CSCI 360

Fall 2019, Test 1

  1. For the equation $f(t) = S(1-t) + E(t)$
    1. [1 point] What is the purpose of this equation?
    2. [3 points] Explain how the three values: S, E, t are used. Are there any limits on these values?
    3. [3 points] Describe an application of this equation in a graphics system.
    4. [3 points] Provide a javascript function that implements this equation.

  2. Primitives and Attributes
    1. [2 points] With respect to a graphics system, define primitive and attribute.
    2. [6 points] Attributes
      1. Name two different primitives supported by the 2d context of the html5 canvas.
      2. What values are required to create each?
      3. Give a close approximation of code required to create each.
    3. [2 points] Name two different attributes supported by one of the primitives you described in the previous part.

  3. Representation
    1. [4 points] Define vector and raster graphics.
    2. [4 points] Compare and contrast each type of graphics (vector and raster)
    3. [2 points] For one of the primitives in the previous question, describe when it is represented as vector graphics and when it is represented as raster graphics.

  4. Pinhole Camera
    1. [4 points] Draw a diagram and describe the basic operation of a pinhole camera. Include
      • The location of the film plane
      • The location of the lense
      • The location of objects in the scene.
    2. [4 points] For a camera with depth d, derive the equation to compute where the point (x,y,z) will be projected onto the film plane for the y coordinate only.
    3. [2 points] How is the pinhole camera model modified in a graphics system?
    Over Please


  5. Transformations
    1. [2 points] Describe the task of a transformation matrix in a graphics system.
    2. [3 points] How is a transformation matrix formed? Describe
      • Initial value.
      • How transformations are added.
      • Include a detailed example.
    3. [2 points] How is a transformation matrix applied to objects in the scene.
    4. [1 point each] Describe the task that each of the following 2d matrices accomplishes. Show the application of the matrix (mathematical and graphical).

      1. $\begin{bmatrix} s_x & 0 & 0 \\ 0 & s_y & 0 \\ 0 & 0 & 1 \end{bmatrix}$

      2. $\begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$

      3. $\begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & h \\ 0 & 0 & 1 \end{bmatrix}$