Dallas, August 18-22

Volume 20, Number 4, 1986

CONTINUOUS TONE REPRESENTATION OF THREE-DIMENSIO;qAL OBJECTSILLUMINATED BY SKY LIGHT

Tomoyuki

Nishitaand1.

Abstract
Naturallighting
models
to
date
have
been
limitedtocalculationof
directsunlight.
However, this paper proposes an improved modelfornaturallighting
calculations
thatadequately
considers both direct sunlight and scatteredlightcausedby clouds and other forms of water vapor in
the air.
Such indirect
naturallight
is termed
skylight
andcan bean importantfactorwhen
attemptingtorenderrealistic looking images as
they might appear under overcast skies.
In the proposed natural lighting model, theskyis considered
to bea hemispherewith a large
radius (called the sky dome) that acts as a sourceof diffuse
light
with
nonuniform intensity.
In
order
to
adequately
tak6
into
account
thenonuniform intensity of such skylight, the sky domeissubdivided
into bands.
The
light intensity
withinindividual
bands
can beassumedto betransversely uniform and longitudinally
nonuniform
and therefore
thetotal luminance emanating fromeach band can be calculated more accurately.
The proposed method significantly
improves
therealismofnaturallighting
effects.
Its
advantages
areparticularly
apparent
whensimmlating lighting under an overcast skyor whenrendering
surfacesthat fall within a shadow castby an obstruction lit by direct sunlight.
CR Categories
andSubject
Descriptors:
1.3.7[Computer Graphics]: Three-Dimensional Graphics andRealism;],3.3[Computer Graphics]: Picture/Image
Generation
Terms: Algorithms

Additional Key Words
andPhrases:shading,skylight,
shadows, interreflection of light, daylight
factor, distributed light source

Permission to copy without fee all or part of this material is granted
provided that the copies are not made or distributed for directcommercial advantage, the ACM copyright notice and the title of the
publication and its date appear, and notice is given that copying is bypermission of the Association for Computing Machinery. To copy
otherwise, or to republish, requires a fee and/or specific permission.
© 1986

ACM0-89791-196-2/86/008/0125

Nakamae

Hiroshima
University
Saijocho,
Higashihiroshima
724, Japan

Fukuyama
University
Higashimura,
Fukuyama
729-02,Japan

GeneralEihachiro$00.75INTRODUCTION

Recently, various display techniques
have
been
developedby numerous researchers, for such things
as trees, natural terrain, clouds andfog effects[1-5].
Still other algorithms have been developedtotreatsuch problems
astexturemapping,reflection,refraction
and transparency[6,7].
Muchof thisresearchhas
beendesignedtofacilitate
generationof more and more realistic
looking simulations of various environments.
The visualappearanceofsuch
simulatedenvironments
depends
to a great
extenton thelighting model used to illuminate
theobjects
intheenvironment.
In this connection~ researchers
have already developed lighting models for various
types
of light sources [8-9] as well as algorithms
that
take
into
account
theeffectofinterreflection among objects [10-12].
However,todate,lighting
modelshave been
limitedtoeitherartificial
lightsourcesordirectsunlight.
In
fact,
though,ahighpercentageof the environments to be simulated arenaturally lit by what is commonly called
daylight;
i.e. a combination of direct sunlight and skylight.
Oneof the mosttroublesome problems when using
only direct sunlight as a lightsourceis thatobjects
inshadow
appear to be unnaturally dark.
One common solution to this problem
is to
add
a
uniform
ambient
light to the lighting model.
But
this tends to hide any surface unenvennessof theobjects
inshadow
since all parts of the surface
are lit evenly,
Another common approach is toaddasecondarylightsourcecoincident
withtheviewer's eye point.
While
this
is a convenientsolution,it detracts
from the realism of shaded
renderings.
In order to overcome such problems
ina general way, this paper proposes a lighting model
forskylight
which,
when
combinedwithdirectsunlight,
allowsincreased realism when rendering
natural environments.
Fundamentally,
skylight
can bethoughttoemanatefrom thesky dome whichsurrounds theearth.
The sky dome can be treated as a hemisphereof very large radius,
However, skylightintensity
is not uniform
accross the entire surface of thesky dome
and will
also vary
greatlywiththeweather(e.g.,
clear
sky or overcast sky).
Inorder to handle such nonuniformity in a consistentmanner,thepaper
introduces
the
idea
of
subdividing the sky dome into light emanating bands
whose intensity is uniform within
its boundaries;
theidea that the intensity of an entire band canbe approximated by
calculatingtheintensityof125

S I G G R A P H

samplelines
located at the center of such bands;
and the idea of alternative methods for calculatingsuch intensities undereitherclear
or overcast
skies.
2. ASSUMPTIONSAND FUNDAMENTAL

band

'86

sourceIDEAS
sample lineAsalready mentioned, daylight is a combinationof direct
sunlight
anddiffuseskylight.
This
paper
will
only
discuss
how to handle skylight.
Direct sunlight can be h a n d l e d in thenormalway,
which is to treat it as a parallel light source.
Intensityofskylight(also
calledsky
luminance)
is notuniformandits distribution
varies significantly depending on whetherthesky
is clearor overcast.
Such variations
due toweather conditions are discussed in this paper.
The color of skylight is also
notuniform
andits
spectral
distribution
variessignificantly
depending on solar altitude.
This is mostobviousatsunriseandsunset w h e n the sun is low on thehorizon.
Althoughsomeof the mostbeautifulnatural lighting effects occur at these
times
of
the
day, the issue of spectral distribution is notdiscussedin thispaper.
However,
spectral
distributionissuggested
as topicforfutureresearchwithintheconceptual
framework of themodel for skylighting proposed here.
Before b e g i n n i n g the calculation ofilluminanceat a given point in the scene, it is n e c e s s a r y totheresultingshadows.
test for obstructions andTheshadowboundaries
that
would
be
caused bydirect sunlight on a clear day are determined by anoverlap test of objects on theperspectiveplanewhen viewed from the sun (see [13]).
The
ill~iminance from skylight can be c a l c u l a t e d
by determining the area of the sky visible from thegiven point in the scene.
In the proposed lighting
model, the skydome
is divided
into bands
whichthemselves
donotnecessarily
have
uniform
luminance.
Therefore, the total luminancefromavisiblearea of the sky must be derived by summingtheluminancesof thevisible
areas
of
the
individual bands.
The illuminance at a given point in the scene is
a combinationof light
from thesky and lightreflected
from thegroundand/orsurrounding
The ratio b e t w e e n skylight and r e f l e c t e dobjects.
light from the ground depends on the declination of
the plane including the given point in the scene.
Interrefleetion of light b e t w e e n objects in thescene mustalso be c o n s i d e r e d in order to acheivean accurate simulation of naturallighting.
Thisis p a r t i c u l a r l yimportantw h e n creating interior
scenes w i t h m a n y objects in a room.
In such cases,
the interreflection luminance can be determinedbyfirst
subdividing
the faces of the objects in thescene (suchas walls,
furniture,
etc.)
into
a
suitable number of subsurfaces and then calculating
theinterreflection
at theverticesof eachsubsurface (see Ill]).
The ground and all other objects
in thescene
areassumedto besets
of convex p o l y h e d r a andconvex polygons.
The surfaces of all p o l y h e d r a are
assumed to be Lambertian surfaces; i.e.,
perfectly
diffuse.
The
ground itself is treated as a large
area surface w i t h u n i f o r m luminance.
3-

ILLUMINANCE126

CALCULATIONFOR SKY LIGHT

%×
Fig.

1 Subdivision of the sky dome to bandsources (P:the calculation point).

If the intensity of sky light were
uniform;
it
has
been
shown
that
the
illtuninance at a given
point can be calculated by using
a configuration
factor.
A configuration factor is the ratio of theareaof the visible sky p r o j e c t e d onto the base of
the sky dome vs. the total area of the base of thesky dome(This ratio is also called the sky factor).
llluminanee
at a given point is then obtained by
the m u l t i p l i c a t i o n of the configuration factor
andthesky luminance.
The c o n f i g u r a t i o n factor isu s u a l l y obtainedbycontourintegrationof thevisible areas of the sky (refer to Eef. [9] for thecontour integration m e t h o d for area sources).
However,thedistributionof sky luminance isnonuniform in most cases.
The d i s t r i b u t i o n of thesky luminance varies depending on sites, time, andseasons.
In
order
to
deal
with
varieddistributions,thefollowing
methodsmight
beconsidered:(a) Generatem a n y s~nple points on the sky domed
and set the w e i g h t i n g factor p r o p o r t i o n a l to sky
luminance of each point.
(b)
Subdividethesky dome
into m a n yfiniteelements (e.g., rectangular elements).
(c) Subdivide the sky dome into m a n y b a n d elements(we call these elements "band sources").
In methods (a) or(b)~ both
theilluminanee
calculation
andthevisibility
test
used
to
calculate the effect taking account of obstructions
have to be done for each pointoreachelement,
respectively.
M e t h o d (e) is less costly comparedw i t h the other methods forthefollowing
reasons(see Fig.l).
(i) The calculation point can always be handled astheeffective
centerof the sky dome h e m i s p h e r ebecause of the dome's very large radius.
(2)Theluminanceofband
sources
is assumed
to becontinuously
varyingwithrespecttothelongitudinal
directionof the band source.
(3)
The center line of thehandsourceis calleda"sampleline" and a plane consisting of the sample
line and thecenterof hemisphereiscalleda"sampleplane".
The sample plane of the i t h bandsource, St, is definedas theintersection
line
betweenthehemisphereand the plane whose tilt
angle is ~£.
The visiblepartsof theband
sources are determined b y using these sample lines.
Thenthe illuminance can be obtained by adding theDallas, August 18-22

Volume 20, Number 4, 1986'

sample lineyZelement

P0
Xx

building
Fig. 2 Calculation of visible areas of a band

Fig. 3 Distribution of sky luminance.

source by using a sample line.
illuminances of the visible parts of the bandsources(Fig.2 shows the visible parts of sample
lines
on
the
orthogonal
projection);theintersections between obstacles and sample lines
can be obtained by testing theintersections
between the obstacles and the sample planes in theobject space (see 3.3).

dA is the area of the sky element (dA=(rd0~)(rd6sin~)) (see Fig.3).
By integrating equation(i) with respect to c~ and 6, the illuminance due tothe band source between 0 and ~ is given by
E%(e) = [ J69,,+IL(~,6) singsin~2dgd~:o "6£
f

3.i Illuminance Calculation from only Sky LightThe
calculation
method of illuminance on
skyward-facing horizontal surfaces, which are top
surfacesofobjectssuch as the ground,isdiscussed here.
In this case, taking reflected
light from the ground into account is unnecessary.
5.1.1 Illuminance from Unobstructed Sky
As mentioned before, the calculation point canalways be handled as the center of the sky dome.
For simple calculation,
we define the coordinate
system so that the horizontal plane including the
calculation pointis the X-Y plane, which iscoincident with the base of the sky dome with aradius r; the calculation point is the origin of
the coordinate system.
The sample planes are determined as declined
planes which include the X-axis and whose elevation
angles are~ ( £ = 1 , 2 ~ .~N;
N=thenumberofsubdivisions) (see Fig.~iThe band source may be
broken down into small "sky elements", each ofwhich may be considered to haveaconstant
luminance.
By treating the sky elements as apoint source Pc" the inverse-square law may be
applied for illuminance at a calculation point P.
By expressing the position of Pe with angle ~ fromX-axis(PP0) to sky element
and angle 6 fromhorizontal plane to sky element, the illuminance at
P due to the sky element represented by Pe is givenbydE = L(~,6)eosO/rZdA,(1)

where L is the sky luminance at PoD 8 is the angle
fromthezenithtoPe(cos@ :sin~sing),rcorresponds to the distance between P and Pe, and

,

(2)

t

where f6
=6£-~,
6Z+ 1 =6£+A6, 246 is the angularwidth o £a band source.
Let 's consider the case of a uniformsky
In this case,L(~,6)=L0(i.e.,
luminance first.
constant),
then equation (2) becomes the following
equation.
E£(~)=0.5d~(c~-cosc~sinc~)L 0 ,(3)where d~=(cos@$Tcos~$+l ). In this paper, we set
the angle of ~he sample plane r @i(J~=i,2,...,N), asd£=i/N (constant).
In the case of nonuniform sky luminance,
if it
is assumed that the luminance in the small width,@~< 6 <61+ 1 ,isconstant,thenL(c~,6)isrepresentedbyL( ~, 6~) .
Thus,
equation(2 )becomes the following equation.

s;

Eg(a)=d z L(a, 6£)sin~ d~(4).

Empirical formulas for calculating theof both overcast
skies and clear skies
determined by the CIE for international
distribution
is defined as the relative
to the luminance of the zenith.
a)theovercastsky(theluminance funetion[lh] )L( 8)=Lz (l+2cos @)/3

CIE

luminance
have beenuse; theluminance

Standard,

Lz: luminance of the zenith,@ :the angle from the zenith
element,

sky

(5)

to

a

sky

where Lz is the function of the solar altitude,
L(0) is independent to thesun position.
above equation means that the sky luminance ishighest at the zenith and the lowest around

but
The
the
the

127

//

~. S I G G R A P H

horizon.
b) the clear sky (the CIE Standard sky luminancefunction[15])(. 91+10exp ( -37) + .45cos¥) (l-exp(-. 32sec@) )L ( O , ¢ ) =L zz0.274(0.91+10exp(-3z0)+0.45cosz0)(6)
y : the angle from the sun to a sky element;(eosY=cosz0.eose+sinz0.sine'eos(@-¢0))z0: the angle from the zenith to the sun,: the azimuth angle from X-axis to the sky
element,@0: the azimuth angle from X-axis to the sun.
The above mentioned equation means that the sky
luminance varies with thesun position.
Sky
luminanceis highest in the region of the sun andlowest at about 90 ° from it.
3.1.2 Illuminance Calculation Taking Account of
Obstructions
E~(~).in equation (2) is the illuminance due tothe reglon between 0 and ~ in a band source.
Therefore, if the region between ~I and ~2 , where~i~2,
is visible
from the calculation point, P(see Fig.2), the illuminance by the source in thisregion can be easily obtained as Ei(~2)-Ez(~i).
The visible parts detection method is describedinthe section 3.3 o£ this paper.
It is convenient toprecalculate values of E£(~) and store them in lookup tables.
In this paper, values are prepared
every ten degrees, and the E l at an arbitrary e iscomputed by linear interpolation.
In casesuch as a partly cloudy sky which fall
between a completely overcast sky and a completely
clear sky, we can blend the results of equations(5) and (6) even though the approximation precision
is not very accurate because ofthevarieddistribution of clouds.
Using a distribution of
measured data would be better.
Look up tables
could be obtained for any particular kind of sky

conditions if the distribution was given.
And ifthe measured data included spectral distributions,
it would be possible to compute illuminanee taking
into account spectral variations by preparing lookup tables as functions of the spectrum.
3.2 Illuminance Calculation Taking into AccountReflected Light
Reflected light is composed of light reflectedfrom the ground,light reflected from buildings,
and the interrefleetion of light between buildings,
ground and other objects(see Ref.[ll~12]
forinterreflection of light).
First, we describe thereflected light from the ground.
Slopedsurfacesare usually illuminated byreflected light from the ground.
Assuming thatthe ground is a large
surface with a uniform
brightness, the illuminanee on the sloped surfaces
can be obtained by inclining the hemisphere (seeFig. h-a ).
Thatis, the upper partofthehemisphere above the horizontal plane including the
calculation point has the sky luminances and thelower part has the luminance of the ground.
Theilluminanceof the groundis obtained by the
productof the sky illuminance and the groundreflectance, where the illuminance on the ground isassumed to be the illuminance from the unobstructedsky.
When the inclined angle of the face Sf is 8, theilluminance on Sf can be calculated with a look up
table, EZB(~) which is pre-calculated by inclining
L(C~,6) by the angle 8The part of L(c~,6) under
the horizontal plane is set as the luminance of theground(the dotted area in Fig. h-b shows theluminance of the ground).
In order to simplify the calculation, we assume
that the illuminanee of each face is uniform(thearea, which can't be assumed uniform, may be
subdivided
into subsurfaces ). Let 's consider thereflected light from a face S in Fig. 4-b, the face
S exists between c~z and c~2 oL the sample line, thenYsky light/Jhorizontal plane
including p[ Iground~reflcction

~<__
~

S

~

.

~

iiiiiiiiiiiilijiiiiiii!iliiii

uminance of ground(a):side view(b):projection onto the base of the hemisphere
Fig. 4 Illuminance calculation for a sloped plane(the origin of the coordinate system is the calculation point P;
the X-axis is parallel to the horizontal plane)

128

'86

Dallas, August 18-22
I

I

Volume 20, Number 4, 1986

I

plane

iZ

?

•

i

I

I

Y

sf
(a)

(b)

Fig. S Intersection test between sample planes and objects.
the illuminance due to this region can be obtainedby substituting Lo in equation (2) to the luminanceof S.
This calculation is done only for faces
visible from the calculation point, and can beomitted for small and low reflectance faces.

I

\

\

/ /

\

\

3.3 Calculation of the Visible Parts of the Sky
In order to consider the effect of obstructions,the visible parts of the sky viewed from thecalculation point mustbedetermined,The
illuminance at a point P on a face ST can beobtained by extracting the visible sections--of theband sources; the procedure is as follows:i) Extract the objects that cast shadows on theface Sf (i.e., objects existing in front of S~;
e.g. , IV in Fig.4-a).
2) Transform the coordinates of these objects inorder to set S~ as the base of hemisphere
(see

L

!

L

k

L~
~l

"

,,I

Fig.5-a).
3) Calculate the existing range of each object(the range is defined by the elevation
angle;
e.g., 6min and 6mG~ in Fig.5-a).
4) Extract the contour lines of each object whenviewed from the calculation point.
5) Execute the following calculation sequence foreach sample plane;i) Extract the objects intersecting with thesample plane by using the range solved in 3) andthe elevation angle of the sample plane.
ii)
Calculate the intersections between thecontour line of each object and the sample plane,
and get the angles, ~ ( i = 1 , 2 .... m), corresponding
to the intersections (in Fig.5-h, ~, is obtained by
the inner product of vectors PPI and PP0).
iii) Extract the visible sections of the sample
line (e.g., the section ele2 in Fig.2, see [16] for
hidden line elimination).
iv) Calculate the iliuminance due to each visible
section by using the look up table, El.
3.4

IlluminanceInteriors

Calculationfor

Naturally

Lit

The illuminance at a calculation point in a room
is usually influenced not only by the sky light andthe ground light coming in through the windows but
also by interreflection of light between objects in
the room.
Therefore,
in the first step, theilluminance due to the light source from thewindows is calculated, and then the interreflection
is calculated by using the direct illuminance from
windows(see Ref.[ll]for the calculation ofinterreflection).

lJ

r / I l l / I / I l l

1 / / I / I / 1 / /I///I//1/l/

Fig. 6 Components of light in a room.
(Ll:direct light from sky, L2:reflected lightfrom the ground, L3:interreflection of light)
It is unnecessary to consider the whole sky forthe shading calculation of an interior because of
the limited regions of the windows.
Therefore, for the calculation of the directcomponent from the sky light, the following terms
should be considered for interiors :a) The illuminance on a face, from which allwindows are invisible, is zero (e.g., the window
is on the back side of the faces such as Sl, $2,
S~, $s in Fig.6).
b) Sample planes are only required to be generated
within the range of the windows.
c) For shadow calculations,
it is enough toextract the objects only within the pyramids
composed by the windows and the calculation
point (see Fig.6).

4. DAYLIGHT FACTORS
The illuminanee from windows depends on the sky
ituninance.
Therefore, the daylight factor isusually used for lighting design in daytime: it isdefined as the
ratio
betweenthedaylight
illuuninance at a point in the interior and the129

S I G G R A P H '86

BII

simultaneous exterior illuminance available on ahorizontal plane from an unobstructed sky expressed
as a percentage.
Superimposing the color belts of the daylight
factor on the shaded images is used in the examples
here; each color corresponds to the value of its
daylight factor(see examples in Fig.10). With
this depiction method, we can easily grasp thenumerical values and the scene simultaneously.

(All sample images found in this paper were made inthis room.)
Fig.10 shows examples of daylight
factors.
Pictures(a) and (b) show the distribution of
daylight factors with an overcast sky and with aclear sky, respectively;
the daylight factor isdefined only for sky light, then(b) does notinclude direct sunlight.
Picture(c) shows the
distribution of daylight factors with a clear sky.
The color belts on the images show that the
distribution of illuminance caused by the sky lightis very complex and depends greatly on the sun's
position.
However, using the proposed method, we
can design the daylighting of the room accurately.
Table 1 shows the computation times for Fig.8(b)and Fig.9. All computation was performed on a
TOSBAC
DS-600/80 32bit minicomputer.
In thispaper, the multi-scanning method is usedfor
anti-aliasing(see section 2.5 in Ref.[17]).
Inthese examples, Mach bands are slightly visible,
because the illuminance at the calculation point issampled along the sample lines.
In these examples,the ground reflectance is0.25, and the number of sample planes (see section
3)
for
Fig.8
and
Fig.9
are 20 and 200,
respectively.
Note that the effective
sampleplanes for Fig.9 are limited (see 3.4).
These examples make clear that accounting forsky light and its shadow effects is very useful for
generating realistic images, especially in cloudy
weather, and is helpful for designing buildings andlighting interiors.

5. EXAMPLES
Fig.7 shows the shaded images of a simple
object.
Picture (a) shows the object with only
( b ) ; uniform skylight, (c): an
direct sunlight,
overcast sky, (d): a clear sky (only skylight), and(e): a clear sky (including direct sunlight).
Fig.8 shows the outdoor scenes of a building
undervariousconditions.
Picture (a) shows
the building with direct
sunlight and uniform
ambient light.
Pictures (b) and (c) are with an
overcastsky
and a clear sky, respectively.
Pictures in this sequence takeinto
account
reflected light from the ground and other objects.
In
the previous methods,
shadows under an
overcast sky are ignored. As shown in Fig.8-b andc,there are penumbrae which means that theboundaries of shadows are not sharp.
Thesepenumbrae are more realistic and make it easy torecognize the shapes of objects
in shadows.
InFig.
8-a and Fig.7-a, it is difficult bo grasp the
shapes of objects
in the shadows because only
direct sunlight and uniform ambient light areconsidered.
Fig.9 shows the interior of a computer room
illuminated by a clear sky; in this figure theinterrefleetion of light from walIs and objects istaken into account.
Notice that the parts of thewalles farther from the window are also bright.

(a)I

6. CONCLUSION
A representation method for three-dimensional
objects
illuminated by
sky
light
has
been
proposed.
The following conclusions can be stated from the

(c)

(b)

(d)
Fig. 7 Example for a simple shaped o b j e c t .

(e)a:dlrect sunlight, b:uniform skylight, c:overcast sky,d:clear sky, e:clear sky(including direct sunlight)

130

Dallas, August 18-22

Volume 20, Number 4, 1986

Fig. 9 Example

for interior scene.

(a)

(a)

(6)

(6)

(c)
Fig. 8 Examples for exterior scene.
a: direct sunlight, b: overcast sky
c: clear sky (including direct sunlight)(c)Fig. i0 Examples for daylight factors.
(a:overeast sky, b:elear sky, c:clear sky)131

S I G G R A P H

I
Table i.

Computation times

numberm o d e l i n g andof,image s i z e h i d d e n - s u r f a c e
faces
removal(min.)shading(min.)direct~interreflection
illumination of light

Pig.S(b)239!480x317

1.56

27.67

6.90*

Fig.9

231

480x32S

1.81

20.91

16.08

*only the I s t order 0£ r e f l e c t i o nresults.
(i) Images are much realistic using sky light andits reflections.
The proposed method
especially
improves
the realismof buildings
under both
overcastskies and clear skies, as
wellasinteriors
illuminatedbyskylight throughwindows.
(2) The illuminance from sky light can be obtainedby considering the sky as a hemisphere with a large
radius,Subdividing
the hemisphere
into
band
sources allows us to compute the illuminance due tononuniform sky luminance.
(3) The effect of sky light obstructed by objects
can be computed by summing the illuminances due tothe visible parts of each band source viewed fromthe calculation point;
the illuminancefor eachvisible part can be easily calculated by a look up
table for integrated illuminanee°(4) The effect of light reflected from the ground%o sloped surfaces
can be computed by the groundluminance for the under partof the horizontal
plane including the calculation point.
(5) Displaying
daylight
factor considering the
distributionof sky luminanceisusefulforlighting design.

ACKNOWLEDGEMENT
The authors ~ishhelpful advice.

tothank Laurin Herr for his

REFERENCES[i] Gardner G.Y.:
Simulationof Natural
ScenesUsing Textured
Quadric
Surfaces,
ComputerGraphics, Vol.18, No.3(1984) pp.ll-20.
~2] Gardner,
G.: Visual
Simulationof Clouds,
Computer Graphics,
Vol.19,No.3(1985)
pp.297303.
[3] Cook, R.C.: Shade Tree, Computer Graphics, Vol.
18, No. 3 (1984) pp.223-231.
[4] Aono, M. and Kunii,L.:
Botanical Tree Image
Generation, IEEE CG and A, Vol.4,
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