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!AWSep91/Goodies/PD/QRTinfo/Discuss
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File contents
This document discusses:
The transmission of light in the QRT world
Removing sections from a planar object
Transmission of light
=====================
Transmission of light through surfaces now works, allowing one to model
glass surfaces. Some additions to and changes from the original grammar were
necessary to provide the desired functionality. A new keyword, "DENSITY",
has been added, and the function of the old "TRANS" keyword has been
changed. Also, a "THRESHOLD" parameter has been added to the default
structure. Since transmission is a complex operation, this entire Addendum
will discuss aspects of modeling glass surfaces.
The DENSITY keyword
~~~~~~~~~~~~~~~~~~~
It was my previous intent that the TRANS keyword would specify the
percent transmission of light though the surface. After thinking a little
more about the nature of light transmission, it was clear that this wasn't
adequate. The amount of light transmitted depends not only on a fixed
coefficient of the surface, but on the thickness of the surface. For
example, a hollow glass sphere will appear darker (transmit less light) near
the edges, where the glass is thickest. To account for this effect, the
"DENSITY" keyword was added. Density specifies what percentage of
transmitted light will be removed per unit distance travelled though the
object. For example, the following density attribute would remove 2 percent
of all light per unit distance:
DENSITY = (.02, .02, .02);
If a sphere, at its widest point, was 10 units thick, 20 percent of the
light would be removed. Near the edge of the sphere, less light would be
removed.
Since density is a function of distance, the same density factor will
have different effects on objects of different sizes. To remove the same
percentage of light from an object half as thick, double the density factor.
Shadows from Transparent Surfaces
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The old "TRANS" keyword still exists, but it performs a different
function. It does not affect the appearance of the object, but rather, the
attenuation of light passed through the surface. QRT knows how glass
surfaces bend light, and so it can model the magnifying effects of looking
through curved glass, etc. But for computing shadows, it cannot properly
bend the light from lamps. This means that you can model lenses that the
observer looks through, but not lenses used to focus light. In order to
provide some attenuation effects, use "TRANS" to tell QRT how much light is
passed through the surface. This information is ONLY used for computing
shadows. For example, blue glass should cast a blue shadow. Use something
similar to:
TRANS = (0, 0, .7)
to cast a blue shadow (this lets 70 percent of the blue light pass). Note
that by using strange combinations of DENSITY and TRANS, you can model
illogical objects which appear, for example, blue, but cast a red shadow.
These shadows will be entirely of one intensity, and will not vary with the
thickness of the glass.
Using MIRROR with Transparent surfaces
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Glass surfaces not only refract light, but also reflect a percentage of
it. This means that to realistically model glass, the glass should reflect a
small percentage of the light. Try starting with 20 to 25 percent
reflection. Note that all glass objects reflect light from both the outside
and the inside surfaces of the glass.
Index of Refraction
~~~~~~~~~~~~~~~~~~~
The index of refraction for an object governs how much the light is bent
upon entering or exiting the object. A higher index will bend the light
more. The index of refraction of air is 1.00, and for glass is roughly 1.33.
Some substances, such as diamond, have a higher index.
Modeling Hollow Objects
~~~~~~~~~~~~~~~~~~~~~~~
When designing the QRT transmission routines, I wanted to be able to
model both solid glass and hollow glass objects. To understand how this is
done, it is necessary to understand a little about how QRT's transmission
model works.
A ray, after leaving the observer, has two states: either it is inside a
glass object, or it is outside. The ray starts out outside. When it first
encounters a glass surface, it is bent, and its state is toggled from
OUTSIDE to INSIDE. It continues on until encountering another surface,
whereupon it is bent again, and its state is once more toggled. This has
several implications for modeling glass. The first is that ALL glass
surfaces MUST have two sides - that is, once the ray enters the glass, there
must be no way for it to exit without again passing through a surface. The
second is that a ray must go from glass to air, or air to glass, but not
from glass with index of refraction A to glass with index of refraction B;
i.e, the two glass surfaces cannot touch each other, even though they may be
placed very close together.
As an example of how this works, consider a solid glass sphere. The ray
encounters the sphere, and is bent (in this case, towards the normal
vector). QRT now remembers that the ray is INSIDE a glass surface. The ray
continues on until it hits the back side of the sphere, whereupon it is bent
(away from the normal vector), and its state is toggled to OUTSIDE. In
summary, the INSIDE/OUTSIDE flag tells QRT how to bend the ray.
Consider now the case of a hollow glass sphere. This is modeled using two
concentric spheres, one with a smaller radius. The ray will first hit the
outside sphere, be bent, and have its state toggled to INSIDE. There are now
two possible cases. First, the ray may miss the inside sphere, in which case
the simulation proceeds as in the above paragraph. Second, it may hit the
inside sphere. In this case, it is bent, and its state is toggled to
OUTSIDE. The ray is now considered to be back in air, so that the inside
sphere has modeled the hollow portion of the glass. In a similar manner, the
ray reaches the other side of the inside sphere, enters the glass again, and
finally leaves the outside sphere. Note that even though the inside sphere
is thought of as the "air" in the center of the object, it MUST have the
same index of refraction as the outside sphere. This is necessary so that
QRT can correctly bend the light when it exits the glass.
Chromatic Aberration
~~~~~~~~~~~~~~~~~~~~
In QRT, all rays, regardless of color, are refracted exactly the same.
This is contrast to the real world, in which the amount the light is bent
depends on its wavelength. This appears, so far as I can tell, to be a bug
in the real world, and I saw no reason to include it in a ray tracer.
Threshold attribute
~~~~~~~~~~~~~~~~~~~
A new keyword, THRESHOLD, has been added to the default structure. In
previous versions of QRT, there was a mechanism for detecting infinite
recursion provided that objects reflected less that 100 percent of the light
reaching them. QRT stopped the recursion when the intensity of the light
reached 1 percent of its original value. When transmission was added, I made
this value adjustable. With glass objects, both surfaces reflect light, and
if QRT waits until the 1 percent mark before stopping recursion, the time
necessary to complete the image is greatly increased with little or no
increase in image quality. The default is now 10 percent, and is changeable
as follows:
DEFAULT ( threshold = .05
)
This would stop recursion when the intensity reaches 5 percent of the
original value. An added effect is that if the objects surface reflects (or
transmits) less than the threshold amount of light, the reflection or
transmission will be ignored completely.
Affect of Glass on Speed
~~~~~~~~~~~~~~~~~~~~~~~~
Unfortunately, the presence of any glass objects will slow the ray tracer
down. This effect may range from barely noticeable, for few, small objects
to excruciatingly miserably slow, for many, large objects. Sorry, there is
nothing I can do to speed it up - the 68000 simply won't go any faster. The
reason for the slowdown is that for every ray/glass surface intersection,
TWO additional rays must be sent out (as opposed to one, for reflection).
And remember, each ray intersects a glass object twice: once on the way in,
and once on the way out. Also, the two generated rays may intersect the
glass, as well. You can see how this process could get very slow.
Notes, etc.
~~~~~~~~~~~
Watch for control characters in the QRT input file. I had accidentally
imbedded an invisible control character in a file I was working on, and the
QRT parser refused to parse the file. After closely checking the file, I
began to look for a bug in the parser code. Finally, I discovered the
control character, but only after spending 1 hour checking the parser code.
The QRT parser will generate a SYNTAX ERROR, CODE 207 upon encountering any
special characters in the input file.
Since transmission involves heavy recursion, don't forget to set the
default stack size to something larger than the default 4000 bytes. A stack
size of 40000 to 50000 bytes seems safe for most images.
The REMOVE command
==================
The 'REMOVE' command was added to allow sections of a planar primitive to
be removed. This makes it much easier to create flat objects that are not
shaped like QRT's planar primitives. For example, I had a QRT input file
which created the image of a grand piano. The top of the piano, because of
its complex shape, initially was created from 11 planar primitives. Now, it
is only 1 PARALLELOGRAM primitive, and a section of the parallelogram is
removed to create the shape of a piano top.
Before the REMOVE command can be used, a pattern must be created using
any of QRT's pattern primitives (the piano uses a polygon). This pattern
need not be given any surface characteristics - it simply defines the region
to be removed from the planar primitive. The pattern is attached to the
primitive in exactly the same way as a normal pattern, except that the
REMOVE command is used instead of the PATTERN command:
PARALLELOGRAM ( loc = (0, 0, 0)
v1 = (10, 0, 0)
v2 = (0, 0, 10)
diff = (1, 0, 0)
remove = SECTION_TO_REMOVE
pattern = ANY_PATTERN
)
This example shows that the PATTERN command can be used on the same
primitive as the REMOVE command.
Several things should be noted about the REMOVE command. First, the
pattern defines the sections to remove, not the sections which will remain.
In the piano example, the pattern mapped all of the parallelogram except the
part that composed the actual piano top. Second, even though the remove
command can be used with the curved surface primitives (SPHERE, QUADRATIC),
the results will not be quite right. To use the sphere as an example, the
front surface of the sphere would have the correct pattern removed from it,
but the back surface of the sphere would be completely gone. This is
because the SPHERE intersect routine ignores completely the back surface of
the sphere. I will probably fix this in a future version.
00000000 20 20 20 54 68 69 73 20 64 6f 63 75 6d 65 6e 74 | This document| 00000010 20 64 69 73 63 75 73 73 65 73 3a 0a 0a 20 20 20 | discusses:.. | 00000020 20 20 54 68 65 20 74 72 61 6e 73 6d 69 73 73 69 | The transmissi| 00000030 6f 6e 20 6f 66 20 6c 69 67 68 74 20 69 6e 20 74 |on of light in t| 00000040 68 65 20 51 52 54 20 77 6f 72 6c 64 0a 20 20 20 |he QRT world. | 00000050 20 20 52 65 6d 6f 76 69 6e 67 20 73 65 63 74 69 | Removing secti| 00000060 6f 6e 73 20 66 72 6f 6d 20 61 20 70 6c 61 6e 61 |ons from a plana| 00000070 72 20 6f 62 6a 65 63 74 0a 0a 0a 54 72 61 6e 73 |r object...Trans| 00000080 6d 69 73 73 69 6f 6e 20 6f 66 20 6c 69 67 68 74 |mission of light| 00000090 0a 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d |.===============| 000000a0 3d 3d 3d 3d 3d 3d 0a 20 0a 20 20 20 54 72 61 6e |======. . Tran| 000000b0 73 6d 69 73 73 69 6f 6e 20 6f 66 20 6c 69 67 68 |smission of ligh| 000000c0 74 20 74 68 72 6f 75 67 68 20 73 75 72 66 61 63 |t through surfac| 000000d0 65 73 20 6e 6f 77 20 77 6f 72 6b 73 2c 20 61 6c |es now works, al| 000000e0 6c 6f 77 69 6e 67 20 6f 6e 65 20 74 6f 20 6d 6f |lowing one to mo| 000000f0 64 65 6c 0a 67 6c 61 73 73 20 73 75 72 66 61 63 |del.glass surfac| 00000100 65 73 2e 20 53 6f 6d 65 20 61 64 64 69 74 69 6f |es. Some additio| 00000110 6e 73 20 74 6f 20 61 6e 64 20 63 68 61 6e 67 65 |ns to and change| 00000120 73 20 66 72 6f 6d 20 74 68 65 20 6f 72 69 67 69 |s from the origi| 00000130 6e 61 6c 20 67 72 61 6d 6d 61 72 20 77 65 72 65 |nal grammar were| 00000140 0a 6e 65 63 65 73 73 61 72 79 20 74 6f 20 70 72 |.necessary to pr| 00000150 6f 76 69 64 65 20 74 68 65 20 64 65 73 69 72 65 |ovide the desire| 00000160 64 20 66 75 6e 63 74 69 6f 6e 61 6c 69 74 79 2e |d functionality.| 00000170 20 41 20 6e 65 77 20 6b 65 79 77 6f 72 64 2c 20 | A new keyword, | 00000180 22 44 45 4e 53 49 54 59 22 2c 0a 68 61 73 20 62 |"DENSITY",.has b| 00000190 65 65 6e 20 61 64 64 65 64 2c 20 61 6e 64 20 74 |een added, and t| 000001a0 68 65 20 66 75 6e 63 74 69 6f 6e 20 6f 66 20 74 |he function of t| 000001b0 68 65 20 6f 6c 64 20 22 54 52 41 4e 53 22 20 6b |he old "TRANS" k| 000001c0 65 79 77 6f 72 64 20 68 61 73 20 62 65 65 6e 0a |eyword has been.| 000001d0 63 68 61 6e 67 65 64 2e 20 41 6c 73 6f 2c 20 61 |changed. Also, a| 000001e0 20 22 54 48 52 45 53 48 4f 4c 44 22 20 70 61 72 | "THRESHOLD" par| 000001f0 61 6d 65 74 65 72 20 68 61 73 20 62 65 65 6e 20 |ameter has been | 00000200 61 64 64 65 64 20 74 6f 20 74 68 65 20 64 65 66 |added to the def| 00000210 61 75 6c 74 0a 73 74 72 75 63 74 75 72 65 2e 20 |ault.structure. | 00000220 53 69 6e 63 65 20 74 72 61 6e 73 6d 69 73 73 69 |Since transmissi| 00000230 6f 6e 20 69 73 20 61 20 63 6f 6d 70 6c 65 78 20 |on is a complex | 00000240 6f 70 65 72 61 74 69 6f 6e 2c 20 74 68 69 73 20 |operation, this | 00000250 65 6e 74 69 72 65 20 41 64 64 65 6e 64 75 6d 0a |entire Addendum.| 00000260 77 69 6c 6c 20 64 69 73 63 75 73 73 20 61 73 70 |will discuss asp| 00000270 65 63 74 73 20 6f 66 20 6d 6f 64 65 6c 69 6e 67 |ects of modeling| 00000280 20 67 6c 61 73 73 20 73 75 72 66 61 63 65 73 2e | glass surfaces.| 00000290 0a 20 0a 54 68 65 20 44 45 4e 53 49 54 59 20 6b |. .The DENSITY k| 000002a0 65 79 77 6f 72 64 0a 7e 7e 7e 7e 7e 7e 7e 7e 7e |eyword.~~~~~~~~~| 000002b0 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 0a 20 0a 20 20 20 |~~~~~~~~~~. . | 000002c0 49 74 20 77 61 73 20 6d 79 20 70 72 65 76 69 6f |It was my previo| 000002d0 75 73 20 69 6e 74 65 6e 74 20 74 68 61 74 20 74 |us intent that t| 000002e0 68 65 20 54 52 41 4e 53 20 6b 65 79 77 6f 72 64 |he TRANS keyword| 000002f0 20 77 6f 75 6c 64 20 73 70 65 63 69 66 79 20 74 | would specify t| 00000300 68 65 0a 70 65 72 63 65 6e 74 20 74 72 61 6e 73 |he.percent trans| 00000310 6d 69 73 73 69 6f 6e 20 6f 66 20 6c 69 67 68 74 |mission of light| 00000320 20 74 68 6f 75 67 68 20 74 68 65 20 73 75 72 66 | though the surf| 00000330 61 63 65 2e 20 41 66 74 65 72 20 74 68 69 6e 6b |ace. After think| 00000340 69 6e 67 20 61 20 6c 69 74 74 6c 65 0a 6d 6f 72 |ing a little.mor| 00000350 65 20 61 62 6f 75 74 20 74 68 65 20 6e 61 74 75 |e about the natu| 00000360 72 65 20 6f 66 20 6c 69 67 68 74 20 74 72 61 6e |re of light tran| 00000370 73 6d 69 73 73 69 6f 6e 2c 20 69 74 20 77 61 73 |smission, it was| 00000380 20 63 6c 65 61 72 20 74 68 61 74 20 74 68 69 73 | clear that this| 00000390 20 77 61 73 6e 27 74 0a 61 64 65 71 75 61 74 65 | wasn't.adequate| 000003a0 2e 20 54 68 65 20 61 6d 6f 75 6e 74 20 6f 66 20 |. The amount of | 000003b0 6c 69 67 68 74 20 74 72 61 6e 73 6d 69 74 74 65 |light transmitte| 000003c0 64 20 64 65 70 65 6e 64 73 20 6e 6f 74 20 6f 6e |d depends not on| 000003d0 6c 79 20 6f 6e 20 61 20 66 69 78 65 64 0a 63 6f |ly on a fixed.co| 000003e0 65 66 66 69 63 69 65 6e 74 20 6f 66 20 74 68 65 |efficient of the| 000003f0 20 73 75 72 66 61 63 65 2c 20 62 75 74 20 6f 6e | surface, but on| 00000400 20 74 68 65 20 74 68 69 63 6b 6e 65 73 73 20 6f | the thickness o| 00000410 66 20 74 68 65 20 73 75 72 66 61 63 65 2e 20 46 |f the surface. F| 00000420 6f 72 0a 65 78 61 6d 70 6c 65 2c 20 61 20 68 6f |or.example, a ho| 00000430 6c 6c 6f 77 20 67 6c 61 73 73 20 73 70 68 65 72 |llow glass spher| 00000440 65 20 77 69 6c 6c 20 61 70 70 65 61 72 20 64 61 |e will appear da| 00000450 72 6b 65 72 20 28 74 72 61 6e 73 6d 69 74 20 6c |rker (transmit l| 00000460 65 73 73 20 6c 69 67 68 74 29 20 6e 65 61 72 0a |ess light) near.| 00000470 74 68 65 20 65 64 67 65 73 2c 20 77 68 65 72 65 |the edges, where| 00000480 20 74 68 65 20 67 6c 61 73 73 20 69 73 20 74 68 | the glass is th| 00000490 69 63 6b 65 73 74 2e 20 54 6f 20 61 63 63 6f 75 |ickest. To accou| 000004a0 6e 74 20 66 6f 72 20 74 68 69 73 20 65 66 66 65 |nt for this effe| 000004b0 63 74 2c 20 74 68 65 0a 22 44 45 4e 53 49 54 59 |ct, the."DENSITY| 000004c0 22 20 6b 65 79 77 6f 72 64 20 77 61 73 20 61 64 |" keyword was ad| 000004d0 64 65 64 2e 20 44 65 6e 73 69 74 79 20 73 70 65 |ded. Density spe| 000004e0 63 69 66 69 65 73 20 77 68 61 74 20 70 65 72 63 |cifies what perc| 000004f0 65 6e 74 61 67 65 20 6f 66 0a 74 72 61 6e 73 6d |entage of.transm| 00000500 69 74 74 65 64 20 6c 69 67 68 74 20 77 69 6c 6c |itted light will| 00000510 20 62 65 20 72 65 6d 6f 76 65 64 20 70 65 72 20 | be removed per | 00000520 75 6e 69 74 20 64 69 73 74 61 6e 63 65 20 74 72 |unit distance tr| 00000530 61 76 65 6c 6c 65 64 20 74 68 6f 75 67 68 20 74 |avelled though t| 00000540 68 65 0a 6f 62 6a 65 63 74 2e 20 46 6f 72 20 65 |he.object. For e| 00000550 78 61 6d 70 6c 65 2c 20 74 68 65 20 66 6f 6c 6c |xample, the foll| 00000560 6f 77 69 6e 67 20 64 65 6e 73 69 74 79 20 61 74 |owing density at| 00000570 74 72 69 62 75 74 65 20 77 6f 75 6c 64 20 72 65 |tribute would re| 00000580 6d 6f 76 65 20 32 20 70 65 72 63 65 6e 74 0a 6f |move 2 percent.o| 00000590 66 20 61 6c 6c 20 6c 69 67 68 74 20 70 65 72 20 |f all light per | 000005a0 75 6e 69 74 20 64 69 73 74 61 6e 63 65 3a 0a 20 |unit distance:. | 000005b0 0a 20 20 20 44 45 4e 53 49 54 59 20 3d 20 28 2e |. DENSITY = (.| 000005c0 30 32 2c 20 2e 30 32 2c 20 2e 30 32 29 3b 0a 20 |02, .02, .02);. | 000005d0 0a 20 20 20 49 66 20 61 20 73 70 68 65 72 65 2c |. If a sphere,| 000005e0 20 61 74 20 69 74 73 20 77 69 64 65 73 74 20 70 | at its widest p| 000005f0 6f 69 6e 74 2c 20 77 61 73 20 31 30 20 75 6e 69 |oint, was 10 uni| 00000600 74 73 20 74 68 69 63 6b 2c 20 32 30 20 70 65 72 |ts thick, 20 per| 00000610 63 65 6e 74 20 6f 66 20 74 68 65 0a 6c 69 67 68 |cent of the.ligh| 00000620 74 20 77 6f 75 6c 64 20 62 65 20 72 65 6d 6f 76 |t would be remov| 00000630 65 64 2e 20 4e 65 61 72 20 74 68 65 20 65 64 67 |ed. Near the edg| 00000640 65 20 6f 66 20 74 68 65 20 73 70 68 65 72 65 2c |e of the sphere,| 00000650 20 6c 65 73 73 20 6c 69 67 68 74 20 77 6f 75 6c | less light woul| 00000660 64 20 62 65 0a 72 65 6d 6f 76 65 64 2e 0a 20 0a |d be.removed.. .| 00000670 20 20 20 53 69 6e 63 65 20 64 65 6e 73 69 74 79 | Since density| 00000680 20 69 73 20 61 20 66 75 6e 63 74 69 6f 6e 20 6f | is a function o| 00000690 66 20 64 69 73 74 61 6e 63 65 2c 20 74 68 65 20 |f distance, the | 000006a0 73 61 6d 65 20 64 65 6e 73 69 74 79 20 66 61 63 |same density fac| 000006b0 74 6f 72 20 77 69 6c 6c 0a 68 61 76 65 20 64 69 |tor will.have di| 000006c0 66 66 65 72 65 6e 74 20 65 66 66 65 63 74 73 20 |fferent effects | 000006d0 6f 6e 20 6f 62 6a 65 63 74 73 20 6f 66 20 64 69 |on objects of di| 000006e0 66 66 65 72 65 6e 74 20 73 69 7a 65 73 2e 20 54 |fferent sizes. T| 000006f0 6f 20 72 65 6d 6f 76 65 20 74 68 65 20 73 61 6d |o remove the sam| 00000700 65 0a 70 65 72 63 65 6e 74 61 67 65 20 6f 66 20 |e.percentage of | 00000710 6c 69 67 68 74 20 66 72 6f 6d 20 61 6e 20 6f 62 |light from an ob| 00000720 6a 65 63 74 20 68 61 6c 66 20 61 73 20 74 68 69 |ject half as thi| 00000730 63 6b 2c 20 64 6f 75 62 6c 65 20 74 68 65 20 64 |ck, double the d| 00000740 65 6e 73 69 74 79 20 66 61 63 74 6f 72 2e 0a 20 |ensity factor.. | 00000750 0a 53 68 61 64 6f 77 73 20 66 72 6f 6d 20 54 72 |.Shadows from Tr| 00000760 61 6e 73 70 61 72 65 6e 74 20 53 75 72 66 61 63 |ansparent Surfac| 00000770 65 73 0a 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e |es.~~~~~~~~~~~~~| 00000780 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e |~~~~~~~~~~~~~~~~| 00000790 7e 7e 7e 7e 0a 20 0a 20 20 20 54 68 65 20 6f 6c |~~~~. . The ol| 000007a0 64 20 22 54 52 41 4e 53 22 20 6b 65 79 77 6f 72 |d "TRANS" keywor| 000007b0 64 20 73 74 69 6c 6c 20 65 78 69 73 74 73 2c 20 |d still exists, | 000007c0 62 75 74 20 69 74 20 70 65 72 66 6f 72 6d 73 20 |but it performs | 000007d0 61 20 64 69 66 66 65 72 65 6e 74 0a 66 75 6e 63 |a different.func| 000007e0 74 69 6f 6e 2e 20 49 74 20 64 6f 65 73 20 6e 6f |tion. It does no| 000007f0 74 20 61 66 66 65 63 74 20 74 68 65 20 61 70 70 |t affect the app| 00000800 65 61 72 61 6e 63 65 20 6f 66 20 74 68 65 20 6f |earance of the o| 00000810 62 6a 65 63 74 2c 20 62 75 74 20 72 61 74 68 65 |bject, but rathe| 00000820 72 2c 20 74 68 65 0a 61 74 74 65 6e 75 61 74 69 |r, the.attenuati| 00000830 6f 6e 20 6f 66 20 6c 69 67 68 74 20 70 61 73 73 |on of light pass| 00000840 65 64 20 74 68 72 6f 75 67 68 20 74 68 65 20 73 |ed through the s| 00000850 75 72 66 61 63 65 2e 20 51 52 54 20 6b 6e 6f 77 |urface. QRT know| 00000860 73 20 68 6f 77 20 67 6c 61 73 73 0a 73 75 72 66 |s how glass.surf| 00000870 61 63 65 73 20 62 65 6e 64 20 6c 69 67 68 74 2c |aces bend light,| 00000880 20 61 6e 64 20 73 6f 20 69 74 20 63 61 6e 20 6d | and so it can m| 00000890 6f 64 65 6c 20 74 68 65 20 6d 61 67 6e 69 66 79 |odel the magnify| 000008a0 69 6e 67 20 65 66 66 65 63 74 73 20 6f 66 20 6c |ing effects of l| 000008b0 6f 6f 6b 69 6e 67 0a 74 68 72 6f 75 67 68 20 63 |ooking.through c| 000008c0 75 72 76 65 64 20 67 6c 61 73 73 2c 20 65 74 63 |urved glass, etc| 000008d0 2e 20 42 75 74 20 66 6f 72 20 63 6f 6d 70 75 74 |. But for comput| 000008e0 69 6e 67 20 73 68 61 64 6f 77 73 2c 20 69 74 20 |ing shadows, it | 000008f0 63 61 6e 6e 6f 74 20 70 72 6f 70 65 72 6c 79 0a |cannot properly.| 00000900 62 65 6e 64 20 74 68 65 20 6c 69 67 68 74 20 66 |bend the light f| 00000910 72 6f 6d 20 6c 61 6d 70 73 2e 20 54 68 69 73 20 |rom lamps. This | 00000920 6d 65 61 6e 73 20 74 68 61 74 20 79 6f 75 20 63 |means that you c| 00000930 61 6e 20 6d 6f 64 65 6c 20 6c 65 6e 73 65 73 20 |an model lenses | 00000940 74 68 61 74 20 74 68 65 0a 6f 62 73 65 72 76 65 |that the.observe| 00000950 72 20 6c 6f 6f 6b 73 20 74 68 72 6f 75 67 68 2c |r looks through,| 00000960 20 62 75 74 20 6e 6f 74 20 6c 65 6e 73 65 73 20 | but not lenses | 00000970 75 73 65 64 20 74 6f 20 66 6f 63 75 73 20 6c 69 |used to focus li| 00000980 67 68 74 2e 20 49 6e 20 6f 72 64 65 72 20 74 6f |ght. In order to| 00000990 0a 70 72 6f 76 69 64 65 20 73 6f 6d 65 20 61 74 |.provide some at| 000009a0 74 65 6e 75 61 74 69 6f 6e 20 65 66 66 65 63 74 |tenuation effect| 000009b0 73 2c 20 75 73 65 20 22 54 52 41 4e 53 22 20 74 |s, use "TRANS" t| 000009c0 6f 20 74 65 6c 6c 20 51 52 54 20 68 6f 77 20 6d |o tell QRT how m| 000009d0 75 63 68 20 6c 69 67 68 74 20 69 73 0a 70 61 73 |uch light is.pas| 000009e0 73 65 64 20 74 68 72 6f 75 67 68 20 74 68 65 20 |sed through the | 000009f0 73 75 72 66 61 63 65 2e 20 54 68 69 73 20 69 6e |surface. This in| 00000a00 66 6f 72 6d 61 74 69 6f 6e 20 69 73 20 4f 4e 4c |formation is ONL| 00000a10 59 20 75 73 65 64 20 66 6f 72 20 63 6f 6d 70 75 |Y used for compu| 00000a20 74 69 6e 67 0a 73 68 61 64 6f 77 73 2e 20 46 6f |ting.shadows. Fo| 00000a30 72 20 65 78 61 6d 70 6c 65 2c 20 62 6c 75 65 20 |r example, blue | 00000a40 67 6c 61 73 73 20 73 68 6f 75 6c 64 20 63 61 73 |glass should cas| 00000a50 74 20 61 20 62 6c 75 65 20 73 68 61 64 6f 77 2e |t a blue shadow.| 00000a60 20 55 73 65 20 73 6f 6d 65 74 68 69 6e 67 0a 73 | Use something.s| 00000a70 69 6d 69 6c 61 72 20 74 6f 3a 0a 20 0a 20 20 20 |imilar to:. . | 00000a80 54 52 41 4e 53 20 3d 20 28 30 2c 20 30 2c 20 2e |TRANS = (0, 0, .| 00000a90 37 29 0a 20 0a 74 6f 20 63 61 73 74 20 61 20 62 |7). .to cast a b| 00000aa0 6c 75 65 20 73 68 61 64 6f 77 20 28 74 68 69 73 |lue shadow (this| 00000ab0 20 6c 65 74 73 20 37 30 20 70 65 72 63 65 6e 74 | lets 70 percent| 00000ac0 20 6f 66 20 74 68 65 20 62 6c 75 65 20 6c 69 67 | of the blue lig| 00000ad0 68 74 20 70 61 73 73 29 2e 20 4e 6f 74 65 0a 74 |ht pass). Note.t| 00000ae0 68 61 74 20 62 79 20 75 73 69 6e 67 20 73 74 72 |hat by using str| 00000af0 61 6e 67 65 20 63 6f 6d 62 69 6e 61 74 69 6f 6e |ange combination| 00000b00 73 20 6f 66 20 44 45 4e 53 49 54 59 20 61 6e 64 |s of DENSITY and| 00000b10 20 54 52 41 4e 53 2c 20 79 6f 75 20 63 61 6e 20 | TRANS, you can | 00000b20 6d 6f 64 65 6c 0a 69 6c 6c 6f 67 69 63 61 6c 20 |model.illogical | 00000b30 6f 62 6a 65 63 74 73 20 77 68 69 63 68 20 61 70 |objects which ap| 00000b40 70 65 61 72 2c 20 66 6f 72 20 65 78 61 6d 70 6c |pear, for exampl| 00000b50 65 2c 20 62 6c 75 65 2c 20 62 75 74 20 63 61 73 |e, blue, but cas| 00000b60 74 20 61 20 72 65 64 20 73 68 61 64 6f 77 2e 0a |t a red shadow..| 00000b70 54 68 65 73 65 20 73 68 61 64 6f 77 73 20 77 69 |These shadows wi| 00000b80 6c 6c 20 62 65 20 65 6e 74 69 72 65 6c 79 20 6f |ll be entirely o| 00000b90 66 20 6f 6e 65 20 69 6e 74 65 6e 73 69 74 79 2c |f one intensity,| 00000ba0 20 61 6e 64 20 77 69 6c 6c 20 6e 6f 74 20 76 61 | and will not va| 00000bb0 72 79 20 77 69 74 68 20 74 68 65 0a 74 68 69 63 |ry with the.thic| 00000bc0 6b 6e 65 73 73 20 6f 66 20 74 68 65 20 67 6c 61 |kness of the gla| 00000bd0 73 73 2e 0a 20 0a 55 73 69 6e 67 20 4d 49 52 52 |ss.. .Using MIRR| 00000be0 4f 52 20 77 69 74 68 20 54 72 61 6e 73 70 61 72 |OR with Transpar| 00000bf0 65 6e 74 20 73 75 72 66 61 63 65 73 0a 7e 7e 7e |ent surfaces.~~~| 00000c00 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e |~~~~~~~~~~~~~~~~| * 00000c20 7e 7e 7e 0a 20 0a 20 20 20 47 6c 61 73 73 20 73 |~~~. . Glass s| 00000c30 75 72 66 61 63 65 73 20 6e 6f 74 20 6f 6e 6c 79 |urfaces not only| 00000c40 20 72 65 66 72 61 63 74 20 6c 69 67 68 74 2c 20 | refract light, | 00000c50 62 75 74 20 61 6c 73 6f 20 72 65 66 6c 65 63 74 |but also reflect| 00000c60 20 61 20 70 65 72 63 65 6e 74 61 67 65 20 6f 66 | a percentage of| 00000c70 0a 69 74 2e 20 54 68 69 73 20 6d 65 61 6e 73 20 |.it. This means | 00000c80 74 68 61 74 20 74 6f 20 72 65 61 6c 69 73 74 69 |that to realisti| 00000c90 63 61 6c 6c 79 20 6d 6f 64 65 6c 20 67 6c 61 73 |cally model glas| 00000ca0 73 2c 20 74 68 65 20 67 6c 61 73 73 20 73 68 6f |s, the glass sho| 00000cb0 75 6c 64 20 72 65 66 6c 65 63 74 20 61 0a 73 6d |uld reflect a.sm| 00000cc0 61 6c 6c 20 70 65 72 63 65 6e 74 61 67 65 20 6f |all percentage o| 00000cd0 66 20 74 68 65 20 6c 69 67 68 74 2e 20 54 72 79 |f the light. Try| 00000ce0 20 73 74 61 72 74 69 6e 67 20 77 69 74 68 20 32 | starting with 2| 00000cf0 30 20 74 6f 20 32 35 20 70 65 72 63 65 6e 74 0a |0 to 25 percent.| 00000d00 72 65 66 6c 65 63 74 69 6f 6e 2e 20 4e 6f 74 65 |reflection. Note| 00000d10 20 74 68 61 74 20 61 6c 6c 20 67 6c 61 73 73 20 | that all glass | 00000d20 6f 62 6a 65 63 74 73 20 72 65 66 6c 65 63 74 20 |objects reflect | 00000d30 6c 69 67 68 74 20 66 72 6f 6d 20 62 6f 74 68 20 |light from both | 00000d40 74 68 65 20 6f 75 74 73 69 64 65 0a 61 6e 64 20 |the outside.and | 00000d50 74 68 65 20 69 6e 73 69 64 65 20 73 75 72 66 61 |the inside surfa| 00000d60 63 65 73 20 6f 66 20 74 68 65 20 67 6c 61 73 73 |ces of the glass| 00000d70 2e 0a 20 0a 49 6e 64 65 78 20 6f 66 20 52 65 66 |.. .Index of Ref| 00000d80 72 61 63 74 69 6f 6e 0a 7e 7e 7e 7e 7e 7e 7e 7e |raction.~~~~~~~~| 00000d90 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 0a 20 0a 20 20 |~~~~~~~~~~~. . | 00000da0 20 54 68 65 20 69 6e 64 65 78 20 6f 66 20 72 65 | The index of re| 00000db0 66 72 61 63 74 69 6f 6e 20 66 6f 72 20 61 6e 20 |fraction for an | 00000dc0 6f 62 6a 65 63 74 20 67 6f 76 65 72 6e 73 20 68 |object governs h| 00000dd0 6f 77 20 6d 75 63 68 20 74 68 65 20 6c 69 67 68 |ow much the ligh| 00000de0 74 20 69 73 20 62 65 6e 74 0a 75 70 6f 6e 20 65 |t is bent.upon e| 00000df0 6e 74 65 72 69 6e 67 20 6f 72 20 65 78 69 74 69 |ntering or exiti| 00000e00 6e 67 20 74 68 65 20 6f 62 6a 65 63 74 2e 20 41 |ng the object. A| 00000e10 20 68 69 67 68 65 72 20 69 6e 64 65 78 20 77 69 | higher index wi| 00000e20 6c 6c 20 62 65 6e 64 20 74 68 65 20 6c 69 67 68 |ll bend the ligh| 00000e30 74 0a 6d 6f 72 65 2e 20 54 68 65 20 69 6e 64 65 |t.more. The inde| 00000e40 78 20 6f 66 20 72 65 66 72 61 63 74 69 6f 6e 20 |x of refraction | 00000e50 6f 66 20 61 69 72 20 69 73 20 31 2e 30 30 2c 20 |of air is 1.00, | 00000e60 61 6e 64 20 66 6f 72 20 67 6c 61 73 73 20 69 73 |and for glass is| 00000e70 20 72 6f 75 67 68 6c 79 20 31 2e 33 33 2e 0a 53 | roughly 1.33..S| 00000e80 6f 6d 65 20 73 75 62 73 74 61 6e 63 65 73 2c 20 |ome substances, | 00000e90 73 75 63 68 20 61 73 20 64 69 61 6d 6f 6e 64 2c |such as diamond,| 00000ea0 20 68 61 76 65 20 61 20 68 69 67 68 65 72 20 69 | have a higher i| 00000eb0 6e 64 65 78 2e 0a 20 0a 4d 6f 64 65 6c 69 6e 67 |ndex.. .Modeling| 00000ec0 20 48 6f 6c 6c 6f 77 20 4f 62 6a 65 63 74 73 0a | Hollow Objects.| 00000ed0 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e |~~~~~~~~~~~~~~~~| 00000ee0 7e 7e 7e 7e 7e 7e 7e 0a 20 0a 20 20 20 57 68 65 |~~~~~~~. . Whe| 00000ef0 6e 20 64 65 73 69 67 6e 69 6e 67 20 74 68 65 20 |n designing the | 00000f00 51 52 54 20 74 72 61 6e 73 6d 69 73 73 69 6f 6e |QRT transmission| 00000f10 20 72 6f 75 74 69 6e 65 73 2c 20 49 20 77 61 6e | routines, I wan| 00000f20 74 65 64 20 74 6f 20 62 65 20 61 62 6c 65 20 74 |ted to be able t| 00000f30 6f 0a 6d 6f 64 65 6c 20 62 6f 74 68 20 73 6f 6c |o.model both sol| 00000f40 69 64 20 67 6c 61 73 73 20 61 6e 64 20 68 6f 6c |id glass and hol| 00000f50 6c 6f 77 20 67 6c 61 73 73 20 6f 62 6a 65 63 74 |low glass object| 00000f60 73 2e 20 54 6f 20 75 6e 64 65 72 73 74 61 6e 64 |s. To understand| 00000f70 20 68 6f 77 20 74 68 69 73 20 69 73 0a 64 6f 6e | how this is.don| 00000f80 65 2c 20 69 74 20 69 73 20 6e 65 63 65 73 73 61 |e, it is necessa| 00000f90 72 79 20 74 6f 20 75 6e 64 65 72 73 74 61 6e 64 |ry to understand| 00000fa0 20 61 20 6c 69 74 74 6c 65 20 61 62 6f 75 74 20 | a little about | 00000fb0 68 6f 77 20 51 52 54 27 73 20 74 72 61 6e 73 6d |how QRT's transm| 00000fc0 69 73 73 69 6f 6e 0a 6d 6f 64 65 6c 20 77 6f 72 |ission.model wor| 00000fd0 6b 73 2e 0a 20 0a 20 20 20 41 20 72 61 79 2c 20 |ks.. . A ray, | 00000fe0 61 66 74 65 72 20 6c 65 61 76 69 6e 67 20 74 68 |after leaving th| 00000ff0 65 20 6f 62 73 65 72 76 65 72 2c 20 68 61 73 20 |e observer, has | 00001000 74 77 6f 20 73 74 61 74 65 73 3a 20 65 69 74 68 |two states: eith| 00001010 65 72 20 69 74 20 69 73 20 69 6e 73 69 64 65 20 |er it is inside | 00001020 61 0a 67 6c 61 73 73 20 6f 62 6a 65 63 74 2c 20 |a.glass object, | 00001030 6f 72 20 69 74 20 69 73 20 6f 75 74 73 69 64 65 |or it is outside| 00001040 2e 20 54 68 65 20 72 61 79 20 73 74 61 72 74 73 |. The ray starts| 00001050 20 6f 75 74 20 6f 75 74 73 69 64 65 2e 20 57 68 | out outside. Wh| 00001060 65 6e 20 69 74 20 66 69 72 73 74 0a 65 6e 63 6f |en it first.enco| 00001070 75 6e 74 65 72 73 20 61 20 67 6c 61 73 73 20 73 |unters a glass s| 00001080 75 72 66 61 63 65 2c 20 69 74 20 69 73 20 62 65 |urface, it is be| 00001090 6e 74 2c 20 61 6e 64 20 69 74 73 20 73 74 61 74 |nt, and its stat| 000010a0 65 20 69 73 20 74 6f 67 67 6c 65 64 20 66 72 6f |e is toggled fro| 000010b0 6d 0a 4f 55 54 53 49 44 45 20 74 6f 20 49 4e 53 |m.OUTSIDE to INS| 000010c0 49 44 45 2e 20 49 74 20 63 6f 6e 74 69 6e 75 65 |IDE. It continue| 000010d0 73 20 6f 6e 20 75 6e 74 69 6c 20 65 6e 63 6f 75 |s on until encou| 000010e0 6e 74 65 72 69 6e 67 20 61 6e 6f 74 68 65 72 20 |ntering another | 000010f0 73 75 72 66 61 63 65 2c 0a 77 68 65 72 65 75 70 |surface,.whereup| 00001100 6f 6e 20 69 74 20 69 73 20 62 65 6e 74 20 61 67 |on it is bent ag| 00001110 61 69 6e 2c 20 61 6e 64 20 69 74 73 20 73 74 61 |ain, and its sta| 00001120 74 65 20 69 73 20 6f 6e 63 65 20 6d 6f 72 65 20 |te is once more | 00001130 74 6f 67 67 6c 65 64 2e 20 54 68 69 73 20 68 61 |toggled. This ha| 00001140 73 0a 73 65 76 65 72 61 6c 20 69 6d 70 6c 69 63 |s.several implic| 00001150 61 74 69 6f 6e 73 20 66 6f 72 20 6d 6f 64 65 6c |ations for model| 00001160 69 6e 67 20 67 6c 61 73 73 2e 20 54 68 65 20 66 |ing glass. The f| 00001170 69 72 73 74 20 69 73 20 74 68 61 74 20 41 4c 4c |irst is that ALL| 00001180 20 67 6c 61 73 73 0a 73 75 72 66 61 63 65 73 20 | glass.surfaces | 00001190 4d 55 53 54 20 68 61 76 65 20 74 77 6f 20 73 69 |MUST have two si| 000011a0 64 65 73 20 2d 20 74 68 61 74 20 69 73 2c 20 6f |des - that is, o| 000011b0 6e 63 65 20 74 68 65 20 72 61 79 20 65 6e 74 65 |nce the ray ente| 000011c0 72 73 20 74 68 65 20 67 6c 61 73 73 2c 20 74 68 |rs the glass, th| 000011d0 65 72 65 0a 6d 75 73 74 20 62 65 20 6e 6f 20 77 |ere.must be no w| 000011e0 61 79 20 66 6f 72 20 69 74 20 74 6f 20 65 78 69 |ay for it to exi| 000011f0 74 20 77 69 74 68 6f 75 74 20 61 67 61 69 6e 20 |t without again | 00001200 70 61 73 73 69 6e 67 20 74 68 72 6f 75 67 68 20 |passing through | 00001210 61 20 73 75 72 66 61 63 65 2e 20 54 68 65 0a 73 |a surface. The.s| 00001220 65 63 6f 6e 64 20 69 73 20 74 68 61 74 20 61 20 |econd is that a | 00001230 72 61 79 20 6d 75 73 74 20 67 6f 20 66 72 6f 6d |ray must go from| 00001240 20 67 6c 61 73 73 20 74 6f 20 61 69 72 2c 20 6f | glass to air, o| 00001250 72 20 61 69 72 20 74 6f 20 67 6c 61 73 73 2c 20 |r air to glass, | 00001260 62 75 74 20 6e 6f 74 0a 66 72 6f 6d 20 67 6c 61 |but not.from gla| 00001270 73 73 20 77 69 74 68 20 69 6e 64 65 78 20 6f 66 |ss with index of| 00001280 20 72 65 66 72 61 63 74 69 6f 6e 20 41 20 74 6f | refraction A to| 00001290 20 67 6c 61 73 73 20 77 69 74 68 20 69 6e 64 65 | glass with inde| 000012a0 78 20 6f 66 20 72 65 66 72 61 63 74 69 6f 6e 20 |x of refraction | 000012b0 42 3b 0a 69 2e 65 2c 20 74 68 65 20 74 77 6f 20 |B;.i.e, the two | 000012c0 67 6c 61 73 73 20 73 75 72 66 61 63 65 73 20 63 |glass surfaces c| 000012d0 61 6e 6e 6f 74 20 74 6f 75 63 68 20 65 61 63 68 |annot touch each| 000012e0 20 6f 74 68 65 72 2c 20 65 76 65 6e 20 74 68 6f | other, even tho| 000012f0 75 67 68 20 74 68 65 79 20 6d 61 79 20 62 65 0a |ugh they may be.| 00001300 70 6c 61 63 65 64 20 76 65 72 79 20 63 6c 6f 73 |placed very clos| 00001310 65 20 74 6f 67 65 74 68 65 72 2e 0a 20 0a 20 20 |e together.. . | 00001320 20 41 73 20 61 6e 20 65 78 61 6d 70 6c 65 20 6f | As an example o| 00001330 66 20 68 6f 77 20 74 68 69 73 20 77 6f 72 6b 73 |f how this works| 00001340 2c 20 63 6f 6e 73 69 64 65 72 20 61 20 73 6f 6c |, consider a sol| 00001350 69 64 20 67 6c 61 73 73 20 73 70 68 65 72 65 2e |id glass sphere.| 00001360 20 54 68 65 20 72 61 79 0a 65 6e 63 6f 75 6e 74 | The ray.encount| 00001370 65 72 73 20 74 68 65 20 73 70 68 65 72 65 2c 20 |ers the sphere, | 00001380 61 6e 64 20 69 73 20 62 65 6e 74 20 28 69 6e 20 |and is bent (in | 00001390 74 68 69 73 20 63 61 73 65 2c 20 74 6f 77 61 72 |this case, towar| 000013a0 64 73 20 74 68 65 20 6e 6f 72 6d 61 6c 0a 76 65 |ds the normal.ve| 000013b0 63 74 6f 72 29 2e 20 51 52 54 20 6e 6f 77 20 72 |ctor). QRT now r| 000013c0 65 6d 65 6d 62 65 72 73 20 74 68 61 74 20 74 68 |emembers that th| 000013d0 65 20 72 61 79 20 69 73 20 49 4e 53 49 44 45 20 |e ray is INSIDE | 000013e0 61 20 67 6c 61 73 73 20 73 75 72 66 61 63 65 2e |a glass surface.| 000013f0 20 54 68 65 20 72 61 79 0a 63 6f 6e 74 69 6e 75 | The ray.continu| 00001400 65 73 20 6f 6e 20 75 6e 74 69 6c 20 69 74 20 68 |es on until it h| 00001410 69 74 73 20 74 68 65 20 62 61 63 6b 20 73 69 64 |its the back sid| 00001420 65 20 6f 66 20 74 68 65 20 73 70 68 65 72 65 2c |e of the sphere,| 00001430 20 77 68 65 72 65 75 70 6f 6e 20 69 74 20 69 73 | whereupon it is| 00001440 20 62 65 6e 74 0a 28 61 77 61 79 20 66 72 6f 6d | bent.(away from| 00001450 20 74 68 65 20 6e 6f 72 6d 61 6c 20 76 65 63 74 | the normal vect| 00001460 6f 72 29 2c 20 61 6e 64 20 69 74 73 20 73 74 61 |or), and its sta| 00001470 74 65 20 69 73 20 74 6f 67 67 6c 65 64 20 74 6f |te is toggled to| 00001480 20 4f 55 54 53 49 44 45 2e 20 49 6e 0a 73 75 6d | OUTSIDE. In.sum| 00001490 6d 61 72 79 2c 20 74 68 65 20 49 4e 53 49 44 45 |mary, the INSIDE| 000014a0 2f 4f 55 54 53 49 44 45 20 66 6c 61 67 20 74 65 |/OUTSIDE flag te| 000014b0 6c 6c 73 20 51 52 54 20 68 6f 77 20 74 6f 20 62 |lls QRT how to b| 000014c0 65 6e 64 20 74 68 65 20 72 61 79 2e 0a 20 0a 20 |end the ray.. . | 000014d0 20 20 43 6f 6e 73 69 64 65 72 20 6e 6f 77 20 74 | Consider now t| 000014e0 68 65 20 63 61 73 65 20 6f 66 20 61 20 68 6f 6c |he case of a hol| 000014f0 6c 6f 77 20 67 6c 61 73 73 20 73 70 68 65 72 65 |low glass sphere| 00001500 2e 20 54 68 69 73 20 69 73 20 6d 6f 64 65 6c 65 |. This is modele| 00001510 64 20 75 73 69 6e 67 20 74 77 6f 0a 63 6f 6e 63 |d using two.conc| 00001520 65 6e 74 72 69 63 20 73 70 68 65 72 65 73 2c 20 |entric spheres, | 00001530 6f 6e 65 20 77 69 74 68 20 61 20 73 6d 61 6c 6c |one with a small| 00001540 65 72 20 72 61 64 69 75 73 2e 20 54 68 65 20 72 |er radius. The r| 00001550 61 79 20 77 69 6c 6c 20 66 69 72 73 74 20 68 69 |ay will first hi| 00001560 74 20 74 68 65 0a 6f 75 74 73 69 64 65 20 73 70 |t the.outside sp| 00001570 68 65 72 65 2c 20 62 65 20 62 65 6e 74 2c 20 61 |here, be bent, a| 00001580 6e 64 20 68 61 76 65 20 69 74 73 20 73 74 61 74 |nd have its stat| 00001590 65 20 74 6f 67 67 6c 65 64 20 74 6f 20 49 4e 53 |e toggled to INS| 000015a0 49 44 45 2e 20 54 68 65 72 65 20 61 72 65 20 6e |IDE. There are n| 000015b0 6f 77 0a 74 77 6f 20 70 6f 73 73 69 62 6c 65 20 |ow.two possible | 000015c0 63 61 73 65 73 2e 20 46 69 72 73 74 2c 20 74 68 |cases. First, th| 000015d0 65 20 72 61 79 20 6d 61 79 20 6d 69 73 73 20 74 |e ray may miss t| 000015e0 68 65 20 69 6e 73 69 64 65 20 73 70 68 65 72 65 |he inside sphere| 000015f0 2c 20 69 6e 20 77 68 69 63 68 20 63 61 73 65 0a |, in which case.| 00001600 74 68 65 20 73 69 6d 75 6c 61 74 69 6f 6e 20 70 |the simulation p| 00001610 72 6f 63 65 65 64 73 20 61 73 20 69 6e 20 74 68 |roceeds as in th| 00001620 65 20 61 62 6f 76 65 20 70 61 72 61 67 72 61 70 |e above paragrap| 00001630 68 2e 20 53 65 63 6f 6e 64 2c 20 69 74 20 6d 61 |h. Second, it ma| 00001640 79 20 68 69 74 20 74 68 65 0a 69 6e 73 69 64 65 |y hit the.inside| 00001650 20 73 70 68 65 72 65 2e 20 49 6e 20 74 68 69 73 | sphere. In this| 00001660 20 63 61 73 65 2c 20 69 74 20 69 73 20 62 65 6e | case, it is ben| 00001670 74 2c 20 61 6e 64 20 69 74 73 20 73 74 61 74 65 |t, and its state| 00001680 20 69 73 20 74 6f 67 67 6c 65 64 20 74 6f 0a 4f | is toggled to.O| 00001690 55 54 53 49 44 45 2e 20 54 68 65 20 72 61 79 20 |UTSIDE. The ray | 000016a0 69 73 20 6e 6f 77 20 63 6f 6e 73 69 64 65 72 65 |is now considere| 000016b0 64 20 74 6f 20 62 65 20 62 61 63 6b 20 69 6e 20 |d to be back in | 000016c0 61 69 72 2c 20 73 6f 20 74 68 61 74 20 74 68 65 |air, so that the| 000016d0 20 69 6e 73 69 64 65 0a 73 70 68 65 72 65 20 68 | inside.sphere h| 000016e0 61 73 20 6d 6f 64 65 6c 65 64 20 74 68 65 20 68 |as modeled the h| 000016f0 6f 6c 6c 6f 77 20 70 6f 72 74 69 6f 6e 20 6f 66 |ollow portion of| 00001700 20 74 68 65 20 67 6c 61 73 73 2e 20 49 6e 20 61 | the glass. In a| 00001710 20 73 69 6d 69 6c 61 72 20 6d 61 6e 6e 65 72 2c | similar manner,| 00001720 20 74 68 65 0a 72 61 79 20 72 65 61 63 68 65 73 | the.ray reaches| 00001730 20 74 68 65 20 6f 74 68 65 72 20 73 69 64 65 20 | the other side | 00001740 6f 66 20 74 68 65 20 69 6e 73 69 64 65 20 73 70 |of the inside sp| 00001750 68 65 72 65 2c 20 65 6e 74 65 72 73 20 74 68 65 |here, enters the| 00001760 20 67 6c 61 73 73 20 61 67 61 69 6e 2c 20 61 6e | glass again, an| 00001770 64 0a 66 69 6e 61 6c 6c 79 20 6c 65 61 76 65 73 |d.finally leaves| 00001780 20 74 68 65 20 6f 75 74 73 69 64 65 20 73 70 68 | the outside sph| 00001790 65 72 65 2e 20 4e 6f 74 65 20 74 68 61 74 20 65 |ere. Note that e| 000017a0 76 65 6e 20 74 68 6f 75 67 68 20 74 68 65 20 69 |ven though the i| 000017b0 6e 73 69 64 65 20 73 70 68 65 72 65 0a 69 73 20 |nside sphere.is | 000017c0 74 68 6f 75 67 68 74 20 6f 66 20 61 73 20 74 68 |thought of as th| 000017d0 65 20 22 61 69 72 22 20 69 6e 20 74 68 65 20 63 |e "air" in the c| 000017e0 65 6e 74 65 72 20 6f 66 20 74 68 65 20 6f 62 6a |enter of the obj| 000017f0 65 63 74 2c 20 69 74 20 4d 55 53 54 20 68 61 76 |ect, it MUST hav| 00001800 65 20 74 68 65 0a 73 61 6d 65 20 69 6e 64 65 78 |e the.same index| 00001810 20 6f 66 20 72 65 66 72 61 63 74 69 6f 6e 20 61 | of refraction a| 00001820 73 20 74 68 65 20 6f 75 74 73 69 64 65 20 73 70 |s the outside sp| 00001830 68 65 72 65 2e 20 54 68 69 73 20 69 73 20 6e 65 |here. This is ne| 00001840 63 65 73 73 61 72 79 20 73 6f 20 74 68 61 74 0a |cessary so that.| 00001850 51 52 54 20 63 61 6e 20 63 6f 72 72 65 63 74 6c |QRT can correctl| 00001860 79 20 62 65 6e 64 20 74 68 65 20 6c 69 67 68 74 |y bend the light| 00001870 20 77 68 65 6e 20 69 74 20 65 78 69 74 73 20 74 | when it exits t| 00001880 68 65 20 67 6c 61 73 73 2e 0a 20 0a 43 68 72 6f |he glass.. .Chro| 00001890 6d 61 74 69 63 20 41 62 65 72 72 61 74 69 6f 6e |matic Aberration| 000018a0 0a 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e |.~~~~~~~~~~~~~~~| 000018b0 7e 7e 7e 7e 7e 0a 20 0a 20 20 20 49 6e 20 51 52 |~~~~~. . In QR| 000018c0 54 2c 20 61 6c 6c 20 72 61 79 73 2c 20 72 65 67 |T, all rays, reg| 000018d0 61 72 64 6c 65 73 73 20 6f 66 20 63 6f 6c 6f 72 |ardless of color| 000018e0 2c 20 61 72 65 20 72 65 66 72 61 63 74 65 64 20 |, are refracted | 000018f0 65 78 61 63 74 6c 79 20 74 68 65 20 73 61 6d 65 |exactly the same| 00001900 2e 0a 54 68 69 73 20 69 73 20 63 6f 6e 74 72 61 |..This is contra| 00001910 73 74 20 74 6f 20 74 68 65 20 72 65 61 6c 20 77 |st to the real w| 00001920 6f 72 6c 64 2c 20 69 6e 20 77 68 69 63 68 20 74 |orld, in which t| 00001930 68 65 20 61 6d 6f 75 6e 74 20 74 68 65 20 6c 69 |he amount the li| 00001940 67 68 74 20 69 73 20 62 65 6e 74 0a 64 65 70 65 |ght is bent.depe| 00001950 6e 64 73 20 6f 6e 20 69 74 73 20 77 61 76 65 6c |nds on its wavel| 00001960 65 6e 67 74 68 2e 20 54 68 69 73 20 61 70 70 65 |ength. This appe| 00001970 61 72 73 2c 20 73 6f 20 66 61 72 20 61 73 20 49 |ars, so far as I| 00001980 20 63 61 6e 20 74 65 6c 6c 2c 20 74 6f 20 62 65 | can tell, to be| 00001990 20 61 20 62 75 67 0a 69 6e 20 74 68 65 20 72 65 | a bug.in the re| 000019a0 61 6c 20 77 6f 72 6c 64 2c 20 61 6e 64 20 49 20 |al world, and I | 000019b0 73 61 77 20 6e 6f 20 72 65 61 73 6f 6e 20 74 6f |saw no reason to| 000019c0 20 69 6e 63 6c 75 64 65 20 69 74 20 69 6e 20 61 | include it in a| 000019d0 20 72 61 79 20 74 72 61 63 65 72 2e 0a 0a 54 68 | ray tracer...Th| 000019e0 72 65 73 68 6f 6c 64 20 61 74 74 72 69 62 75 74 |reshold attribut| 000019f0 65 0a 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e 7e |e.~~~~~~~~~~~~~~| 00001a00 7e 7e 7e 7e 7e 0a 20 0a 20 20 20 41 20 6e 65 77 |~~~~~. . A new| 00001a10 20 6b 65 79 77 6f 72 64 2c 20 54 48 52 45 53 48 | keyword, THRESH| 00001a20 4f 4c 44 2c 20 68 61 73 20 62 65 65 6e 20 61 64 |OLD, has been ad| 00001a30 64 65 64 20 74 6f 20 74 68 65 20 64 65 66 61 75 |ded to the defau| 00001a40 6c 74 20 73 74 72 75 63 74 75 72 65 2e 20 49 6e |lt structure. 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QRT stopped | 00001b00 74 68 65 20 72 65 63 75 72 73 69 6f 6e 20 77 68 |the recursion wh| 00001b10 65 6e 20 74 68 65 20 69 6e 74 65 6e 73 69 74 79 |en the intensity| 00001b20 20 6f 66 20 74 68 65 20 6c 69 67 68 74 0a 72 65 | of the light.re| 00001b30 61 63 68 65 64 20 31 20 70 65 72 63 65 6e 74 20 |ached 1 percent | 00001b40 6f 66 20 69 74 73 20 6f 72 69 67 69 6e 61 6c 20 |of its original | 00001b50 76 61 6c 75 65 2e 20 57 68 65 6e 20 74 72 61 6e |value. When tran| 00001b60 73 6d 69 73 73 69 6f 6e 20 77 61 73 20 61 64 64 |smission was add| 00001b70 65 64 2c 20 49 20 6d 61 64 65 0a 74 68 69 73 20 |ed, I made.this | 00001b80 76 61 6c 75 65 20 61 64 6a 75 73 74 61 62 6c 65 |value adjustable| 00001b90 2e 20 57 69 74 68 20 67 6c 61 73 73 20 6f 62 6a |. With glass obj| 00001ba0 65 63 74 73 2c 20 62 6f 74 68 20 73 75 72 66 61 |ects, both surfa| 00001bb0 63 65 73 20 72 65 66 6c 65 63 74 20 6c 69 67 68 |ces reflect ligh| 00001bc0 74 2c 20 61 6e 64 0a 69 66 20 51 52 54 20 77 61 |t, and.if QRT wa| 00001bd0 69 74 73 20 75 6e 74 69 6c 20 74 68 65 20 31 20 |its until the 1 | 00001be0 70 65 72 63 65 6e 74 20 6d 61 72 6b 20 62 65 66 |percent mark bef| 00001bf0 6f 72 65 20 73 74 6f 70 70 69 6e 67 20 72 65 63 |ore stopping rec| 00001c00 75 72 73 69 6f 6e 2c 20 74 68 65 20 74 69 6d 65 |ursion, the time| 00001c10 0a 6e 65 63 65 73 73 61 72 79 20 74 6f 20 63 6f |.necessary to co| 00001c20 6d 70 6c 65 74 65 20 74 68 65 20 69 6d 61 67 65 |mplete the image| 00001c30 20 69 73 20 67 72 65 61 74 6c 79 20 69 6e 63 72 | is greatly incr| 00001c40 65 61 73 65 64 20 77 69 74 68 20 6c 69 74 74 6c |eased with littl| 00001c50 65 20 6f 72 20 6e 6f 0a 69 6e 63 72 65 61 73 65 |e or no.increase| 00001c60 20 69 6e 20 69 6d 61 67 65 20 71 75 61 6c 69 74 | in image qualit| 00001c70 79 2e 20 54 68 65 20 64 65 66 61 75 6c 74 20 69 |y. The default i| 00001c80 73 20 6e 6f 77 20 31 30 20 70 65 72 63 65 6e 74 |s now 10 percent| 00001c90 2c 20 61 6e 64 20 69 73 20 63 68 61 6e 67 65 61 |, and is changea| 00001ca0 62 6c 65 0a 61 73 20 66 6f 6c 6c 6f 77 73 3a 0a |ble.as follows:.| 00001cb0 20 0a 20 20 20 44 45 46 41 55 4c 54 20 28 20 74 | . DEFAULT ( t| 00001cc0 68 72 65 73 68 6f 6c 64 20 3d 20 2e 30 35 0a 20 |hreshold = .05. | 00001cd0 20 20 20 20 20 20 20 20 20 20 29 0a 20 0a 20 20 | ). . | 00001ce0 20 54 68 69 73 20 77 6f 75 6c 64 20 73 74 6f 70 | This would stop| 00001cf0 20 72 65 63 75 72 73 69 6f 6e 20 77 68 65 6e 20 | recursion when | 00001d00 74 68 65 20 69 6e 74 65 6e 73 69 74 79 20 72 65 |the intensity re| 00001d10 61 63 68 65 73 20 35 20 70 65 72 63 65 6e 74 20 |aches 5 percent | 00001d20 6f 66 20 74 68 65 0a 6f 72 69 67 69 6e 61 6c 20 |of the.original | 00001d30 76 61 6c 75 65 2e 20 41 6e 20 61 64 64 65 64 20 |value. 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Since tran| 000022c0 73 6d 69 73 73 69 6f 6e 20 69 6e 76 6f 6c 76 65 |smission involve| 000022d0 73 20 68 65 61 76 79 20 72 65 63 75 72 73 69 6f |s heavy recursio| 000022e0 6e 2c 20 64 6f 6e 27 74 20 66 6f 72 67 65 74 20 |n, don't forget | 000022f0 74 6f 20 73 65 74 20 74 68 65 0a 64 65 66 61 75 |to set the.defau| 00002300 6c 74 20 73 74 61 63 6b 20 73 69 7a 65 20 74 6f |lt stack size to| 00002310 20 73 6f 6d 65 74 68 69 6e 67 20 6c 61 72 67 65 | something large| 00002320 72 20 74 68 61 6e 20 74 68 65 20 64 65 66 61 75 |r than the defau| 00002330 6c 74 20 34 30 30 30 20 62 79 74 65 73 2e 20 41 |lt 4000 bytes. A| 00002340 20 73 74 61 63 6b 0a 73 69 7a 65 20 6f 66 20 34 | stack.size of 4| 00002350 30 30 30 30 20 74 6f 20 35 30 30 30 30 20 62 79 |0000 to 50000 by| 00002360 74 65 73 20 73 65 65 6d 73 20 73 61 66 65 20 66 |tes seems safe f| 00002370 6f 72 20 6d 6f 73 74 20 69 6d 61 67 65 73 2e 0a |or most images..| 00002380 0a 0a 54 68 65 20 52 45 4d 4f 56 45 20 63 6f 6d |..The REMOVE com| 00002390 6d 61 6e 64 0a 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d 3d |mand.===========| 000023a0 3d 3d 3d 3d 3d 3d 3d 0a 0a 20 20 20 54 68 65 20 |=======.. The | 000023b0 27 52 45 4d 4f 56 45 27 20 63 6f 6d 6d 61 6e 64 |'REMOVE' command| 000023c0 20 77 61 73 20 61 64 64 65 64 20 74 6f 20 61 6c | was added to al| 000023d0 6c 6f 77 20 73 65 63 74 69 6f 6e 73 20 6f 66 20 |low sections of | 000023e0 61 20 70 6c 61 6e 61 72 20 70 72 69 6d 69 74 69 |a planar primiti| 000023f0 76 65 20 74 6f 0a 62 65 20 72 65 6d 6f 76 65 64 |ve to.be removed| 00002400 2e 20 54 68 69 73 20 6d 61 6b 65 73 20 69 74 20 |. This makes it | 00002410 6d 75 63 68 20 65 61 73 69 65 72 20 74 6f 20 63 |much easier to c| 00002420 72 65 61 74 65 20 66 6c 61 74 20 6f 62 6a 65 63 |reate flat objec| 00002430 74 73 20 74 68 61 74 20 61 72 65 20 6e 6f 74 0a |ts that are not.| 00002440 73 68 61 70 65 64 20 6c 69 6b 65 20 51 52 54 27 |shaped like QRT'| 00002450 73 20 70 6c 61 6e 61 72 20 70 72 69 6d 69 74 69 |s planar primiti| 00002460 76 65 73 2e 20 46 6f 72 20 65 78 61 6d 70 6c 65 |ves. For example| 00002470 2c 20 49 20 68 61 64 20 61 20 51 52 54 20 69 6e |, I had a QRT in| 00002480 70 75 74 20 66 69 6c 65 0a 77 68 69 63 68 20 63 |put file.which c| 00002490 72 65 61 74 65 64 20 74 68 65 20 69 6d 61 67 65 |reated the image| 000024a0 20 6f 66 20 61 20 67 72 61 6e 64 20 70 69 61 6e | of a grand pian| 000024b0 6f 2e 20 54 68 65 20 74 6f 70 20 6f 66 20 74 68 |o. The top of th| 000024c0 65 20 70 69 61 6e 6f 2c 20 62 65 63 61 75 73 65 |e piano, because| 000024d0 20 6f 66 0a 69 74 73 20 63 6f 6d 70 6c 65 78 20 | of.its complex | 000024e0 73 68 61 70 65 2c 20 69 6e 69 74 69 61 6c 6c 79 |shape, initially| 000024f0 20 77 61 73 20 63 72 65 61 74 65 64 20 66 72 6f | was created fro| 00002500 6d 20 31 31 20 70 6c 61 6e 61 72 20 70 72 69 6d |m 11 planar prim| 00002510 69 74 69 76 65 73 2e 20 4e 6f 77 2c 20 69 74 0a |itives. 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Th| 00002840 69 73 20 65 78 61 6d 70 6c 65 20 73 68 6f 77 73 |is example shows| 00002850 20 74 68 61 74 20 74 68 65 20 50 41 54 54 45 52 | that the PATTER| 00002860 4e 20 63 6f 6d 6d 61 6e 64 20 63 61 6e 20 62 65 |N command can be| 00002870 20 75 73 65 64 20 6f 6e 20 74 68 65 20 73 61 6d | used on the sam| 00002880 65 0a 70 72 69 6d 69 74 69 76 65 20 61 73 20 74 |e.primitive as t| 00002890 68 65 20 52 45 4d 4f 56 45 20 63 6f 6d 6d 61 6e |he REMOVE comman| 000028a0 64 2e 0a 20 0a 20 20 20 53 65 76 65 72 61 6c 20 |d.. . Several | 000028b0 74 68 69 6e 67 73 20 73 68 6f 75 6c 64 20 62 65 |things should be| 000028c0 20 6e 6f 74 65 64 20 61 62 6f 75 74 20 74 68 65 | noted about the| 000028d0 20 52 45 4d 4f 56 45 20 63 6f 6d 6d 61 6e 64 2e | REMOVE command.| 000028e0 20 46 69 72 73 74 2c 20 74 68 65 0a 70 61 74 74 | First, the.patt| 000028f0 65 72 6e 20 64 65 66 69 6e 65 73 20 74 68 65 20 |ern defines the | 00002900 73 65 63 74 69 6f 6e 73 20 74 6f 20 72 65 6d 6f |sections to remo| 00002910 76 65 2c 20 6e 6f 74 20 74 68 65 20 73 65 63 74 |ve, not the sect| 00002920 69 6f 6e 73 20 77 68 69 63 68 20 77 69 6c 6c 20 |ions which will | 00002930 72 65 6d 61 69 6e 2e 0a 49 6e 20 74 68 65 20 70 |remain..In the p| 00002940 69 61 6e 6f 20 65 78 61 6d 70 6c 65 2c 20 74 68 |iano example, th| 00002950 65 20 70 61 74 74 65 72 6e 20 6d 61 70 70 65 64 |e pattern mapped| 00002960 20 61 6c 6c 20 6f 66 20 74 68 65 20 70 61 72 61 | all of the para| 00002970 6c 6c 65 6c 6f 67 72 61 6d 20 65 78 63 65 70 74 |llelogram except| 00002980 20 74 68 65 0a 70 61 72 74 20 74 68 61 74 20 63 | the.part that c| 00002990 6f 6d 70 6f 73 65 64 20 74 68 65 20 61 63 74 75 |omposed the actu| 000029a0 61 6c 20 70 69 61 6e 6f 20 74 6f 70 2e 20 53 65 |al piano top. Se| 000029b0 63 6f 6e 64 2c 20 65 76 65 6e 20 74 68 6f 75 67 |cond, even thoug| 000029c0 68 20 74 68 65 20 72 65 6d 6f 76 65 0a 63 6f 6d |h the remove.com| 000029d0 6d 61 6e 64 20 63 61 6e 20 62 65 20 75 73 65 64 |mand can be used| 000029e0 20 77 69 74 68 20 74 68 65 20 63 75 72 76 65 64 | with the curved| 000029f0 20 73 75 72 66 61 63 65 20 70 72 69 6d 69 74 69 | surface primiti| 00002a00 76 65 73 20 28 53 50 48 45 52 45 2c 20 51 55 41 |ves (SPHERE, QUA| 00002a10 44 52 41 54 49 43 29 2c 0a 74 68 65 20 72 65 73 |DRATIC),.the res| 00002a20 75 6c 74 73 20 77 69 6c 6c 20 6e 6f 74 20 62 65 |ults will not be| 00002a30 20 71 75 69 74 65 20 72 69 67 68 74 2e 20 54 6f | quite right. To| 00002a40 20 75 73 65 20 74 68 65 20 73 70 68 65 72 65 20 | use the sphere | 00002a50 61 73 20 61 6e 20 65 78 61 6d 70 6c 65 2c 20 74 |as an example, t| 00002a60 68 65 0a 66 72 6f 6e 74 20 73 75 72 66 61 63 65 |he.front surface| 00002a70 20 6f 66 20 74 68 65 20 73 70 68 65 72 65 20 77 | of the sphere w| 00002a80 6f 75 6c 64 20 68 61 76 65 20 74 68 65 20 63 6f |ould have the co| 00002a90 72 72 65 63 74 20 70 61 74 74 65 72 6e 20 72 65 |rrect pattern re| 00002aa0 6d 6f 76 65 64 20 66 72 6f 6d 20 69 74 2c 0a 62 |moved from it,.b| 00002ab0 75 74 20 74 68 65 20 62 61 63 6b 20 73 75 72 66 |ut the back surf| 00002ac0 61 63 65 20 6f 66 20 74 68 65 20 73 70 68 65 72 |ace of the spher| 00002ad0 65 20 77 6f 75 6c 64 20 20 62 65 20 63 6f 6d 70 |e would be comp| 00002ae0 6c 65 74 65 6c 79 20 67 6f 6e 65 2e 20 54 68 69 |letely gone. Thi| 00002af0 73 20 69 73 0a 62 65 63 61 75 73 65 20 74 68 65 |s is.because the| 00002b00 20 53 50 48 45 52 45 20 69 6e 74 65 72 73 65 63 | SPHERE intersec| 00002b10 74 20 72 6f 75 74 69 6e 65 20 69 67 6e 6f 72 65 |t routine ignore| 00002b20 73 20 63 6f 6d 70 6c 65 74 65 6c 79 20 74 68 65 |s completely the| 00002b30 20 62 61 63 6b 20 73 75 72 66 61 63 65 20 6f 66 | back surface of| 00002b40 0a 74 68 65 20 73 70 68 65 72 65 2e 20 49 20 77 |.the sphere. I w| 00002b50 69 6c 6c 20 70 72 6f 62 61 62 6c 79 20 66 69 78 |ill probably fix| 00002b60 20 74 68 69 73 20 69 6e 20 61 20 66 75 74 75 72 | this in a futur| 00002b70 65 20 76 65 72 73 69 6f 6e 2e 0a |e version..| 00002b7b
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