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Text File | 1989-05-23 | 10.9 KB | 224 lines

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.