Graphics Qualifier

Fall 2001

Answer 4 out of the 6 general questions and 3 out of 4 for each of the two sub-areas you chose (rendering and VR/AR)

GENERAL

  1. Color

    1. Describe the commonly used approach to specify device independent color, by which we can achieve a common set of colors across a variety of devices.
    2. The standard color system used by device independent color has a number of limitations. One is that the colors space is not perceptually uniform. What does this mean, and what color spaces have been proposed to rectify this problem? What are the limitations of these other spaces?
    3. Even if we use a device independent color specification, there is no guarantee that colors displayed on different devices will actually appear the same. On one hand, colors used in different images may not appear the same. On the other hand, the same images may not appear the same on different devices. Discuss the causes of both of these situations.

  2. Perspective

    1. Consider using, in the popular hardware graphics pipeline, a transformation mapping (x,y,z) into (dx/(z+d), dy/(z+d), 0). Explain and show with a simple example why it does not work.
    2. Consider using, in the popular hardware graphics pipeline a transformation mapping (x,y,z) into (dx/(z+d), dy/(z+d), z). Explain and show with a simple example why it does not work.
    3. Consider the common perspective transformation that maps (x,y,z) into (dx/(z+d), dy/(z+d), dz/(z+d)). Prove that it maps quadric surfaces to quadric surfaces.
    4. Assume that a sphere is completely visible on the screen. Under perspective projection will it appear as a disk? Prove your answer.

  3. Distance

    1. What is the Hausdorff distance H(A,B) between two pointsets A and B?
    2. Let C*r be the union of all balls with radius and center in C. Show that H(A,B)=r if and only if A is contained in B*r and B is contained in A*r.
    3. Consider that A and B are solids bounded by manifold triangle meshes. Describe a practical algorithm for computing H(A,B). Provide enough details to guide an implementation.

  4. IBR

    1. List the various effects that could make an image generate from a lightfield incorrect. Illustrate each effect with a simple example.
    2. The lightfield technique is based on the assumption that color remainsconstant along a ray that is free of occlusion. Yet, the density of photons that are emitted by a light-reflecting point Q on a diffuse surface S and that reach a viewpoint V decreases with the square of the distance ||QV||. Thus, although the color may be the same, the perceived intensity of light should vary along a ray. Which is correct? Explain.

  5. Hidden surface. Describe 4 polygon hidden-surface algorithms and describe their computational complexity in terms of the O() order of operations on whatever the most relevant measure is for each algorithm. For the complexity analysis, you can assume that you know all of the simple facts about each polygon (area, number of sides, etc).

  6. Graphics pipeline. Describe the three most popular broad approaches of parallelization of the traditional rendering pipeline. Analyze the rade-offs between these approaches, and give an example of scenes/datasets that will make each parallel scheme perform at peak efficiency and at minimal efficiency.

VR/AR
  1. Registration. When overlaying graphics on a user's view of the world using see-through head-worn displays, there are a variety of factors that contribute to registration errors. What are they? Discuss how to correct each of these factors. Consider the factors in the context of both video see-through and optical see-through displays.

  2. Displays. The goal of many augmented reality systems is to merge 3D graphics with the user's view of the world. Simple solutions using off-the-shelf displays (such as creating a video-mixed display using an opaque display and one or more cameras) suffer from a variety of perceptual and practical problems. Discuss the problems with current AR displays, and possible solutions to these problems (if there are any). Discuss both solutions that have been proposed, as well as those that have been implemented in research systems.

  3. Picking. Describe three different techniques from the VR literature for picking a single object in a 3D immersive space. For each of your three techniques, describe their advantages and disadvantages with respect to accuracy, speed, picking objects at a distance, picking objects in zones of high depth complexity and any special characteristics of hardware or technique required.

  4. Tracking. Describe three different techniques from the VR literature for picking a single object in a 3D immersive space. For each of your three techniques, describe their advantages and disadvantages with respect to accuracy, speed, picking objects at a distance, picking objects in zones of high depth complexity and any special characteristics of hardware or technique required.

RENDERING
  1. BRDF. BRDFs provide a well-established way to represent reflective properties of opaque materials. Discuss ways to generalize the notion of a BRDF in a way which allows to describe the following physical phenomena:

    1. light transmission
    2. subsurface scattering
    3. scattering in a cubical volume filled with floating particles (smoke, aerosol or like).

    Discuss the dimensionality of your representations.

  2. Antialiasing
    1. Describe a typical way in which an anti-aliased polygon may be drawn (that is, no jagged edges). Include details about the shape of a good reconstruction filter and how it is applied. Make sure this answer isn't a duplicate of part (c).
    2. Describe a typical way an anti-aliased line may be drawn, including details about the reconstruction filter.
    3. Describe how an anti-aliased polygon may be drawn by first drawing a crude aliased plygon and then overdrawing the edges with anti-aliased lines. How are the pixels from the anti-aliased lines blended with the pixels already in the framebuffer? Will the result of this method be the same as from (a), and why?

  3. Distribution raytracing. Distribution ray tracing is a method by which particular integrals are calculated for rendering. For each rendering effect listed in the sub-parts below, write the equation for the integral that is being calculated. Describe the quantities you use in the equation, especially the domain of integration.

    1. Soft shadows (penumbra)
    2. Motion blur
    3. Glossy reflection
    4. Depth-of-field

  4. Caustics You are going to simulate the patterns of light called caustics that are created by the way light is focused by water onto the bottom of a swimming pool. You will render an image that shows the pool and the caustics from the point-of-view of an observer outside of the water at the side of the pool.

    1. Explain what creates the caustics, including the interaction of light with each surface along the light's path from the light source to the observer's eye.
    2. Describe a rendering method that is capable of rendering this scene, and explain how it is that the caustics are created.
      3.