CSCI 384 Final Exam Review Problems

Final Exam Review Problems

The following problems will be similar to the type of problems that will be on the exam. However, not all problems on the exam are necessarily represented here, and not all the types of problems here will necessarily be on the exam.

Problem 1: Clipping
Given a clipping rectangle defined by

For the pairs of points in parts a and b, indicate the outcodes for Cohen-Sutherland outcode for each point. State what the algorithm will dictate concerning the rendering or the line-segment (entirely rendered, clipped with part rendered, entirely clipped (i.e. not rendered) or not known), and briefly state why the algorithm gives this output. If clipping is required, or if it is not known, calculate the intersection points to determine where to clip.

a) P0 = (2, 3), P1 = (5, 5)

b) P0 = (7, 1), P1 = (8, 3)

c) For the following pair of points, determine the clipping values using Liang-Barsky clipping. Indicate whether the line is discarded entirely, rendered entirely, or clipped. If the line is clipped, indicate the (x, y) value(s) at which it is clipped.

P0 = (4, 3), P1 = (5,1)

Problem 2: Line Drawing
Given the line, y = 1/3x + 2 and the starting and ending points of a line segment:

For each pixel between x = 0 and x = 6, what y value will be colored as part of the line in:
a) The DDA algorithm?

b) The Bresenham algorithm. (Show your work, indicating the values of dk at each step).

c) Which of the 2 algorithms is preferred and why?

Problem 3: Curves
Given the following four points:

Find the parametric representations, x(u), y(u), z(u) for the Bezier (also know Interpolation and Hermite techniques) curve that fits these points.

Problem 4: The LookAt function
Consider the following call to gluLookat:

gluLookAt(1.0, 2.0, 3.0, 2.0, 4.0, 5.0, 0.0, 1.0, 0.0);
Answer the following questions:
a) What is the VRP (view reference point)?

b) What is VPN (view plane normal)?

c) What is VUP (view-up vector)?

d) If the image plane is defined by vectors v and u described in the book (p. 206), does VUP equal v? Why or why not? (You should not have to calculate v exactly to answer this question).

Problem 5: (Not a problem, but more things to study)
Be prepared to discuss some of the topics discussed more generally, such as aliasing (why is it a problem, and what can be done about it), polygon clipping and filling, texture mapping techniques, etc. Also be prepared to solve problems involving transformations (similar to those on the homework), lighting and shading, and viewing.

Constance Royden--croyden@mathcs.holycross.edu
Computer Science 384, Computer Graphics
Date Created: August 17, 1999
Last Modified: December 10, 2003
Page Expires: August 17, 2004