AN EXPERIMENT IN RADIOSITY©

Submitted as partial fulfillment of the requirements of
Master of Computer Science
Arizona State University
College of Engineering and Applied Sciences
Department of Computer Science

Submitted by:

William S. Cochell

April 24, 1991

SYNOPSIS

The goal of this research was to investigate methods to implement a standard radiosity solution for displaying real environments, the key word being real. "It is indisputable that radiosity has produced the most realistic and impressive images to date." 1 Three different methods for calculating the amount of light received at each point were analyzed. In addition, a commercial lighting application program was examined to see if the output could be used to create suitable images.

COMPUTER GRAPHICS BACKGROUND

The first use of the radiosity method was documented by Goral, Torrance, Greenberg, and Battaile. 2 This solution was for an empty room and provided color bleeding but did not support shadows. A paper by Nishita and Nakamae 3 describes an approach which produces shadows but does not implement color bleeding.

Subsequent papers describe various methods for improving on the basic method. They include the Hemi-Cube method of Cohen and Greenberg, 4 Adaptive Subdivision by Cohen, Greenberg, Immel, and Brock, 5 and the approach of Wallace, Elmquist and Haines which uses ray tracing to implement Progressive Radiosity. 6 It was this last paper which was the inspiration for this research project. Each method will be discussed along with their respective advantages and disadvantages later in this paper.

ILLUMINATION ENGINEERING BACKGROUND

The basis of the radiosity method is in thermal and illumination engineering models. Radiation, whether it be heat or light, follow very well defined laws as it propagates through space. Most any physics text book will describe these laws so only the relevant parts will be discussed.

Papers by Jensen 7 and DiLaura 8 influenced the early work in radiosity. These papers are geared toward determining the lighting levels in real environments. They attempt to predict various quantities such as visual comfort in addition to average illuminance. A paper by Brackett, Fink, and Pierpoint, 9 was of special interest to this research as it describes the method used by the commercial lighting application program that was a part of this research.

MATHEMATICS

The radiosity approach models light sources as having area. In addition to the initial light sources, the surfaces in the environment also become sources as light is reflected from them. Typically the environment to be modeled is divided into a number of patches, each of which is at some point considered to be an emitter. The methods by which the number of patches is determined varies among the algorithms. The geometry of the radiosity equation is well known and oft presented in the computer graphics community, therefore, it will not be repeated here. Foley, van Dam, Feiner, and Hughes give the following explanation of the radiosity equation: 10 The result is a set of simultaneous equations for the interaction between all the patches in the environment. By taking advantage of reciprocity and simplifying, the equations can be expressed in matrix form: Solving the above equations for the Bis yields the radiosity for each patch. These values can then be used in a display program that removes hidden surfaces and has the capability to interpolate shading.

IMPLEMENTATIONS

Common to each of the methods presented in this paper is the test for shadows. Determining if a vertex is visible from a source involves checking the normal of the source to see if it points towards or away from the vertex. If the cosine of the angle between the normal of the source and the line between the source and vertex is greater than 0, then the source is potentially visible from the vertex. An occlusion test must be made for objects between the source and vertex. If the normal of the source points towards the vertex and there are no objects obstructing the view of the source, then the vertex receives light from the source.

Matrix Solution

Solving a matrix equation of this magnitude is difficult at best. A method such as the Gauss Seidel can be used but the number of patches 1 required for high quality images is prohibitive. The matrix solution would require n x n int terms of memory storage. Nishita and Nakamae describe a method whereby the rows of the coefficient are stored on disk and read in as needed. 3 However, as disk access is slow, this method will be slower than one that executes completely in memory.

Hemi-cube

Cohen and Greenberg describe the use of a hemi-cube to obtain form factors: "For a finite area, the form factor is equivalent to the fraction of the circle (which is the base of the hemi-sphere) covered by projecting the area onto the hemisphere and then orthographically down onto the circle." 4 To approximate this, Cohen and Greenberg use a hemi-cube at the center of each patch in the environment. The environment is transformed so the center of the patch is at the origin of the hemi-cube, and the patch's normal is aligned with the positive Z axis of the hemi-cube. This method like the previous can provide for shadows by testing for occlusion when the patches are projected onto the hemi-cube. "Iterative techniques are much less computationally intense than Gaussian elimination (as used by Goral) if quick convergence is assured." 11

However, there are drawbacks to this solution. Since the projection onto the hemi-cube is to rectangular "pixels" alias can occur. This can especially be a problem at the intersection of two patches. Higher resolution on the hemi-cube can help solve this problem, but at additional expense. Another problem is that the algorithm is very difficult to code. While this is only a function of the programmer's skill, simpler solutions often provide better and quicker results.

Progressive Refinement

Wallace et. al. use ray tracing in with progressive refinement to solve the radiosity problem. The basic approach is to start with the brightest surface (i.e. a light source) in the environment. A ray is "shot" from the light source to each vertex in the environment. If the vertex can "see" the light source, the contribution from that light source is added to the vertex. This technique has the following advantages: 10
  1. Radiosities are computed at the vertices themselves, where they are ultimately needed for shading.
  2. Vertex normals can be used, allowing polygonal meshes that approximate curved surfaces.
  3. If desired, the ray intersection calculations can be performed with a resolution independent true curved-surface database, so that the time for an individual ray test does not depend on the number of polygons.
  4. Nonphysical point light sources can be handled by tracing a single ray to the light source and using its illumination equation to determine the irradiance at each vertex.
  5. The number of areas into which a source is decomposed and whether rays are actually fired (i.e. if shadow testing is to be performed) can all be determined individually for each vertex.
It was these advantages and the simplicity of the concept that were the inspiration for this research.

Implementation of this research

The Wallace algorithm was used with only minor modifications. For displaying the images the program uses the 3D viewing algorithms as discussed in "Practical techniques for producing 3D graphical images" by Thomas A. Foley and Gregory M. Nielson. 12 These algorithms allow for the use of a hardware Z-buffering system and Gouraud shading. As such, this project does not implement color bleeding, but does provide for shadows. In addition, aliasing and mach banding are (unfortunately) very well demonstrated. A complete radiosity package that eliminates these problems is beyond the scope of this project. Therefore, variations on equation 3 were used to determine if a better, simpler, approach would work. The ray intersection algorithm used is based on the one given by Didier Badouel in the book Graphics Gems. 13

The first method by which the room illumination was determined followed that of Wallace's paper. Each surface is considered in turn. The sample points for each surface are the centers of the patches shown in the wireframe of Photo 1. If the surface points towards the vertex in question (i.e. q1 > 0) a ray is cast from every vertex not on this surface to each sample point on the emitter. After the light is shot from the first source to every other point in the environment that is not on the source, the new surface emissivities are calculating by taking the average of the intensities of the points that make up each surface. The next emitter is chosen as the surface that has the highest emissivity and hasn't yet been considered as a source. This is repeated until every surface in the environment has been considered or no surface exists that has an emissivity greater than zero. The resulting image is shown in Photo 2.



Photo 1 - Wireframe

Emitters

Photo 2 - Method 1 - each surface as an emitter
(217 x 364 29k)

The second method is a variation of the first. It would seem that to take the average illumination of the surface could cause problems when a vertex can see only a part of the surface that is in shadow. To account for shaded sources, the second approach was to consider each patch as a source instead of the whole surface. The basic steps are the same as were described above, only now the average intensity of the four points that make up each patch are used in Equation 3. That is, n in the equation is 1 and the summation is eliminated. The resulting image is shown below in Photo 3.

In order to make comparisons of the various methods the same environment is demonstrated. A different environment appears at the end of this report which contains elements which would be affected by using the average surface intensity.

The third technique was to use the patches as emitters, but instead of using the center of the patch for a sample point, the vertex that make up the patch are used. This increases the number of sample points and therefore the computation time. Inadequate sampling of sources can cause problems but in this case it does not make a difference. Photo 4 below demonstrates this method.

Photo 3 - Method 2 - each patch as an emitter



Photo 4 - Method 3 - sampling at patch vertices



A fourth method, a variation on the second, was tried. In this method the equation is based on that given for point light sources in the 1984 edition of the IES Lighting Handbook, Reference Volume. 14

The method used was to combine the Inverse-Square Law with the Lambert cosine law. The Inverse-Square Law states: The above equation was used to calculated the vertex intensities shown in Photo 7. This equation is computational less intense. The final intensity calculation only has three multiplications (I included the reflectance of the receiving surface to gain more control over the results) and a single divide. Note that this equation does not involve the cosine of the angle between the surface normal and the ray to the source. Since the intensity is being calculated at a point, there is no normal. However, the normal is calculated since it will determine if the point the surface is on looks towards or away from the source. Since surfaces that point away from the source won't receive any direct light from the source, the shadow intersection test can be avoided. The determination of the cosine is a much less expensive computation.

Photo 5 - Method 4 - inverse square/Lambert cosine



This method is not a true radiosity solution since the areas of the emitters are not considered. That is, this is not an energy balance equation. To achieve decent results, it was necessary to experiment with the initial emissivities and reflectances.

Visually the first method yields the best results. The execution times on an Iris 3130 workstation for each method were: This environment is fairly simple and as such should not be used alone when making a value judgement. A more complex environment was created to better judge the merits of each method. The environment was modeled on the Graphics Laboratory in the Engineering Center, room G-205, at Arizona State University. The environment is 26 feet wide by 24 feet deep and has a height of 10 feet. The colors of the walls and floor were changed in this simulation to add interest. Also, so a less even illuminance level would result, only 6 light sources are used whereas the real room has nine 2x4 fluorescent lights.

The initial environment consists of 132 points which define 69 separate surfaces. The input file contains the colors for each surface as well as the number of patches each is to be divided into. The subdivision results in 2059 points and 1484 patches. Method 4 was used to render the complex environment shown in Photo 6 with the patches superimposed. Additional views of this environment appear in Photos 7 and 8.

Photo 6 - Complex environment with patches superimposed



Complex environment view 1

Photo 7 - Complex environment view 1
(240 x 368 45k)

Complex environment view 2

Photo 8 - Complex environment view 2
(242 x 364 48k)

Batch summary report produced on ASU Cray computer are given in Appendix A for each method when used on this environment. Unfortunately only Method 3 produced reasonable results. The best method for the simple environment generated a floating point exception before it completed execution. From these reports, the execution time for each method is: The fifth and final method by which the intensities where determined was to use a commercially available lighting program. There are several manufacturers of light fixtures that make programs for determining the light levels in interior and exterior spaces. Among them is a program called Point by Lighting Analysts, Inc. 15 For this project I used the Point program to generate vertex intensity with surprisingly good results.

The point program takes as input a description of the spaces. This description includes the room dimensions and reflectivities of the surfaces. It has the capability of allowing for "inserts" which are areas that have a different reflective value. These can be used for objects such as throw rugs or blackboards. The program also requires an input file for each luminaire type that is to be used in the room. This is the biggest advantage of using this method, the data for each luminaire has been compiled empirically by the manufacturer and thus constitutes real lighting conditions as opposed to arbitrary conditions created by the programmer.

To see how different light fixtures illuminate a space, I chose two fixtures with different lens. The first type was an ordinary 2x4 fluorescent fixture with an acrylic lens. This is the fixture type used in the Computer Graphics Lab. Its distribution pattern is fairly uniform about its axis. The second type of luminaire used was a 16 cell parabolic reflector. This type of light is normally used spaces where ceiling glare is a problem, that is, rooms with Video Display Terminals. The reflector focuses much of the light towards the floor to minimize "hot spots" on the ceiling. Hot spots cause visual strain when they show up as reflections in a computer screen.

Photo 9 is a radiosity solution for the empty room with the patch subdivision superimposed. Photo 10 is the same view without the patches. Photo 11 shows the distribution of light from above. Photo 12 shows the output for the first luminaire type and Photo 13 shows that for the second. Photo 14 is the output for a standard radiosity approach.

Photo 9 - empty rom with patches superimposed



Photo 10 - radiosity Method 4



Photo 11 - from above

Acrylic Lens

Photo 12 - 2x4 with acrylic lens
(242 x 362 47k)

Photo 13 - from above

Parabolic reflector

Photo 14 - 2x4 with parabolic reflector
(241 x 365 47k)

Photo 15 - from above



As you can see the results of the Point program and the radiosity solution are very similar. There is a more even distribution from the first luminaire. The ceiling is brighter for the second luminaire since it only receives light reflected from the floor and this luminaire focuses more of its output on the floor.

This room consists of 1588 points and 1324 patches. The Point program took 143 seconds to compute the lighting levels for this space. The program was executed on a 20 MHz 386 machine with 4 megabytes of main memory. This time included the creation of the output files which appear in Appendices B and C. The creation of the Gray-Scale plots is an additional step which took 243 seconds.

The radiosity solution took only 21.3765 seconds of CPU time on the Cray to process when no shadow testing was done. The same space took 65.1479 seconds when each point is checked to see if it is in a shadow. The program was not, however, written to take advantage of the Cray's hardware; that is another project in itself. The program took 721 seconds to compute the radiosity solution on the same PC as the Point program was run. When the shadow intersection test is included, the radiosity program took 6060 seconds on the PC.

The point program does not provide for shadows. The method by which the Point program calculates the intensity is described in the paper "Interior point-by-point calculations in obstructed spaces.9"

The data files for light fixtures are created by taking measurements a unit distance away from a source at regular intervals as shown in Figure 1 below. 9
 10.0  +  +  +  +  +  +     +        +              +                +                 . . .                 +
       .  .  .  .  .  .     .        .              .                .                                       .
       .  .  .  .  .  .     .        .              .                .                                       .
       .  .  .  .  .  .     .        .              .                .                                       .
  5.0  +  +  +  +  +  +     +        +              +                +                 . . .                 +
       .  .  .  .  .  .     .        .              .                .                                       .
       .  .  .  .  .  .     .        .              .                .                                       .
       .  .  .  .  .  .     .        .              .                .                                       .
 3.5   +  +  +  +  +  +     +        +              +                +                 . . .                 +
      
      
      
      
 2.5   +  +  +  +  +  +     +        +              +                +                 . . .                 +
      
      
 1.75  +  +  +  +  +  +     +        +              +                +                 . . .                 +
      
 1.25  +  +  +  +  +  +     +        +              +                +                 . . .                 +
 1.0   +  +  +  +  +  +     +        +              +                +                 . . .                 +
  .75  +  +  +  +  +  +     +        +              +                +                 . . .                 +
  .50  +  +  +  +  +  +     +        +              +                +                 . . .                 +
  .25  +  +  +  +  +  +     +        +              +                +                 . . .                 +
 0.0   +  +  +  +  +  +     +        +              +                +                 . . .                 +

        .25   .75  1.25              2.5                            5.00
      0.0  .50  1.0   1.75                          3.50                                                    10.00

Figure 1:
It is assumed that the light's distribution is symmetrical about its axis so only one quadrant needs to be measured. Using the Inverse- Square Law the amount of light received at different mounting heights can be calculated. The data file for the light fixtures only have data for horizontal and vertical planes. The Point program allows for the lights to be titled to provide for wall washers and the like. The calculations therefore reduce to a 2d interpolation in a table for each light source used. By taking advantage of geometry, titled lights can (and titled surfaces could) be accommodated.

The inter-reflection between surfaces is at the surface level, that is, each wall's average illuminance is used to compute the amount of light it contributes to every other surface in the space. Likewise are the floor and ceiling. This limits the accuracy of the Point program for reproducing the effect of point sources (ironic isn't it). This program works best for either strips or a grid of fluorescent lights. A spot light on a wall would illuminate the wall, but there would be no local reflection on the floor or ceiling from the wall.

CONCLUSIONS

Ray tracing to obtain form-factors is not without problems. Uniform distribution of sample points can produce aliasing, particularly at shadow edges. Since the intensities are computed at the vertices and the vertices may be several pixels apart, stochastic anti-aliasing methods typically become artifacts. Wallace uses "successively greater numbers of uniformly distributed sample points, until the difference between the resulting form-factors drops below a certain criterion." 6 Areas completely inside or outside of shadows need fewer rays to obtain acceptable results.

Another problem is that of a large source close to a receiver. If a small number of sample points is used, hot spots result. Wallace uses adaptive sub division to eliminate this problem. The source is divided into smaller patches until the amount of energy received by the source falls below a user specified minimum. If the source is divided into unequal areas, Equation 3 must be modified by the weighted average of the form-factors due to each of the new patches.

The various methods used to solve the radiosity problem all yield good results on the small test case. Unfortunately they didn't generalize very well to the more complex environment.

The method used by the Point program deserves further investigation. It has limitations as implemented in that the reflections between surfaces are generalized. However, for quick evaluation of a general lighting scheme it is very appropriate. It also has the advantage that it uses measured data to model the light sources. In the quest for realism using empirical data, when used properly, should be the method of choice.

APPENDIX A

Cray Batch Reports

APPENDIX B

Point output and cut sheets for acrylic lens light

--------------------------------------------------------------------
                                POINT
POINT (tm) (c) copyright 1984 - 1988 by Lighting Analysts, Inc.
--------------------------------------------------------------------
CLIENT...........Alyn Rockwood
                 Computer Science Department, Arizona State University

CALCULATED BY....William S. Cochell

REFERENCE #......1

DATE.............03-31-1991

JOB DESCRIPTION :

Sample data for MCS project.

2SP 340 fixtures

INPUT FILENAME : data4sp.IN

2SPG 340 ACF        
LTL 3440       
2X4 3L SPEC TROF,ACRYLIC LENS                                              
LAMP= 3150 LM LAMP
TILT=NONE
 3  3150  1  11  5  1  1  2  4  0 
 .95  1  139 
 0  5  15  25  35  45  55  65  75  85 
 90 
 0  22.5  45  67.5  90 
 1729  1726  1666  1549  1379  1157  904  628  350  96 
 4 
 1729  1729  1666  1550  1379  1160  900  625  346  95 
 5 
 1729  1726  1666  1548  1374  1150  888  612  335  86 
 3 
 1729  1720  1657  1535  1363  1142  879  610  334  85 
 3 
 1729  1706  1645  1525  1354  1132  875  608  339  89 
 3 
 1729  1720  1657  1535  1363  1142  879  610  334  85  

INSIGHT (c) copyright 1990 by Lighting Analysts, Inc.
Licensed material - program property of Lighting Analysts, Inc.

PRINTOUT CLARIFICATION
----------------------
Orientation  (ORIENT)  refers  to  the  counterclockwise  rotation  of  the
luminaire from zero degrees, zero degrees being east (see  diagram  below).

                                 90                        +y
                                  |                         |
                                  |                         |
    ORIENTATION          180 -----+----- 0                  +---- +x
     CONVENTION                   |
                                  |
                                 270

Tilt is the + or - angular displacement of the  luminaire  along  its  zero
degree photometric plane.

Cant is the + or - angular displacement  of  the luminaire along its ninety
degree photometric plane.

Metal halide lamp correction factor  (MHLCF)  is applied to luminaires with
metal halide lamps which when  tilted, affect the lumen output of the lamp.

LUMINAIRE DESCRIPTION
---------------------
LUMINAIRE TYPE  1 
FILENAME = 2spg-9.ies

2SPG 340 ACF        
LTL 3440       
2X4 3L SPEC TROF,ACRYLIC LENS                                              
LAMP= 3150 LM LAMP

LUMINOUS DIMENSIONS  : ACROSS =  2  ALONG =  4  HEIGHT =  0 
TEST LAMP LUMENS    : 3150
INITIAL LAMP LUMENS : 3150
LIGHT LOSS FACTOR   : .81
BASED ON LAMP LUMEN DEPRECIATION x LUMINAIRE DIRT DEPRECIATION x BALLAST FACTOR

ROOM DESCRIPTION
----------------
COORDINATES IN FEET

DIMENSIONS      REFLECTANCES
X = 26          WEST WALL  = .4     
Y = 24          NORTH WALL = .4     
Z = 10          EAST WALL  = .4     
                SOUTH WALL = .4     
                FLOOR      = .4     
                CEILING    = .8     

LUMINAIRE LOCATION PARAMETERS
-----------------------------
COORDINATES IN FEET

GRID  LUMINAIRE                  MOUNTING
 NO.    TYPE    X-COORD  Y-COORD  HEIGHT   ORIENT   TILT     CANT 
----    ----    -------  -------  -------  -------  -------  -------
 1      1       7        8        10       90       0        0      
 1      1       7        16       10       90       0        0      
 1      1       13       8        10       90       0        0      
 1      1       13       16       10       90       0        0      
 1      1       19       8        10       90       0        0      
 1      1       19       16       10       90       0        0      

LUMINAIRE TYPE  1 : NUMBER OF UNIQUE LOCATIONS =    6

AVERAGE TILTED LAMP CORRECTION FACTOR APPLIED = 1.000

ILLUMINANCE -- LOOKING DOWN     
---------------------------
HORIZONTAL PLANE OF POINTS				Y
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	|
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET  			|
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES	+------- X

BASE OF PLANE LOCATED AT Z=   2.50
  24.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   9.8 12.9 14.3 15.9 17.3 18.5 19.5 20.1 20.4 20.5 20.3 19.8 18.9 17.7 16.4 14.9 13.3 11.8
  22.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  12.9 15.1 17.3 19.6 21.8 23.6 25.0 25.9 26.4 26.4 26.1 25.4 24.1 22.5 20.4 18.1 15.8 13.8
  21.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  14.4 17.4 20.5 24.0 27.2 29.8 31.7 32.9 33.6 33.7 33.2 32.2 30.5 28.1 25.1 21.7 18.3 15.5
  19.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  16.0 19.9 24.2 29.1 33.7 37.3 39.8 41.4 42.3 42.4 41.8 40.4 38.2 35.0 30.8 25.9 21.2 17.3
  18.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  17.5 22.2 27.8 34.1 39.9 44.5 47.6 49.6 50.6 50.7 50.0 48.4 45.6 41.6 36.2 29.9 23.9 19.1
  16.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  18.7 24.1 30.6 37.9 44.6 50.0 53.5 55.7 56.9 57.0 56.2 54.4 51.2 46.6 40.3 33.0 26.0 20.5
  15.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  19.6 25.3 32.2 40.0 47.2 52.9 56.8 59.1 60.4 60.6 59.7 57.7 54.3 49.3 42.6 34.8 27.3 21.4
  13.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.1 25.9 32.9 40.8 48.1 53.9 57.9 60.3 61.7 61.8 60.9 58.8 55.3 50.2 43.4 35.5 28.0 22.0
  12.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.2 26.1 33.1 40.9 48.2 54.0 58.1 60.5 61.9 62.0 61.2 59.0 55.4 50.4 43.5 35.7 28.2 22.1
  10.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.1 25.9 32.9 40.8 48.1 53.9 57.9 60.3 61.7 61.8 60.9 58.8 55.3 50.2 43.4 35.5 28.0 22.0
   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  19.6 25.3 32.2 40.0 47.2 52.9 56.8 59.1 60.4 60.6 59.7 57.7 54.3 49.3 42.6 34.8 27.3 21.4
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  18.7 24.1 30.6 37.9 44.6 50.0 53.5 55.7 56.9 57.0 56.2 54.4 51.2 46.6 40.3 33.0 26.0 20.5
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  17.5 22.2 27.8 34.1 39.9 44.5 47.6 49.6 50.6 50.7 50.0 48.4 45.6 41.6 36.2 29.9 23.9 19.1
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  16.0 19.9 24.2 29.1 33.7 37.3 39.8 41.4 42.3 42.4 41.8 40.4 38.2 35.0 30.8 25.9 21.2 17.3
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  14.4 17.4 20.5 24.0 27.2 29.8 31.7 32.9 33.6 33.7 33.2 32.2 30.5 28.1 25.1 21.7 18.3 15.5
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  12.9 15.1 17.3 19.6 21.8 23.6 25.0 25.9 26.4 26.4 26.1 25.4 24.1 22.5 20.4 18.1 15.8 13.8
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   9.8 12.9 14.3 15.9 17.3 18.5 19.5 20.1 20.4 20.5 20.3 19.8 18.9 17.7 16.4 14.9 13.3 11.8
          -------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00

               NUMERICAL ANALYSIS:
               -------------------
               AVERAGE=    33.9    MAX.=    62.0    MIN.=     9.8
               AVERAGE/MINIMUM=     3.47:1
               MAXIMUM/MINIMUM=     6.35:1

ILLUMINANCE -- LOOKING NORTH    
----------------------------
VERTICAL PLANE OF POINTS					Z
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	|
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET             	+----X
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES       

BASE OF PLANE LOCATED AT Y=  24.00


   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.6  9.6 10.2 10.9 11.5 12.0 12.3 12.5 12.6 12.6 12.5 12.4 12.1 11.7 11.1 10.5  9.8  9.1
        |
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.4 11.9 13.2 14.7 16.0 17.1 17.7 18.2 18.4 18.5 18.3 17.9 17.3 16.4 15.1 13.7 12.3 11.0
        |
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.8 13.7 15.5 17.4 19.2 20.6 21.6 22.2 22.5 22.6 22.4 21.8 20.9 19.7 18.1 16.2 14.3 12.5
        |
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  12.9 15.0 17.0 18.9 20.8 22.3 23.4 24.1 24.5 24.6 24.3 23.7 22.7 21.4 19.6 17.6 15.7 13.7
        |
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  13.6 15.8 17.7 19.5 21.2 22.6 23.7 24.4 24.8 24.9 24.6 24.0 23.0 21.7 20.1 18.3 16.4 14.4
        |
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  13.8 16.2 17.9 19.4 20.9 22.1 23.1 23.8 24.1 24.1 23.9 23.4 22.5 21.3 19.9 18.4 16.8 14.7
        |
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  12.0 16.1 17.4 18.6 19.8 20.8 21.6 22.2 22.5 22.6 22.3 21.9 21.1 20.2 19.0 17.8 16.6 15.1
        |
          -------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00



               NUMERICAL ANALYSIS:
               -------------------

               AVERAGE=    17.9    MAX.=    24.9    MIN.=     8.6
               AVERAGE/MINIMUM=     2.07:1
               MAXIMUM/MINIMUM=     2.88:1

ILLUMINANCE -- LOOKING WEST     
---------------------------

VERTICAL PLANE OF POINTS					Z
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	|
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET             	+----Y
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES       

BASE OF PLANE LOCATED AT X=   0.00


   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.7  9.6 10.3 11.1 11.8 12.4 12.7 12.7 12.7 12.7 12.7 12.4 11.8 11.1 10.3  9.6  8.7
        |
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.4 11.9 13.4 15.1 16.8 18.1 18.7 18.8 18.7 18.8 18.7 18.1 16.8 15.1 13.4 11.9 10.4
        |
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.9 13.8 15.7 17.8 19.9 21.5 22.4 22.7 22.7 22.7 22.4 21.5 19.9 17.8 15.7 13.8 11.9
        |
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  13.0 15.1 17.1 19.3 21.3 22.9 23.9 24.3 24.5 24.3 23.9 22.9 21.3 19.3 17.1 15.1 13.0
        |
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  13.6 15.8 17.8 19.7 21.5 22.9 23.9 24.4 24.5 24.4 23.9 22.9 21.5 19.7 17.8 15.8 13.6
        |
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  13.8 16.1 17.9 19.4 20.9 22.1 23.0 23.4 23.6 23.4 23.0 22.1 20.9 19.4 17.9 16.1 13.8
        |
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  12.1 16.2 17.4 18.6 19.8 20.7 21.4 21.9 22.0 21.9 21.4 20.7 19.8 18.6 17.4 16.2 12.1
        |
          --------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00


               NUMERICAL ANALYSIS:
               -------------------

               AVERAGE=    17.7    MAX.=    24.5    MIN.=     8.7
               AVERAGE/MINIMUM=     2.04:1
               MAXIMUM/MINIMUM=     2.83:1

ILLUMINANCE -- LOOKING UP       
-------------------------
HORIZONTAL PLANE OF POINTS
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	Y
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET             	|
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES	+----X  

BASE OF PLANE LOCATED AT Z=  10.00
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   6.2  8.1  8.3  8.5  8.6  8.7  8.8  8.8  8.8  8.8  8.8  8.8  8.7  8.6  8.5  8.4  8.2  7.8
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.1  8.7  8.9  9.1  9.3  9.4  9.5  9.5  9.5  9.5  9.5  9.5  9.4  9.3  9.2  9.0  8.8  8.5
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.3  8.9  9.2  9.4  9.5  9.7  9.8  9.8  9.9  9.8  9.8  9.8  9.7  9.6  9.4  9.3  9.0  8.6
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.5  9.1  9.4  9.6  9.8  9.9 10.0 10.1 10.1 10.1 10.1 10.1 10.0  9.8  9.7  9.5  9.2  8.8
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.6  9.2  9.5  9.8 10.0 10.1 10.2 10.3 10.4 10.3 10.3 10.3 10.2 10.0  9.9  9.6  9.4  8.9
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.7  9.3  9.6  9.9 10.1 10.3 10.4 10.5 10.5 10.5 10.5 10.4 10.3 10.2 10.0  9.7  9.5  9.0
   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.7  9.4  9.7 10.0 10.2 10.4 10.5 10.6 10.6 10.6 10.6 10.5 10.4 10.3 10.1  9.8  9.5  9.0
  10.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.8  9.5  9.8 10.1 10.3 10.4 10.6 10.6 10.7 10.7 10.7 10.6 10.5 10.3 10.1  9.9  9.6  9.1
  12.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.8  9.5  9.8 10.1 10.3 10.5 10.6 10.7 10.7 10.7 10.7 10.6 10.5 10.4 10.2  9.9  9.6  9.1
  13.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.8  9.5  9.8 10.1 10.3 10.4 10.6 10.6 10.7 10.7 10.7 10.6 10.5 10.3 10.1  9.9  9.6  9.1
  15.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.7  9.4  9.7 10.0 10.2 10.4 10.5 10.6 10.6 10.6 10.6 10.5 10.4 10.3 10.1  9.8  9.5  9.0
  16.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.7  9.3  9.6  9.9 10.1 10.3 10.4 10.5 10.5 10.5 10.5 10.4 10.3 10.2 10.0  9.7  9.5  9.0
  18.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.6  9.2  9.5  9.8 10.0 10.1 10.2 10.3 10.4 10.3 10.3 10.3 10.2 10.0  9.9  9.6  9.4  8.9
  19.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.5  9.1  9.4  9.6  9.8  9.9 10.0 10.1 10.1 10.1 10.1 10.1 10.0  9.8  9.7  9.5  9.2  8.8
  21.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.3  8.9  9.2  9.4  9.5  9.7  9.8  9.8  9.9  9.8  9.8  9.8  9.7  9.6  9.4  9.3  9.0  8.6
  22.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.1  8.7  8.9  9.1  9.3  9.4  9.5  9.5  9.5  9.5  9.5  9.5  9.4  9.3  9.2  9.0  8.8  8.5
  24.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   6.2  8.1  8.3  8.5  8.6  8.7  8.8  8.8  8.8  8.8  8.8  8.8  8.7  8.6  8.5  8.4  8.2  7.8
          -------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00

               NUMERICAL ANALYSIS:
               -------------------
               AVERAGE=     9.6    MAX.=    10.7    MIN.=     6.2
               AVERAGE/MINIMUM=     1.56:1
               MAXIMUM/MINIMUM=     1.74:1

ILLUMINANCE -- LOOKING DOWN     
---------------------------
HORIZONTAL PLANE OF POINTS
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	Y
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET             	|
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES	+----X       

BASE OF PLANE LOCATED AT Z=   0.00
  24.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.1 14.1 15.5 16.9 18.3 19.5 20.5 21.1 21.4 21.5 21.3 20.7 19.8 18.7 17.5 16.0 14.6 13.1
  22.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  14.2 16.2 18.2 20.1 21.9 23.6 24.9 25.7 26.1 26.2 26.0 25.1 24.0 22.5 20.8 18.8 16.9 15.0
  21.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  15.6 18.1 20.6 23.2 25.6 27.8 29.3 30.5 31.1 31.2 30.7 29.8 28.3 26.4 24.0 21.5 19.0 16.5
  19.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  17.0 20.1 23.2 26.5 29.6 32.3 34.3 35.7 36.4 36.6 36.1 34.9 33.0 30.6 27.6 24.4 21.1 18.1
  18.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  18.3 21.9 25.6 29.6 33.3 36.6 38.9 40.6 41.4 41.6 41.0 39.6 37.4 34.5 30.9 27.0 23.1 19.5
  16.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  19.4 23.4 27.6 32.1 36.4 40.1 42.7 44.5 45.5 45.7 45.0 43.4 41.0 37.7 33.6 29.2 24.8 20.8
  15.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.4 24.6 29.2 34.0 38.6 42.6 45.4 47.4 48.4 48.7 47.9 46.2 43.6 40.0 35.7 30.8 26.1 21.7
  13.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.8 25.2 30.0 35.0 39.7 43.9 46.9 49.0 50.0 50.3 49.5 47.8 45.0 41.3 36.7 31.7 26.8 22.3
  12.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  21.0 25.4 30.3 35.4 40.1 44.3 47.4 49.6 50.6 50.9 50.0 48.4 45.5 41.7 37.0 32.0 27.1 22.5
  10.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.8 25.2 30.0 35.0 39.7 43.9 46.9 49.0 50.0 50.3 49.5 47.8 45.0 41.3 36.7 31.7 26.8 22.3
   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.4 24.6 29.2 34.0 38.6 42.6 45.4 47.4 48.4 48.7 47.9 46.2 43.6 40.0 35.7 30.8 26.1 21.7
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  19.4 23.4 27.6 32.1 36.4 40.1 42.7 44.5 45.5 45.7 45.0 43.4 41.0 37.7 33.6 29.2 24.8 20.8
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  18.3 21.9 25.6 29.6 33.3 36.6 38.9 40.6 41.4 41.6 41.0 39.6 37.4 34.5 30.9 27.0 23.1 19.5
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  17.0 20.1 23.2 26.5 29.6 32.3 34.3 35.7 36.4 36.6 36.1 34.9 33.0 30.6 27.6 24.4 21.1 18.1
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  15.6 18.1 20.6 23.2 25.6 27.8 29.3 30.5 31.1 31.2 30.7 29.8 28.3 26.4 24.0 21.5 19.0 16.5
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  14.2 16.2 18.2 20.1 21.9 23.6 24.9 25.7 26.1 26.2 26.0 25.1 24.0 22.5 20.8 18.8 16.9 15.0
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.1 14.1 15.5 16.9 18.3 19.5 20.5 21.1 21.4 21.5 21.3 20.7 19.8 18.7 17.5 16.0 14.6 13.1
          -------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00

               NUMERICAL ANALYSIS:
               -------------------
               AVERAGE=    30.1    MAX.=    50.9    MIN.=    11.1
               AVERAGE/MINIMUM=     2.71:1
               MAXIMUM/MINIMUM=     4.59:1

GREY SCALE : ILLUMINANCE -- LOOKING DOWN Z = 2.5
------------------------------------------------
RANGE OF VALUES IN FOOTCANDLES               	
                                             	
ÛÛÛÛÛÛÛ²²²²²²²±±±±±±±°°°°°°°ººººººº=======
ÛÛÛÛÛÛÛ²²²²²²²±±±±±±±°°°°°°°ººººººº=======
ÛÛÛÛÛÛÛ²²²²²²²±±±±±±±°°°°°°°ººººººº=======
 9.80  20.01  30.01  40.01  50.01  60.01
  TO     TO     TO     TO     TO     TO
20.00  30.00  40.00  50.00  60.00  70.00

   24.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   22.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛ
   21.0-|    ÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²ÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛ²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²ÛÛÛÛÛ
   19.5-|    ÛÛÛÛÛÛ²²²²²²²²²²±±±±±±±±±±±±±±±°°°°°°°°°°°°°°°°°°°°°°°°°±±±±±±±±±±±±±±±²²²²²²²²²²²ÛÛÛÛ
        |    ÛÛÛÛÛ²²²²²²²²²²±±±±±±±±±±±°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°±±±±±±±±±±±±²²²²²²²²²²ÛÛÛ
        |    ÛÛÛÛ²²²²²²²²²±±±±±±±±±±°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°±±±±±±±±±²²²²²²²²²²ÛÛ
   18.0-|    ÛÛÛ²²²²²²²²²±±±±±±±±±°°°°°°°°°°°°°°°°°ºººººººººººº°°°°°°°°°°°°°°°°°±±±±±±±±²²²²²²²²²²Û
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   16.5-|    ÛÛ²²²²²²²²±±±±±±±°°°°°°°°°ºººººººººººººººººººººººººººººººººººº°°°°°°°°°±±±±±±±²²²²²²²²
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GREY SCALE : ILLUMINANCE -- LOOKING WEST     
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RANGE OF VALUES IN FOOTCANDLES

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GREY SCALE : ILLUMINANCE -- LOOKING UP Z = 10.0
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RANGE OF VALUES IN FOOTCANDLES

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        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
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GREY SCALE : ILLUMINANCE -- LOOKING DOWN Z = 0.0
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            0.0       3.0       6.0       9.0      12.0      15.0      18.0      21.0      24.0   
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APPENDIX C

PointÔ output and cut sheets
for parabolic reflector light



------------------------------------------------------------------------------
                                POINT

POINT (tm) (c) copyright 1984 - 1988 by Lighting Analysts, Inc.
------------------------------------------------------------------------------

CLIENT...........Alyn Rockwood
                 Computer Science Department, Arizona State University

CALCULATED BY....William S. Cochell

REFERENCE #......1

DATE.............03-31-1991

JOB DESCRIPTION :

Sample data for MCS project.

Using 2PM3g 340-18d fixtures

INPUT FILENAME : data4pm.IN

2PM3G 340-18D
ERL 6730       
2X4 3LP, 3", 18 CELL PARABOLIC                                             
LAMP= 3150 LM LAMP
TILT=NONE
 3  3150  1  11  5  1  1  2  4  0 
 .95  1  140 
 0  5  15  25  35  45  55  65  75  85 
 90 
 0  22.5  45  67.5  90 
 2845  2799  2657  2389  2157  1770  1299  602  37  4 
 0 
 2845  2805  2684  2450  2241  1849  1395  519  43  5 
 0 
 2845  2814  2748  2528  2342  2136  1132  315  45  6 
 0 
 2845  2825  2807  2574  2732  1972  810  234  42  5 
 0 
 2845  2829  2833  2626  2840  1891  761  172  36  5 
 0 

INSIGHT (c) copyright 1990 by Lighting Analysts, Inc.
Licensed material - program property of Lighting Analysts, Inc.

PRINTOUT CLARIFICATION
----------------------

Orientation  (ORIENT)  refers  to  the  counterclockwise  rotation  of  the
luminaire from zero degrees, zero degrees being east (see  diagram  below).

                                 90                        +y
                                  |                         |
                                  |                         |
    ORIENTATION          180 -----+----- 0                  +---- +x
     CONVENTION                   |
                                  |
                                 270

Tilt is the + or - angular displacement of the  luminaire  along  its  zero
degree photometric plane.

Cant is the + or - angular displacement  of  the luminaire along its ninety
degree photometric plane.

Metal halide lamp correction factor  (MHLCF)  is applied to luminaires with
metal halide lamps which when  tilted, affect the lumen output of the lamp.

LUMINAIRE DESCRIPTION
---------------------
LUMINAIRE TYPE  1 
FILENAME = 2pm-9.ies

2PM3G 340-18D
ERL 6730       
2X4 3LP, 3", 18 CELL PARABOLIC                                             
LAMP= 3150 LM LAMP

LUMINOUS DIMENSIONS  : ACROSS =  2  ALONG =  4  HEIGHT =  0 
TEST LAMP LUMENS    : 3150
INITIAL LAMP LUMENS : 3150
LIGHT LOSS FACTOR   : .81
BASED ON LAMP LUMEN DEPRECIATION x LUMINAIRE DIRT DEPRECIATION x BALLAST FACTOR

ROOM DESCRIPTION
----------------
COORDINATES IN FEET

DIMENSIONS      REFLECTANCES
X = 26          WEST WALL  = .4     
Y = 24          NORTH WALL = .4     
Z = 10          EAST WALL  = .4     
                SOUTH WALL = .4     
                FLOOR      = .4     
                CEILING    = .8     

LUMINAIRE LOCATION PARAMETERS
-----------------------------
COORDINATES IN FEET

GRID  LUMINAIRE                  MOUNTING
 NO.    TYPE    X-COORD  Y-COORD  HEIGHT   ORIENT   TILT     CANT 
----    ----    -------  -------  -------  -------  -------  -------
 1      1       7        8        10       90       0        0      
 1      1       7        16       10       90       0        0      
 1      1       13       8        10       90       0        0      
 1      1       13       16       10       90       0        0      
 1      1       19       8        10       90       0        0      
 1      1       19       16       10       90       0        0      

LUMINAIRE TYPE  1 : NUMBER OF UNIQUE LOCATIONS =    6

AVERAGE TILTED LAMP CORRECTION FACTOR APPLIED = 1.000

ILLUMINANCE -- LOOKING DOWN     
---------------------------
HORIZONTAL PLANE OF POINTS
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	Y
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET				|
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES	+----X  

BASE OF PLANE LOCATED AT Z=   2.50
  24.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.0 15.5 17.9 20.1 22.4 24.7 26.5 27.6 28.2 28.3 27.9 26.9 25.3 23.2 20.9 18.6 16.2 13.7
  22.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  15.0 19.0 22.5 25.9 29.5 33.0 35.6 37.2 38.3 38.5 37.6 36.1 33.9 30.8 27.1 23.6 20.2 16.5
  21.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  17.5 22.9 27.9 33.0 38.4 43.4 46.9 49.2 51.0 51.2 50.0 47.6 44.6 40.2 34.9 29.5 24.5 19.5
  19.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.3 27.4 34.4 41.6 49.3 56.1 60.9 63.8 66.4 66.7 65.0 61.8 57.8 51.8 44.3 36.6 29.6 22.8
  18.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  23.0 31.9 40.9 50.2 60.2 69.1 74.9 78.5 81.8 82.3 79.9 76.0 71.1 63.4 53.7 43.8 34.7 25.9
  16.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  25.1 35.5 45.8 56.8 68.5 78.9 85.5 89.7 93.6 94.2 91.3 86.8 81.3 72.2 60.8 49.3 38.7 28.5
  15.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  26.3 37.5 48.5 60.1 72.5 83.7 90.8 95.3 99.5 100. 97.0 92.2 86.3 76.6 64.4 52.1 40.9 30.0
  13.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  27.0 38.1 49.2 60.8 73.3 84.5 91.9 96.6 101. 101. 98.4 93.3 87.2 77.4 65.1 52.8 41.6 30.7
  12.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  27.2 38.2 49.2 60.7 73.1 84.1 91.6 96.5 101. 101. 98.3 93.1 86.8 77.1 65.0 52.8 41.7 30.9
  10.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  27.0 38.1 49.2 60.8 73.3 84.5 91.9 96.6 101. 101. 98.4 93.3 87.2 77.4 65.1 52.8 41.6 30.7
   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  26.3 37.5 48.5 60.1 72.5 83.7 90.8 95.3 99.5 100. 97.0 92.2 86.3 76.6 64.4 52.1 40.9 30.0
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  25.1 35.5 45.8 56.8 68.5 78.9 85.5 89.7 93.6 94.2 91.3 86.8 81.3 72.2 60.8 49.3 38.7 28.5
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  23.0 31.9 40.9 50.2 60.2 69.1 74.9 78.5 81.8 82.3 79.9 76.0 71.1 63.4 53.7 43.8 34.7 25.9
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.3 27.4 34.4 41.6 49.3 56.1 60.9 63.8 66.4 66.7 65.0 61.8 57.8 51.8 44.3 36.6 29.6 22.8
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  17.5 22.9 27.9 33.0 38.4 43.4 46.9 49.2 51.0 51.2 50.0 47.6 44.6 40.2 34.9 29.5 24.5 19.5
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  15.0 19.0 22.5 25.9 29.5 33.0 35.6 37.2 38.3 38.5 37.6 36.1 33.9 30.8 27.1 23.6 20.2 16.5
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.0 15.5 17.9 20.1 22.4 24.7 26.5 27.6 28.2 28.3 27.9 26.9 25.3 23.2 20.9 18.6 16.2 13.7
          -------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00

               NUMERICAL ANALYSIS:
               -------------------
               AVERAGE=    51.1    MAX.=   101.5    MIN.=    11.0
               AVERAGE/MINIMUM=     4.65:1
               MAXIMUM/MINIMUM=     9.23:1

ILLUMINANCE -- LOOKING NORTH    
----------------------------
VERTICAL PLANE OF POINTS
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	Z
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET				|
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES	+----X  

BASE OF PLANE LOCATED AT Y=  24.00

   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   9.9 11.1 11.5 11.8 12.0 12.2 12.3 12.4 12.4 12.4 12.4 12.4 12.2 12.1 11.9 11.6 11.2 10.5
        |
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.5 11.8 12.8 13.9 14.9 15.5 15.7 15.9 16.1 16.1 15.9 15.8 15.6 15.2 14.3 13.2 12.1 11.0
        |
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.5 13.5 15.6 17.9 19.9 21.3 22.1 22.5 22.6 22.7 22.6 22.3 21.5 20.4 18.7 16.4 14.1 12.2
        |
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  13.2 16.1 19.2 22.1 24.5 26.6 28.5 29.4 29.3 29.3 29.4 28.9 27.3 25.3 22.9 20.2 17.1 14.3
        |
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  15.1 18.6 21.7 24.5 27.0 29.4 31.4 32.6 33.0 33.1 32.8 31.9 30.1 27.9 25.4 22.7 19.7 16.3
        |
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  16.6 20.6 23.3 25.8 28.3 30.5 32.2 33.5 34.3 34.4 33.8 32.7 31.1 29.0 26.6 24.2 21.6 18.1
        |
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  15.6 21.9 23.9 26.0 28.1 29.8 31.3 32.5 33.4 33.5 32.9 31.8 30.3 28.7 26.7 24.6 22.6 20.3
        |
          -------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00

               NUMERICAL ANALYSIS:
               -------------------

               AVERAGE=    21.4    MAX.=    34.4    MIN.=     9.9
               AVERAGE/MINIMUM=     2.16:1
               MAXIMUM/MINIMUM=     3.47:1

ILLUMINANCE -- LOOKING WEST     
---------------------------
VERTICAL PLANE OF POINTS
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	Z
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET				|
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES	+----Y  

BASE OF PLANE LOCATED AT X=   0.00

   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.2 11.2 11.6 11.9 12.1 12.3 12.4 12.5 12.5 12.5 12.4 12.3 12.1 11.9 11.6 11.2 10.2
        |
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.7 11.8 12.6 13.3 13.8 14.2 14.5 14.7 14.7 14.7 14.5 14.2 13.8 13.3 12.6 11.8 10.7
        |
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.7 13.2 14.6 16.1 17.5 18.5 19.0 19.1 19.1 19.1 19.0 18.5 17.5 16.1 14.6 13.2 11.7
        |
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  13.3 15.6 17.8 20.1 22.4 24.1 25.1 25.4 25.4 25.4 25.1 24.1 22.4 20.1 17.8 15.6 13.3
        |
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  15.0 17.9 20.7 23.6 26.3 28.3 29.6 30.0 30.1 30.0 29.6 28.3 26.3 23.6 20.7 17.9 15.0
        |
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  16.4 20.2 22.9 25.4 27.8 29.8 31.1 31.8 31.8 31.8 31.1 29.8 27.8 25.4 22.9 20.2 16.4
        |
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  15.3 21.5 23.5 25.6 27.8 29.6 30.8 31.2 31.3 31.2 30.8 29.6 27.8 25.6 23.5 21.5 15.3
        |
          --------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00

               NUMERICAL ANALYSIS:
               -------------------

               AVERAGE=    19.8    MAX.=    31.8    MIN.=    10.2
               AVERAGE/MINIMUM=     1.95:1
               MAXIMUM/MINIMUM=     3.13:1

ILLUMINANCE -- LOOKING UP       
-------------------------
HORIZONTAL PLANE OF POINTS
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	Y
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET             	|
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES	+----X       

BASE OF PLANE LOCATED AT Z=  10.00
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.2 10.6 11.0 11.4 11.6 11.8 12.0 12.0 12.1 12.1 12.1 12.0 11.9 11.7 11.4 11.1 10.8 10.2
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.5 11.5 11.9 12.3 12.6 12.9 13.0 13.2 13.2 13.2 13.2 13.1 12.9 12.7 12.4 12.1 11.6 11.0
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.9 11.8 12.4 12.8 13.2 13.4 13.6 13.8 13.8 13.8 13.8 13.7 13.5 13.3 13.0 12.5 12.0 11.3
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.2 12.2 12.8 13.3 13.7 14.0 14.2 14.3 14.4 14.4 14.3 14.2 14.0 13.8 13.4 12.9 12.4 11.6
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.4 12.5 13.1 13.6 14.0 14.4 14.6 14.7 14.8 14.8 14.8 14.6 14.4 14.2 13.8 13.3 12.7 11.9
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.6 12.7 13.3 13.9 14.3 14.7 14.9 15.0 15.1 15.1 15.1 15.0 14.7 14.4 14.0 13.5 12.9 12.0
   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.7 12.8 13.5 14.1 14.5 14.9 15.1 15.3 15.4 15.4 15.3 15.2 15.0 14.6 14.2 13.7 13.0 12.2
  10.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.8 12.9 13.5 14.2 14.6 15.0 15.2 15.4 15.5 15.5 15.4 15.3 15.1 14.7 14.3 13.8 13.1 12.2
  12.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.8 12.9 13.6 14.2 14.7 15.0 15.3 15.5 15.6 15.6 15.5 15.4 15.1 14.8 14.4 13.8 13.2 12.3
  13.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.8 12.9 13.5 14.2 14.6 15.0 15.2 15.4 15.5 15.5 15.4 15.3 15.1 14.7 14.3 13.8 13.1 12.2
  15.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.7 12.8 13.5 14.1 14.5 14.9 15.1 15.3 15.4 15.4 15.3 15.2 15.0 14.6 14.2 13.7 13.0 12.2
  16.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.6 12.7 13.3 13.9 14.3 14.7 14.9 15.0 15.1 15.1 15.1 15.0 14.7 14.4 14.0 13.5 12.9 12.0
  18.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.4 12.5 13.1 13.6 14.0 14.4 14.6 14.7 14.8 14.8 14.8 14.6 14.4 14.2 13.8 13.3 12.7 11.9
  19.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  11.2 12.2 12.8 13.3 13.7 14.0 14.2 14.3 14.4 14.4 14.3 14.2 14.0 13.8 13.4 12.9 12.4 11.6
  21.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.9 11.8 12.4 12.8 13.2 13.4 13.6 13.8 13.8 13.8 13.8 13.7 13.5 13.3 13.0 12.5 12.0 11.3
  22.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  10.5 11.5 11.9 12.3 12.6 12.9 13.0 13.2 13.2 13.2 13.2 13.1 12.9 12.7 12.4 12.1 11.6 11.0
  24.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |   8.2 10.6 11.0 11.4 11.6 11.8 12.0 12.0 12.1 12.1 12.1 12.0 11.9 11.7 11.4 11.1 10.8 10.2
          -------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00

               NUMERICAL ANALYSIS:
               -------------------
               AVERAGE=    13.4    MAX.=    15.6    MIN.=     8.2
               AVERAGE/MINIMUM=     1.64:1
               MAXIMUM/MINIMUM=     1.91:1

ILLUMINANCE -- LOOKING DOWN     
---------------------------
HORIZONTAL PLANE OF POINTS
SCALE LEFT TO RIGHT    3.00  FEET PER INCH	Y
SCALE TOP TO BOTTOM    3.00  FEET PER INCH	|
COORDINATES ARE GIVEN IN FEET             	|
COMPUTED RESULTS ARE GIVEN IN  FOOTCANDLES	+----X       

BASE OF PLANE LOCATED AT Z=   0.00
  24.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  14.2 18.3 20.6 23.1 25.6 27.6 29.3 30.7 31.8 32.0 31.3 29.8 28.1 26.3 24.1 21.5 19.1 16.8
  22.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  18.5 21.7 24.8 28.2 31.5 34.2 36.6 38.6 39.9 40.0 39.2 37.3 35.0 32.4 29.5 26.0 22.7 19.6
  21.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.9 25.1 29.0 33.4 37.7 41.4 44.2 46.8 48.5 48.8 47.4 45.2 42.4 38.9 34.9 30.5 26.4 22.4
  19.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  23.8 28.6 33.5 39.2 44.9 49.3 52.8 55.9 58.2 58.6 56.8 53.9 50.6 46.4 41.2 35.4 30.3 25.4
  18.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  26.5 32.0 37.8 44.7 51.9 57.0 61.0 64.7 67.8 68.2 65.9 62.4 58.5 53.7 47.3 40.0 33.9 28.3
  16.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  29.0 34.8 41.4 49.4 57.9 63.3 67.8 72.0 75.8 76.2 73.5 69.4 64.9 59.8 52.4 44.0 37.0 30.9
  15.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  30.7 36.8 43.9 52.6 61.7 67.4 72.5 77.0 81.1 81.3 78.6 74.2 69.2 63.5 55.8 46.8 39.1 32.5
  13.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  31.0 37.8 45.2 53.9 62.7 69.2 74.3 79.1 83.0 83.5 80.6 76.2 71.1 65.0 57.0 48.0 40.3 33.2
  12.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  31.1 38.2 45.6 54.3 62.9 69.7 74.9 79.8 83.4 84.0 81.2 76.8 71.6 65.3 57.3 48.5 40.7 33.4
  10.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  31.0 37.8 45.2 53.9 62.7 69.2 74.3 79.1 83.0 83.5 80.6 76.2 71.1 65.0 57.0 48.0 40.3 33.2
   9.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  30.7 36.8 43.9 52.6 61.7 67.4 72.5 77.0 81.1 81.3 78.6 74.2 69.2 63.5 55.8 46.8 39.1 32.5
   7.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  29.0 34.8 41.4 49.4 57.9 63.3 67.8 72.0 75.8 76.2 73.5 69.4 64.9 59.8 52.4 44.0 37.0 30.9
   6.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  26.5 32.0 37.8 44.7 51.9 57.0 61.0 64.7 67.8 68.2 65.9 62.4 58.5 53.7 47.3 40.0 33.9 28.3
   4.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  23.8 28.6 33.5 39.2 44.9 49.3 52.8 55.9 58.2 58.6 56.8 53.9 50.6 46.4 41.2 35.4 30.3 25.4
   3.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  20.9 25.1 29.0 33.4 37.7 41.4 44.2 46.8 48.5 48.8 47.4 45.2 42.4 38.9 34.9 30.5 26.4 22.4
   1.50-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  18.5 21.7 24.8 28.2 31.5 34.2 36.6 38.6 39.9 40.0 39.2 37.3 35.0 32.4 29.5 26.0 22.7 19.6
   0.00-|    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    +    + 
        |  14.2 18.3 20.6 23.1 25.6 27.6 29.3 30.7 31.8 32.0 31.3 29.8 28.1 26.3 24.1 21.5 19.1 16.8
          -------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |
           0.00      3.00      6.00      9.00     12.00     15.00     18.00     21.00     24.00

               NUMERICAL ANALYSIS:
               -------------------
               AVERAGE=    46.1    MAX.=    84.0    MIN.=    14.2
               AVERAGE/MINIMUM=     3.24:1
               MAXIMUM/MINIMUM=     5.90:1

GREY SCALE : ILLUMINANCE -- LOOKING DOWN Z = 2.5
------------------------------------------------
RANGE OF VALUES IN FOOTCANDLES

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   TO     TO     TO     TO     TO     TO     TO     TO     TO     TO  
  20.00  30.00  40.00  50.00  60.00  70.00  80.00  90.00 100.00 101.50

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          ------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |      
            0.0       3.0       6.0       9.0      12.0      15.0      18.0      21.0      24.0   
Y
|
|
+----X

GREY SCALE : ILLUMINANCE -- LOOKING NORTH    
---------------------------------------------
RANGE OF VALUES IN FOOTCANDLES

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          ------------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |      
            0.0       3.0       6.0       9.0      12.0      15.0      18.0      21.0      24.0   
Z
|
|
+----X

GREY SCALE : ILLUMINANCE -- LOOKING WEST     
---------------------------------------------
RANGE OF VALUES IN FOOTCANDLES

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        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
    4.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛÛÛ
    3.0-|    ÛÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²²²²²±±±±±±±±±²²²²²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛÛÛ
    1.5-|    ÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛ
        |    ÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛ
        |    ÛÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛÛ
    0.0-|    ÛÛÛÛ²²²²²²²²²²²²²²²²²²²²²²²±±±±±±±±±±±±±±±±±±±±±±±±±±±²²²²²²²²²²²²²²²²²²²²²²²ÛÛÛÛ

          -------------------------------------------------------------------------------------
             |         |         |         |         |         |         |         |         |      
            0.0       3.0       6.0       9.0      12.0      15.0      18.0      21.0      24.0   
Z
|
|
+----Y

GREY SCALE : ILLUMINANCE -- LOOKING UP Z = 10.0
-----------------------------------------------
RANGE OF VALUES IN FOOTCANDLES

ÛÛÛÛÛÛÛ
ÛÛÛÛÛÛÛ
ÛÛÛÛÛÛÛ
   8.20
   TO  
  20.00

    0.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
    1.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
    3.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
    4.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
    6.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
    7.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
    9.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   10.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   12.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   13.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   15.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   16.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   18.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   19.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   21.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   22.5-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
        |    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ
   24.0-|    ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ

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            0.0       3.0       6.0       9.0      12.0      15.0      18.0      21.0      24.0   
Y
|
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+----X

GREY SCALE : ILLUMINANCE -- LOOKING DOWN Z = 0.0
------------------------------------------------
RANGE OF VALUES IN FOOTCANDLES

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  20.00  30.00  40.00  50.00  60.00  70.00  80.00  90.00

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FOOTNOTES

  1. Throughout this discussion, the term surface will mean an element that can be divided into smaller elements. The resulting smaller element will be called patches. An analogy is that a floor is a surface while the vinyl tile that cover the floor are patches.
  2. Method 2 is faster than Method 4 because of a check for saturation is made before the cosines and distances are calculated. This method accumulates light faster and therefore reaches the threshold before Method 4.

BIBLIOGRAPHY

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