From greg Tue Oct  9 17:38:38 1990
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Received: by hobbes.lbl.gov (3.2/SMI-3.2)
	id AA10214; Tue, 9 Oct 90 17:38:34 PDT
Date: Tue, 9 Oct 90 17:38:34 PDT
From: greg (Gregory J. Ward)
Message-Id: <9010100038.AA10214@hobbes.lbl.gov>
To: globillum@miro.Berkeley.EDU
Subject: example calculation
Cc: greg
Status: RO

Hi Everyone,

I'm not sure how useful this is going to be as a point for comparison, but
I have finished an approximate calculation of a simple rectangular space
with diffuse surfaces.  I wouldn't guarantee the accuracy to six places,
but it should be enough to get us agreeing on ballpark answers, units
and so forth.  Most of the numbers are within 1%, but a few may be off by 
as much as 5%.

The basic space is a 10 by 6 by 3 rectangular room (length units are
irrelevant, but think of them as meters if you like).  At the center
of the ceiling is a single square fixture that measures .5 on a side.
The (monochromatic) emittances and reflectances are as follows:

	Surface		Emittance (w/m^2)	Reflectance (%)
	=======		=================	===============
	Source		31.416			0
	Ceiling		0			70
	Walls		0			50
	Floor		0			30

The final radiosities are given below for each surface.  The calculation
points are separated by .5 in each dimension, starting .25 from the edge.
The given coordinates are measured from the origin at one corner of the
room.  The longer wall is aligned with the x-axis, and the z-axis points up.
Since the room has quadrilateral symmetry, calculations are given for just
one corner of the room.

			CEILING
			-------
X		Y		Radiosity (w/m^2)
=		=		=================
0.25		0.25		0.0113
0.25		0.75		0.0131
0.25		1.25		0.0140
0.25		1.75		0.0149
0.25		2.25		0.0151
0.25		2.75		0.0155
0.75		0.25		0.0131
0.75		0.75		0.0150
0.75		1.25		0.0162
0.75		1.75		0.0168
0.75		2.25		0.0173
0.75		2.75		0.0177
1.25		0.25		0.0147
1.25		0.75		0.0166
1.25		1.25		0.0177
1.25		1.75		0.0185
1.25		2.25		0.0189
1.25		2.75		0.0191
1.75		0.25		0.0163
1.75		0.75		0.0184
1.75		1.25		0.0194
1.75		1.75		0.0202
1.75		2.25		0.0207
1.75		2.75		0.0208
2.25		0.25		0.0178
2.25		0.75		0.0202
2.25		1.25		0.0215
2.25		1.75		0.0224
2.25		2.25		0.0226
2.25		2.75		0.0229
2.75		0.25		0.0198
2.75		0.75		0.0224
2.75		1.25		0.0238
2.75		1.75		0.0244
2.75		2.25		0.0247
2.75		2.75		0.0251
3.25		0.25		0.0216
3.25		0.75		0.0246
3.25		1.25		0.0258
3.25		1.75		0.0264
3.25		2.25		0.0269
3.25		2.75		0.0272
3.75		0.25		0.0237
3.75		0.75		0.0267
3.75		1.25		0.0279
3.75		1.75		0.0283
3.75		2.25		0.0289
3.75		2.75		0.0290
4.25		0.25		0.0251
4.25		0.75		0.0283
4.25		1.25		0.0293
4.25		1.75		0.0298
4.25		2.25		0.0302
4.25		2.75		0.0306
4.75		0.25		0.0260
4.75		0.75		0.0290
4.75		1.25		0.0302
4.75		1.75		0.0307
4.75		2.25		0.0309
4.75		2.75		31.415

			FLOOR
			-----
X		Y		Radiosity (w/m^2)
=		=		=================
0.25		0.25		0.0101
0.25		0.75		0.0112
0.25		1.25		0.0121
0.25		1.75		0.0129
0.25		2.25		0.0134
0.25		2.75		0.0138
0.75		0.25		0.0116
0.75		0.75		0.0128
0.75		1.25		0.0139
0.75		1.75		0.0148
0.75		2.25		0.0156
0.75		2.75		0.0160
1.25		0.25		0.0136
1.25		0.75		0.0151
1.25		1.25		0.0165
1.25		1.75		0.0178
1.25		2.25		0.0189
1.25		2.75		0.0194
1.75		0.25		0.0162
1.75		0.75		0.0181
1.75		1.25		0.0201
1.75		1.75		0.0221
1.75		2.25		0.0236
1.75		2.75		0.0245
2.25		0.25		0.0193
2.25		0.75		0.0220
2.25		1.25		0.0249
2.25		1.75		0.0278
2.25		2.25		0.0303
2.25		2.75		0.0317
2.75		0.25		0.0229
2.75		0.75		0.0267
2.75		1.25		0.0309
2.75		1.75		0.0354
2.75		2.25		0.0392
2.75		2.75		0.0414
3.25		0.25		0.0270
3.25		0.75		0.0320
3.25		1.25		0.0380
3.25		1.75		0.0446
3.25		2.25		0.0504
3.25		2.75		0.0539
3.75		0.25		0.0308
3.75		0.75		0.0373
3.75		1.25		0.0454
3.75		1.75		0.0546
3.75		2.25		0.0630
3.75		2.75		0.0682
4.25		0.25		0.0340
4.25		0.75		0.0417
4.25		1.25		0.0518
4.25		1.75		0.0636
4.25		2.25		0.0747
4.25		2.75		0.0816
4.75		0.25		0.0358
4.75		0.75		0.0443
4.75		1.25		0.0556
4.75		1.75		0.0690
4.75		2.25		0.0819
4.75		2.75		0.0900

			X-WALL
			------
X		Z		Radiosity (w/m^2)
=		=		=================
0.25		0.25		0.0160
0.25		0.75		0.0165
0.25		1.25		0.0160
0.25		1.75		0.0146
0.25		2.25		0.0122
0.25		2.75		0.0094
0.75		0.25		0.0182
0.75		0.75		0.0188
0.75		1.25		0.0183
0.75		1.75		0.0167
0.75		2.25		0.0142
0.75		2.75		0.0110
1.25		0.25		0.0213
1.25		0.75		0.0220
1.25		1.25		0.0213
1.25		1.75		0.0195
1.25		2.25		0.0164
1.25		2.75		0.0124
1.75		0.25		0.0250
1.75		0.75		0.0260
1.75		1.25		0.0253
1.75		1.75		0.0230
1.75		2.25		0.0192
1.75		2.75		0.0140
2.25		0.25		0.0298
2.25		0.75		0.0312
2.25		1.25		0.0304
2.25		1.75		0.0276
2.25		2.25		0.0226
2.25		2.75		0.0158
2.75		0.25		0.0353
2.75		0.75		0.0373
2.75		1.25		0.0369
2.75		1.75		0.0336
2.75		2.25		0.0271
2.75		2.75		0.0180
3.25		0.25		0.0411
3.25		0.75		0.0443
3.25		1.25		0.0443
3.25		1.75		0.0405
3.25		2.25		0.0325
3.25		2.75		0.0204
3.75		0.25		0.0469
3.75		0.75		0.0510
3.75		1.25		0.0519
3.75		1.75		0.0480
3.75		2.25		0.0382
3.75		2.75		0.0232
4.25		0.25		0.0516
4.25		0.75		0.0568
4.25		1.25		0.0586
4.25		1.75		0.0546
4.25		2.25		0.0436
4.25		2.75		0.0255
4.75		0.25		0.0542
4.75		0.75		0.0602
4.75		1.25		0.0624
4.75		1.75		0.0587
4.75		2.25		0.0467
4.75		2.75		0.0268

			Y-WALL
			------
Y		Z		Radiosity (w/m^2)
=		=		=================
0.25		0.25		0.0195
0.25		0.75		0.0202
0.25		1.25		0.0191
0.25		1.75		0.0172
0.25		2.25		0.0141
0.25		2.75		0.0104
0.75		0.25		0.0219
0.75		0.75		0.0225
0.75		1.25		0.0215
0.75		1.75		0.0192
0.75		2.25		0.0160
0.75		2.75		0.0121
1.25		0.25		0.0238
1.25		0.75		0.0243
1.25		1.25		0.0234
1.25		1.75		0.0211
1.25		2.25		0.0177
1.25		2.75		0.0131
1.75		0.25		0.0255
1.75		0.75		0.0261
1.75		1.25		0.0250
1.75		1.75		0.0226
1.75		2.25		0.0187
1.75		2.75		0.0139
2.25		0.25		0.0265
2.25		0.75		0.0272
2.25		1.25		0.0262
2.25		1.75		0.0236
2.25		2.25		0.0196
2.25		2.75		0.0145
2.75		0.25		0.0273
2.75		0.75		0.0279
2.75		1.25		0.0269
2.75		1.75		0.0243
2.75		2.25		0.0200
2.75		2.75		0.0147

All values were produced using the algorithm presented in my `88
Siggraph paper.  These numbers may not be what is needed to validate
a new calculation, but I would be curious to see how they compare to
more conventional radiosity calculations.

-Greg

