Üç boyutlu modellemede ışın izleme yöntemi - Yüksek, Kemal (Fen Bilimleri Enstitüsü, 1994)
in this thesis, the aim is to represent realistic three-dimensional images using mathematical principles, understanding of light, and the povver of the computer. Computerized models of scenes including objects, light source ör sources, and an observer will be created. The process is called ray tracing because the computer traces the path that rays of light in the real world take between light source ör sources, objects, and observer. in other words Ray tracing method can be described as a modelling of visual part of human brain.To do such a modelling, first of ali it is necessary to inspect the structure and behaviour of light. in first part of the thesis, the concept of light is explained giving some information on it. it is explained that, light consists of infinite number of rays which are called a collection of photons in physics. When a light switch is turned on, rays of light travel ali över the image space and strike objects.When a ray of light strikes a surface of the object, a number of things can happen. The light can be reflected. As rays strike the surface they bounce of in different directions.Some of the rays happen to reflect in the observer direction and enter the observer's eyes. The light is interpretered by observer's brain and men observer see the object. it is important to notice that observer just see the reflected rays not the object itself. The ligth can be absorbed. Its energy is usually converted to heat and that's the end of the ray path. Objects that look black do precisely that. Light striking a black surface is absorbed. The light can be transmitted through transparent objects,. which means that light can pass through. Öne other possibility exists. The light can be absorbed and re-emitted. This occurs with fluorescent objects. Any ör ali of the processes described above may occur at önce in varying amounts to a given ray of light. This is because a ray is really many photons and each photon may ör may not be reflected, absorbed. transmitted, refracted, ör re-emitted. Each of these can be described mathematically. For example rays can be represented by an equation representing a line. Objects struck by the rays, such as spheres, planes, geometric surfaces, can be described in mathematical terms.The laws of physics describe how reflection and refraction occur.Using this math and physics, it can be told the computer that, where light source ör sources are, where objects are and where observer is and then let the computer do ali the dirty work of tracing rays of light from the source to objects and onwards to the observer. it sounds relatively simple, but in practice it is virtually impossible because as an individual ray leaves a light source it may end up doing any ör ali of the above processes many. many times. A further simplification of the problem can come when we realize that the only rays which contribute to the scene are those rays whose ultimate destination is the observer's eyes.lt could be spent a great deal of time working on rays that contribute nothing to the image. in fact, most of the rays that come from a light source do not contribute to the image at ali. This problem can not be solved directly. But it can be used some strategies to transform the problem into öne that can be solved.The first öne is that, deciding to treat light as rays.Another strategy is to start with the solution and work backwards. After tracing thousands of rays that do not contribute to the image, it can be wondered how objects can be seen at ali. Yet some rays of light obviously do reach observer'eyes By starting at the end and tracing the path of these relatively few rays backwards from the observer outward towards objects and from there farther to light sources, the problem can be simplified suffîciently to create realistte images with a mathematical model that is backwards from the way light works in the real word. This approach means only rays reaching the observer are examined. Ali others are ignored. This process is called sampling. vii in addition to the above explanations in the first part of the thesis, the elements of ray tracing environment tried to be descired.These are observer, objects, and light sources.lt will be assumed that the observer is a simple camera that is going to take a photograph of the scene. As a result of this, a ray tracing program can be thought of as an imaginary camera that photographs imaginary objects iliuminated by imaginary light sources.The simplest kind of real kamera is called a pin-hole camera. Most ray tracing programs use this pin-hole model ör a model that is functionally equivalent. The objects have to be represented in the computer memory in some mathematical, geometric form. This imposes some limits on the types of objects that can be created. But many everyday objects can be represented by combination of geometric shapes. Real light can come from variety of sources, and these sources have a number of properties; color, intensity, location, size and shape.The physical principles of how light radiate from a source are very complex. it has to be some additional assumptions. The first assumption is that, the light from any given source is of a single color. After explaining the elements of ray tracing environment in the first part of the thesis.lt is noticed that.there ara some types of rays.For example viewing ray that comes from the camera, Shadow rays, transmitted rays, and reflected rays.In the ray tracing method projection plane is usually known viewing window.The camera sends out öne ray for each rectangle of the grid of the viewing window and that ray is used to compute the color of the corresponding pixel in the final image.The program has an internal list of ali of the objects defined in the scene. Every object in the list is tested to see if it is hit by the vievving ray.This process, called a ray-object intersection test, involves solving a set of equations. Many highly accurate, time consuming floating point caculat'ons are required. A ray extends out an infmite distance from its starting point. Therefore, it is necessary to determine which object the ray intersects first. The closest object is the viü one is seen by the camera.Because the order in which objects are tested cannot be determined, the process cannot stop with the first successful intersection test found. There may be closer objects that block the view, so the ray must be tested against every object in the scene. The location of every ray-object intersection point is stored and after all object have been tested the closest one is chosen. When light from a light source strikes an object, the light is scattered in all direction unless the object has a mirrored surface.Because the light spreads outward in all directions this light is called diffuse illumination. Obviously, not every light source illuminates every point of every object. Some points are in shadowed areas because another object may block the light from reaching that point. To determine how much diffuse illumination is at the intersection point. It must be first determined which, if any, light sources have clear path to that point. This requires a new set of rays called shadow rays. Each shadow ray begins at the viewing ray-object intersection point and passes through the location point of a light source. Shadow ray is tested against every object in the scene.If this ray intersects one of the objects. This point must be marked as a shadowed point. When light reflects off a mirror or other smooth surface, it is not scattered in every direction. The incoming ray is reserved and it is called a reflection ray.lt starts at the reflection point and extends outwards along the angle of incidence. Transparent or partially transparent objects permit light to come through them in the form of transmitted rays.Most transmitted rays will pass into and back out of a transparent object. At the end of the first part of the thesis, the limits of ray tracing has been explained. Ray traced images are created by tracing one viewing ray per pixel in order to determine the color of the pixel. This creates a number of problems because every possible ray is not traced. Theoretically, an infinite number of rays can fit in a finite space by bunching them closer together. Higher resolution used with more rays IX and with more pixels provides a better sample. Tiny objects such as raindrops or thin objects such as wire or string can be missed completely when ray tracing at low resolution. In addition to the above problems, rainbow, soft shadow, specular, ambient refractive illumination problems has been explained. In the second part of the thesis, it is explained how caculations given above can be done. Addition to this, general illumination method is obtained. Shadow events, their types and calculations related to reflaction and refraction are explained in this part as well. Rays subject to refraction and reflection keep going on its way. There are three possibilities of the rays which come onto the plane of the object; if the object is transparent refraction,if the object has got a bright surface reflaction, and thirdly according to the structure to the object absorbance will happen. So this structure can be represented by a binary tree. In the last section öf the thesis, implementation of the two models devised in the first two parts are made. The structure of the given ray tracing program is explained as well. Since ray tracing is a time-consuming method some studies are done to speed up the processing time. As a result linear interpolation is used in this thesis.Under some restrictions a speed of 50% is gained. Fundamental of the method is based on locality. Linear interpolation can be used either row or column order or both. In the second approximation surfaces of the object are kept as small as possible so that fewer lights are intersected the objects, and as a result small model of the scene will be obtained.The image obtained is made bigger up to the original size. But this method didn't give a satisfactory result, since aliasing is occured on the edge of the objects which is spherical in shape. Finally this thesis will guide to those who want to study on ray tracing.
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1994
Keywords: Bilgisayar ve Kontrol; Bilgisayar destekli tasarım; Işın izleme tekniği; Mathematical modelling; Computer Science and Control; Computer aided design; Ray tracing technique; Mathematical modelling