greenher,l!
Program of Computer Graphics
Cornel] Univer.~iIY
Ithaca. New York 14K5}
• Los Alamos National Laboratory
Los Alamos, New Mexico H7545

Abstract
This multimedia paper elaborates on the comprehensive physieallybased light reflection model introduced by He et al. [11. To explain
the model more fully. the paper gives an overview of the light reflection process at a surface. and employs an interactive graphical
100110 demonstrate the reflection model's directional behavior. To
make Ihe model more praclical, lhe paper describes an accurate approximation of the reflection model. based on a spline surface. that
i.~ much fa,~ter to compute. The papert'oncJudes with twO animated
sequences. which demonstrate some features of light reflection that
are accounted for by The model. The full paper demonslnl1es the potential of interactive multimedia. IT is written using MediaView [21. a
system for authoring documents that include graphics. sound. video.
and computer animation.
CR Categories and Subject Descriptors: 13.7 (CompuTer GraphicsJ: Three-Dimension:ll Graphics and Realism: J..l.l lCompuTer

Graphics]: Picture/lmage Generation: 1.2 (Physical Sciences and
Engineering]: Physi(',.
Additional Key Words: reflectance model, multimedia.

In this multimedia paper we :lddress bolh of!he,e issues. To help e.splain the light refle('tion model. the paper gi\'es a graphical overview
or the lighT renection process al a surface. and employs an interactive
graphical Tool TO demonstraTe the model's direCTional behavior. This
tool allows Ihe viewer 10 ob,erve The effects on the various terms of
the light distribution function as parameters arc changed.
To make 'he model practical. lhe paper describe, how The infinite
summation Term can be closely approJlimated by a spline surfa('e and
stored as a small lookup table of control point'. Thi~ approximatioo
allows very fasl compuTation of The full BRDF. as demonslrated hy
'he interat·tive sc,sion, themselves.
Finally. the multimedia paper include~ T o ilnimation ..equent·es.
....
which demonstraTe 'ome lcature, of light reflection that are itC·
(ounted for by the ph~'sically·ha,ed model and were nOt Keounted
for hy previou, modeh.
The full paper wa.' wrillen u,ing the MediaView 'y,tcm. developed
by Richard Phillip, 121. [n this e~tcnded ab,traet. we allemplto give
the flavor of the full multimedia documenl hy u,iflg a ,equence of
iIlustraTion~ from iI' imeractive toob and animations.

2

Introduction
For photorealisli<: image generalion it is essential to use a comprehensive light reflection model that provides a smooth transition
from specular 10 diffuse behavior. In additioo. to ensure aCCllr3C)'
The model must be physically based.
For theSt' reasons. a new general lighT refleclion model was preby He 1'/ (/1. at srGGRAPH '91 I J]. The model is based on
physkal optics and describes specular. directional diffuse. and uni1'0(01 diffuse renel.'lium off a surface. The reneelcd Jighl pallem depends on wavelength. incidence angle. two surface roughness paramelers. and lhl' surface refraClive index.. The model applies to a
widc range of materials and surface finishes. and has been experimenIally verified.
.~enled

Understanding the

ph.~'sically-based

model

The bidiret'Tirm;11 reneeTa'1l'e di'lriburion fun,'lion (BR DF) depend,
on a number of geometrititl and physit'al parameters 111. The ~e·
omelrical parameters include. among other things. the pola' angle
of irM:idence (} and The solid angle of lhe inddenl heam d...·. The
physical parameter, include the wavelength of the light A. as well
as .'ome phY'ical parameters of The surface-its "roughne,s:' given
by fY and T. whkh ,peeir) tile height and width of '01,,11 statislical peah on The 'urfa('e: and its index of refracT inn ii. whieh i, a
function of ,X.

Howe,·cr. ttll.' model IIlso hll.s .~ome dis:ldv'lOl;lges. If conlains an intiniTe summmion teml thaI con~'erges very slOWly. In addition. be'·au",.' the rnlxlel i.s l.'omplc.s. iT is difficult TO understand.

The full BRDF can be di"ided into three major reflection
eomponcll1~-specular. diret·tional diffuse. and uniform diffusewhich in tum can be broken into smaller Tcmh. sut·h as Fresnel re·
flecTivily, effective roughne". and surface masking and shadowing.
Each of ,hese lerms can tx· wrillen a, a function of the various geomt.·Tricill and physical parameters of Ih(' reneeting ,urface and thc
illuminating light.

Permi.'.""n r<> ,"'fIY "'lll<,... r ke ~II "r 1""1 ,t{ til" ",.reri.1 i, ~rJnr,'tI
p"uvi<led (Il.tltle (''file, .,e nol m..w: '" <liM'rt-uted for direCl
("mmerei.l ""v.nr.~e, (Ile ACM (''f>Yrighr nn'''''' .nd lhe utlc of (he
puIlT;.;..r;on.nd it> dare appc... and ....Il;.;" i, ~ivc" lhal '"'''pring i, fly
po:rm;"ion "f (Ile Assn,:,a,ion for C"mpuli!l~ Machiocf)'. Tn ,",oP)'
"rller'.",,,,. '" In rel"'flli'h. requi,e,. fcc '0010' ,pceili<: [lCrmr"~'n

[n lhc multimedia paper. the rcader learns ablJut The behavior of lhe
full BRDF by .~tudying Th.. eflect of lhc,e \'arious parameters on
each (If Ihe model's terms. The user imeracl> with the model by
varying the positions of sliders on The menu shown in Figure 2. To
\'ar)' tht· indt'Jl of refraction Ii. the U.~er change' the m.lIerial "type"
(e.g .. aluminum is selected ;n Figure 21. In addition. hy louehrng

souo

25~

SIGGRAPH '92 Chicago, july 26-31, 1992

0==0.07

0=0.10

0==0.14

0=0.12

0=0.15

\:

Figure 1: Effect of surface roughness u (in p,m) on light reflection

the "Play" bulton, the user can watch a "prerecorded" demonstration of this interaction, which is played back along with an audio
track explaining the parameter effects.
The graphical style of this interactive tool is illustrated in the bottom row of Figure I, which shows a sequence of polar plots of the
full BRDF for aluminum as the surface roughness parameter (u) is
increased.

3

A fast approximation

In order to make the light reflection model computationally
tractable, we describe how it can be approximated by a spline surface. This surface can be computed once for all materials and stored
as a two-dimensional lookup table of control points. A table of
80 x 80 points allows any material's reflection function to be approximated to within a relalive error of I %. Using this spline approximation gives a two-to three-orders-of-magnitude speedup over
computing the summation directly 10 within I % error.

4 Animated sequences
To demonstrate some features of the physically-based light reflection model that are not accounted for by previous models, the paper
uses two animated sequences.
The first animation shows the transition of reflections on the faces of
a roughened aluminum box as the surface roughness (0') increases.
Five frames of this sequence are shown in the top row of Figure I.
Above each frame is shown a schematic diagram of the BRDF for
that value of (1.
The second animation shows the emergence of specular reflection
off a gallery floor as the camera moves to grazing angles. Three
frames of this sequence are shown in Figure 3.

Figure 3: Emergence of specular reflection

AcknOWledgments
This work was supponed by the NSF grant, "Interactive Computer
Graphics Input and Display Techniques" (CCR-8617880), by the
NSF/DARPA Science and Technology Center for Computer Graphics and Scientific Visualization (ASC-8920219), and by generous
donations of equipment from Hewlett-Packard and NeXT.

References
(I J Xiao D. He, Kenneth E. Torrance, Fran\;ois X. Sillion, and Donald P. Greenberg. A comprehensive physical model for light re-

flection. Computer Graphics 25(4); 175-86,1991.
Figure 2: Control panel and document
254

r2j Richard L. Phillips. A general multimedia publishing system.
CommunicaTions of the ACM 34(7),1991.

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