Final Exam Questions

The final will consist of two parts: the first part will contain 3 questions similar to those in homework 1. Please carefully review lectures 2 and 3. The second part will contain three questions from the list below (possibly with small variations). You should not use any recorded information at the exam. When you are asked to explain or describe a formula or an algorithm, this means that you have to write a narrative explanation of the idea, not a formal proof or highly -detailed derivation. Please keep in mind that, while final is important, your performance on the homeworks will have primary importance for your grade. To get an A, you have to turn in all the homeworks (and of course do well on them). <
  1. Describe the Bresenham algorithm for drawing lines. Explain the difference between the Bresenham algorithm and DDA.
  2. Explain the algorithm for scan-converting convex polygons. It is not necessary to write the code, a precise narrative description is sufficient.
  3. What is the homogeneous form of a 2D point? What is the homogeneous equation of a line? Write the formula for the intersection of two lines specified in homogeneous form.
  4. Write the matrix of the mapping of a square to a quad and explain how it is derived.
  5. Describe examples of aliasing. Explain what can happen if an image is resized using the "round to nearest-pixel" approach. State and explain the formula for shrinking an image.
  6. Write the convolution formula in 1D. Explain the algorithm for blurring and sharpening the image. Provide 2 examples of blurring filters.
  7. What is the homogeneous form of a 3D point? What is the homogeneous equation of a plane? Write the formula for a translation in homogeneous form. Give examples of transformations that do not commute.
  8. Explain how transformation hierarchy is used to define complex objects. Describe an example in detail, showing the state of the transformation stack.
  9. Describe the transformations at different stages in the graphics pipeline. Explain what each transformation does. In particular, explain what the perspective transformation does, and how the matrix is constructed (you do not have to spell out the complete matrix, but you have to explain from which matrices it is composed, and specify these matrices as precisely as you can).
  10. Explain what a cubic B-spline curve is, and what are the cubic spline basis functions (you do not have to write the explicit formulas, just state the important properties and sketch a plot). Explain how to compute piecewise-linear approximation to the spline curve using subdivision. How the endpoints can be handled?
  11. Describe the Z-buffer algorithm and the painter's algorithm. For what type of scenes Z-buffer does not perform well? What effects are difficult to implement with Z-buffer? Explain why large difference between the far and near distances in the projection transformation will have a negative effect on Z-buffer performance.
  12. Describe the recursive ray-tracing algorithm. Write the formula for the reflected ray; state Snell's law.
  13. Explain how to intersect rays with a cylinder and a cone. You do not have to write down the precise formula, but you have to describe the whole algorithm, and how the equations for intersections are obtained.
  14. Write the equation for the Phong illumination model. Explain what diffuse, specular and ambient terms are. Give examples of diffuse and specular surfaces. How "plastic" and "metallic" appearances can be approximated?