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Addendum to QRT Version 1.4
The following are changes to QRT made since version 1.3
Additions and Enhancements
Transmission
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.
QRT Ray Tracer Page 1 Addendum to 1.4
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.
QRT Ray Tracer Page 2 Addendum to 1.4
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.
QRT Ray Tracer Page 3 Addendum to 1.4
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
QRT Ray Tracer Page 4 Addendum to 1.4
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.
QRT Ray Tracer Page 5 Addendum to 1.4
