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	    RADIANCE Visual Comfort Calculation

		      Gregory J. Ward

		      April 6, 1992

1.  Introduction

This  document	describes  a  visual   comfort	 calculation
developed  by  the LESO	group at EPFL during Spring of 1991.
The calculation	uses the RADIANCE synthetic  imaging  system
[Ward90]  to  compute luminance	values from a computer model
of an architectural space and the lighting  and	 daylighting
of that	space.	These luminance	values are then	applied	to a
selected glare calculation procedure to	 arrive	 at  one  or
more discomfort	glare indices.

Visual comfort calculations are	inherently difficult to	per-
form  because  they  depend  not  only	on the locations and
brightnesses of	light sources, but also	on the apparent	size
(ie.  solid  angle) of the light sources as seen from a	par-
ticular	viewpoint.  By automating the calculation procedure,
we  hope  to  improve  reliability and ease of use of visual
comfort	metrics.  Plus,	since we are starting  from  a	com-
puter model of a space,	it is possible to use visual comfort
as a design criteria instead  of  measure  of  what's  wrong
after it's too late.

2.  General Approach

2.1.  Calculation Requirements

Although there are several different visual comfort  metrics
in  current use	around the world, there	is general agreement
on the factors which influence	discomfort  glare,  and	 the
various	glare calculations in fact start from the same basic
quantities.  These  quantities	are  the  directions,  solid
angles	and average luminances of the light sources, and the
background luminance for a particular viewpoint	[CIE83].

Ultimately, it is luminance in different directions  from  a
particular  point  that	 must be known in order	to calculate
glare values.  Since a RADIANCE	picture	is nothing more	than
a  collection  of  radiance  values from a particular point,
this is	a very convenient place	 to  start.   Unfortunately,
using  such  an	image in a glare calculation requires a	very
large field of view (180 degrees vertically and	180+ degrees
horizontally).	It is possible to generate such	images using
the fish eye view types	provided by RADIANCE,  but  this  is
not  usually  done.   We therefore need	to augment most	pic-
tures with additional luminance	 values	 lying	outside	 the
image borders.	To calculate individual	luminance values, we
use the	program	rtrace,	designed for this  purpose.   It  is
even  possible	to do without a	picture	altogether, although
this will take longer since all	the luminances will have  to
be calculated from scratch.

As a footnote to the above, it may be possible to  obtain  a
luminance  image  from somewhere besides RADIANCE and use it
to compute glare using the methods and programs	described in
this  paper.   However,	 this would require a fish eye image
with a very large dynamic range, and this  is  difficult  to
obtain in practice.

2.2.  A	Two Step Method

Since there are	so many	different glare	indices	in use,	 and
since they all require more or less the	same input, which is
difficult to compute, it makes good sense to  create  a	 two
stage glare calculation.  The first stage computes the loca-
tions, sizes and brightnesses of the light sources  and	 the
background  luminance  level,  and the second stage computes
whatever glare index is	desired.  Multiple glare indices may
be  computed  at  virtually  no	cost, and new indices may be
incorporated in	the  future  with  very	 little	 programming

An  example  output  file  from	 the  first  stage   program
findglare  is  shown  below.  This file	contains the command
that made it and the viewpoint,	followed by  the  locations,
sizes  and brightnesses	of the light sources and the adapta-
tion luminance in each of the requested	directions.

	findglare -ga 10-60:10 -v -vf vf/living2 -av .05 .05 .05 oct/nightcabin
	VIEW= -vth -vp 26.8 16.8 5 -vd -0.667 -0.745 0 -vh 180 -vv 180

	BEGIN glare source
	    Direction (dx,dy,dz)		    Size (sr)	Bright (cd/m^2)
	    -0.739601	-0.666543    0.093333	    0.004289	  37.523939
	    -0.543836	-0.798999    0.256598	    0.004605	1743.527453
	     0.555815	-0.795908    0.240000	    0.004253	 219.619154
	     0.794861	-0.498014    0.346667	    0.008012	 150.790377
	    -0.767600	-0.520973    0.373333	    0.009203	1790.000000
	END glare source
	BEGIN indirect illuminance
	  Angle	(deg)	Ind. Ill. (lux)
		60	9.131035
		50	9.810535
		40	10.533606
		30	11.260834
		20	11.963897
		10	12.521309
		0	12.875862
		-10	13.017022
		-20	12.946500
		-30	12.743195
		-40	12.472590
		-50	12.174556
		-60	11.806406
	END indirect illuminance

Calculating the	indirect illuminance in	multiple  directions
is  relatively inexpensive and it permits the calculation of
glare values in	these directions, thus indicating how visual
comfort	 is  affected by head orientation.  Below is example
output from the	second stage Guth visual comfort probability
(VCP) calculation [Guth63].

	-60	85
	-50	76
	-40	66
	-30	58
	-20	53
	-10	57
	  0	55
	 10	62
	 20	65
	 30	71
	 40	78
	 50	84
	 60	90

This particular	glare index is interpreted as the percentage
of  people  who	 would	say they were comfortable in a given
situation.   We	 see  above  that  the	center	of  view  (0
degrees),  55% of the people would be comfortable, and at 60
degrees	to the right,  90%  would  be  comfortable.   It  is
apparent  in  this  example  that visual comfort is strongly
influenced by view direction.

2.3.  Limitations

The two	step approach as we have implemented  it  here	does
have some limitations.

First, we have limited ourselves to looking at glare changes
only  to  the  left  and  to the right,	and not	up and down.
This is	not a very serious limitation, because what is	con-
sidered	 "horizontal" can be changed by	changing the view up
vector.	 Thus,	left  and  right  can  be  relative  to	 any
head/neck orientation, even changing its meaning to up/down.

Second,	the adaptation level is	computed using the  indirect
vertical illuminance as	the background level.  This value is
the integral of	luminance over the  hemisphere	weighted  by
the  cosine  about  the	central	view direction,	and excludes
any direct contributions from the glare	sources	 themselves.
Although  this is the value recommended	by most	glare calcu-
lations, some researchers claim	that a	different  weighting
of  hemispherical  luminance is	desirable to obtain the	most
accurate adaptation level.  It is possible  to	implement  a
different background luminance calculation in findglare, but
it doesn't make	much sense to use different adaptation	lev-
els  for  different  glare indices since they all use it for
the same purpose.  We therefore	chose to compute only verti-
cal  illuminance  because it is	better defined and more	com-
monly used.

Finally, there is some difficulty in deciding  what  exactly
is a glare source in a particular environment.	All existing
glare calculations were	designed with electric	lighting  in
mind,  where the light sources are easily separated from the
rest of	the visual environment as well as from	each  other.
In a daylight situation, the distinction between what is and
what is	not a light source is not so clear.  Furthermore, it
is  difficult  to  decide  where  to divide daylight sources
since windows are often	placed quite  close  together.	 The
algorithms  and	 heuristics  we	 have  chosen for separating
light sources from the background work well in	most  cases,
but  require  conscientious  control  when large windows are
present	in an already bright environment [DiPasquale91].

3.  Findglare Algorithm

Findglare is the  program  that	 takes	a  RADIANCE  picture
and/or	octree,	locates	the glare sources and calculates the
background levels (indirect  vertical  illuminances)  for  a
specified  view	 field.	  The  basic technique it uses is to
sample the visual field	for bright areas, designate these as
light  sources,	 and  use the rest of the samples to compute
the  indirect  illuminance  (ie.  background  level).	This
method,	 as we discovered, is much simpler in principle	than
it is in practice.

3.1.  Sampling Strategy

Findglare uses a modified hemispherical	 sampling  strategy.
If  a  single  view direction is selected, findglare samples
uniformly on the projected hemisphere.	This means that	 the
actual directions sampled will be densest near the center of
view, and sparser near the limits  of  view.   For  multiple
view  directions, a central view slice is opened up, leaving
the ends as two	half-hemispheres.  The vertical	sample	den-
sity  will  still vary as the cosine of	the angle within the
central	slice, but the horizontal  sample  density  will  be
constant over the specified view field.	 (See Figure 1.)

A projected hemispherical sampling was chosen over a simpler
uniform	 sampling  (ie.	 equal	solid angle for	each sample)
because	it results in more accurate, faster  glare  calcula-
tions.	 Since	the  sources  near  the	 center	have greater
importance in all glare	metrics, it is important  to  define
these sources more accurately.	Sampling the projected hemi-
sphere puts more samples near the center, assuring that	 any
sources	 found	there  will be sampled adequately.  Further-
more, the indirect illuminance is simply the sum of  samples
not striking light sources on the hemispherical	sample grid.
This means that	we are not wasting  time  sending  too	many
rays to	one part of the	visual field at	the expense of accu-
racy in	another	part.  This is particularly  important	when
the  samples  are  coming from rtrace rather than a RADIANCE
picture, since these samples involve new luminance  calcula-

The maximum sample density is set with the  -r	(resolution)
option,	 and  is  not  adjusted	 adaptively  by	the program.
Adaptive sampling might	prove  beneficial  if  very  bright,
small  sources	(such  as the sun) are present in the visual
field, but it is unnecessary for most environments.  If	 all
the  samples  needed  are present in an	input picture, it is
relatively inexpensive to use a	high sample density  in	 the
calculation, but it doesn't make sense to use a	higher reso-
lution than that of the	input picture.

3.2.  Identifying Sources

In manual glare	calculations, light sources are	usually	del-
ineated	 by the	analyst's own notion of	what is	and is not a
light source.  In the case of direct electric lighting,	this
is an easy choice, but when the	lighting is indirect or	from
one or more windows, the choice	is less	clear.	 The  choice
ought  to be made based	on viewer adaptation.  If a particu-
lar direction is especially bright compared to the  rest  of
the visual field, it should be considered as a glare source.
This relative brightness criterion may or may not agree	with
one's  intuitive  notion  of a light source.  For windows in
particular, there may be bright	and dark areas of  the	view
outside, and only part of the window may be bright enough to
really act as a	glare source.  Likewise, parts of the window
may be so bright that they completely drown out	the electric
lighting in a space, and the electric lights themselves	 may
not be sources of glare	in a daylighted	environment.

The basic approach  used  by  findglare	 to  identify  glare
sources	is called "thresholding".  If a	particular direction
in the visual field is above a designated  threshold  value,
then  it  must	be part	of a glare source.  If the threshold
value is not set by the	user manually, it is obtained empir-
ically	by findglare by	multiplying the	average	luminance of
the visual field by 7.	The number 7 was determined by	some
crude  tests  as  producing  a reasonable threshold for	most
scenes.	 Using	an  empirically	 derived  threshold  is	 not
always	the best approach, however, and	that is	why a manual
threshold setting is provided.	The user may use the program
ximage	or  rtrace  to	obtain a threshold value that agrees
with his or her	notion of a glare source for that particular
scene.	 Since there have been no studies, we do not know in
general	what value should serve	as the threshold for a glare
calculation.  This is an important question, which certainly
merits further investigation [DiPasquale91].

When a "glare sample" (ie.  a  sample  above  the  threshold
value)	is  found,  it is merged with neighboring contiguous
glare samples.	Two glare samples are considered  contiguous
if they	are separated by at most one non-glare sample.	This
allowed	separation is to avoid the breakup of something	like
a window with venetian blinds into an unreasonable number of
sources.  Note that a glare source may have  any  number  of
holes in it and	still be considered contiguous.

3.3.  Splitting	Sources

In order to avoid  very	 long  sources	that  might  produce
errors	in  the	glare calculation due to their spread in the
visual field, a	heuristic test	is  applied  to	 each  glare
source.	  If  a	 source	has a solid angle greater than 0.025
steradians and a linearity  (linear  regression	 correlation
coefficient of its samples) of 0.8 or more, it is split	into
two smaller sources of roughly equal area.   This  continues
recursively  until the resulting pieces	are compact by these

3.4.  Merging Sources

If a source is very small and not very bright, it should not
be treated as a	glare source in	most situations.  Therefore,
any source whose solid angle  times  its  average  luminance
(ie.  it's  total  emission)  is  less than 0.005 steradians
times the threshold luminance is either	merged	with  neigh-
boring sources or "absorbed".  A small source is merged	with
a neighboring source if	that neighbor is closer	than 4 times
the radius of a	0.005 steradian	disk.  If no suitable neigh-
bor exists, the	source is absorbed by adding  its  contribu-
tion back into the background level and	removing it from the
list of	glare sources.

Since it is not	always desirable to remove small sources  in
this  manner,  a  -c option is provided	to tell	findglare to
use all	sources	it finds, no matter how	small.

3.5.  Indirect Illuminance

The indirect vertical illuminance values  are  computed	 for
each selected view direction.  If a single view	direction is
selected, the indirect illuminance will	simply equal the sum
of  all	 non-glare samples.  If	multiple view directions are
selected, findglare will weight	 each  sample  appropriately
for  each  vertical  direction.	 The total number of samples
used is	determined by the requested resolution and the width
of the view field.  It is not affected by the number of	view
angles within the view field, so increasing  the  number  of
view  angles  without increasing the width of the view field
does not add much to the calculation time.

4.  Glare Index	Calculation

Thus far, we have implemented only two glare formula  calcu-
lations,  the  Guth  visual  comfort probability and the CIE
glare index due	to Einhorn.  Implementing other	glare formu-
las  is	 straightforward,  but	it was not clear to us which
other formulas were useful.  It	seemed to us that  providing
a multitude of very similar formulas would not be very help-
ful to the designer.

The Guth visual	comfort	probability (VCP) is related to	 the
more  basic  Guth  discomfort  glare ratio (DGR) by a simple
formula.  The DGR in turn is related to	the background lumi-
nance,	source	locations  and sizes, and source luminances.
This information is given by findglare with the	exception of
background  luminance.	This term is somewhat poorly defined
by Guth, so we take the	indirect  vertical  illuminance	 and
divide it by pi to get  the  background  luminance  averaged
over the projected hemisphere.  The Guth calculation  method
is explained in detail in [IES84].

The CIE	glare index (CGI) is the modified  Einhorn  equation
given  in [CIE83].  This formula is similar to the Guth	DGR,
but with a linear relationship to  the	source	solid  angle
that  results  in  better additivity (ie.  breaking up light
sources	differently does not affect the	results).  The	Guth
position index is used by this formula as well,	and its	cal-
culation is described in [Levin75].  Unfortunately, the	 CGI
formula	 does not have a counterpart to	the Guth visual	com-
fort probability.  Thus, the CGI value is  a  little  harder
for  the  designer  to interpret than a	simple percentage of
satisfied customers.  Nevertheless, this is the	formula	that
is recommended by the CIE and therefore	we take	heed because
it is a	standard.  Hopefully, the CIE will propose a  corre-
lation	between	 their CGI value and VCP in the	not too	dis-
tant future.

5.  Glare Script

To make	findglare and the glare	 index	calculation  program
glarendx  easier  to use, a script was written that asks the
user simple questions before running these  programs.	This
script	also  runs the program xglaresrc to identify sources
in a displayed image that have been  located  by  findglare.
After  finding	the  glare sources and displaying them in an
image, the script glare	allows the  user  to  calculate	 the
desired	 glare	index.	This index may be plotted as a func-
tion of	view direction using the  program  igraph,  and	 the
plots  may  be	sent to	the printer.  An example run of	this
script is shown	with its output	in the appendix.

6.  Conclusions

The glare calculation presented	here has undergone a partial
validation and has been	found to be reasonably accurate	when
compared to  manual  calculations  of  a  daylighted  office
[DiPasquale91].	 The calculation has also been compared	with
some simple test geometries to insure that it was performing
as  expected.  Perhaps the most	unreliable part	of any glare
calculation is the setting of the threshold which determines
what is	and is not considered as a glare source.  Especially
in daylight situations,	this can have a	large  influence  on
the results of the calculation.

Further	study is required  into	 the  nature  of  discomfort
glare from daylight windows, since all of the existing glare
formulations were developed and	tested using electric  light
only.	Although  Guth	claims that his	formula	is valid for
large area sources and sources near the	center of view,	 the
sensitivity  of	 the  eye  to light impinging from below the
horizontal plane has not been studied adequately,  and	this
is a frequent condition	in daylighted spaces.

We believe that	the  institution  of  a	 general,  automatic
glare  calculation  is	a very important step towards making
visual comfort metrics practical for the designer.  RADIANCE
offers	the advantage of considering all sources of glare in
a simulated  visual  environment,  not	only  from  electric
lights,	 but also from windows and reflections from specular

7.  References

[CIE83]	Commission Internationale de l'Eclairage,  ``Discom-
fort Glare in the Interior Working Environment,'' CIE Publi-
cation No. 55 (TC-3.4) 1983, pp. 15-18.

[DiPasquale91]	 Francesco   Di	  Pasquale,   ``Possibilites
d'application  du  modele  de  confort	visuel,''  EPFL-LESO
internal report, June 1991.

[Guth63]  Sylvester  Guth,  ``A	 Method	 for  Evaluation  of
Discomfort  Glare,'' Journal of	the Illuminating Engineering
Society, May 1963, pp. 351-364.

[Levin75] Robert Levin,	``Position  Index  in  VCP  Calcula-
tions,''  Journal  of  the Illuminating	Engineering Society,
January	1975, pp. 99-105.

[IES84]	 John  Kaufman,	 IES  Lighting	Handbook,  Reference
Volume,	IESNA, New York, NY, 1984, pp. 9.46-9.49.

[Ward90] Gregory Ward,	``Visualization,''  Lighting  Design
and Application, Vol. 20, No. 6, June 1990.