CSC418/2504F: Fall 2003 Assignment 1 (30 marks)

Sept. 17, 2003. Due: Oct. 1, 2003 in class.

Frequently-asked questions.

Solutions! (you wish)

Questions about marking.

  1. Realism [3 marks] Look at the scenes from the movies Shrek, Matrix and Lord of the Rings in the 5th slide of lecture 1 on the course web site. Can you tell by looking that they are computer generated? List at least 6 reasons to explain your answer.
  2. Camera Models
    3.  [3 marks] The f-number of a camera is the focal length of the lens divided by the aperture. How can the f-number of a camera be changed? How does changing the f-number affect the required exposure time? Do the camera models commonly used in computer graphics have f-numbers? Explain briefly.
  3. Vectors [4 marks] Snoopy's pirate friend has buried a juicy bone on an island with five trees located at the following points: A(20.0 m, -10 m), B(70.0 m, 90.0 m), C(-20.0 m, -20.0 m), D(50.0 m, -40.0 m), and E(-80.0 m, 70.0 m). He gave Snoopy the following instruction. Start at A and move toward B, but to cover only one-half of the distance between A and B. Then move toward C, covering one-third the distance between your current location and C. Next, move toward D, covering one-fourth the distance between where you are and D. Finally, move toward E, covering one-fifth the distance between you and E, stop, and dig.
      1. Where is the juicy bone buried? Give your answer in coordinates.
      2. Suppose there are n trees located at A1, A2, ..., and An. The pirate's instruction is extended to involve all n trees in a similar fashion, i.e. after moving toward Ak, covering 1/k the distance between your current position and Ak, move toward A(k+1), covering 1/(k+1) the distance between where you are and A(k+1). Let a1, a2, ..., and an be the position vectors of A1, A2, ..., and An. Express the position vector of your final location in terms of the position vectors of the trees.
      3. Prove that changing the order of the trees in the instruction while keeping the order of the portions of the distance the same does not change the final location.
  4. Gamma-correction [3 marks] The intensity I of an image is related to the voltage V of the control-grid of monitor A and monitor B according to the following equations respectively.

    5. Ia = Ka Va ga

    Ib = Kb Vb gb , where Ka, Kb, ga, and gb are constants that are specific to the monitors.

    Suppose the intensity of an image shown on monitor A is I1 when the voltage is V1.

      1. In order to display the image with the same intensity on monitor B, what should the voltage be in terms of V1?
      2. Let I2 be the intensity of an image on monitor B when the voltage V1 was applied to it. What would the intensity of the image viewed on monitor A be in terms of I1 if the voltage V2 = K I2 is applied to it?
  5. Transformations
    6.  [5 marks] Given a unit cube with one corner at (0, 0, 0) and the opposite corner at (1, 1, 1), derive the transformations necessary to rotate the cube by q degrees about the main diagonal from (0, 0, 0) to (1, 1, 1) in the counterclockwise direction when looking along the diagonal toward the origin.
  6. [12 marks] Write a program using OpenGL that:
    1. [2 marks] Allows you to plot a sequence of 6 points on the screen by clicking the mouse 6 times. Treat the sequence of points as a polygon. Connect the points with yellow line segments according to the order of entry. Also connect the last point to the first to complete the polygon.
    2. [6 marks] A fixed viewport will be drawn on the screen in red. Its coordinates are (-1.5,-1.5), (-1.5,1.5), (1.5,1.5), (1.5,-1.5). Clip the polygon to lie inside the viewport.
    3. [4 marks] Determine whether the polygon is convex. If so, colour the portion of the polygon within the viewport green. Otherwise, fill each portion not divided by an edge with a different colour. Note that you do not have to write a scan conversion algorithm to colour the inside of a polygon.

Use the template code provided at:

Submit your code electronically on CDF, using one of the following commands:

Submit a printed copy as well.