Midterm ITCS 4120/5120 Fall 2005

Score is out of 100 points. There are 11 questions. Note, different questions are worth different amount of points. Generally, the later questions are longer and worth more points.

Name: ______

## 6)  [6pts] Illustrate the basic architecture of a computer graphics workstation at the level of key processors, buses, memory, etc.

7)  [6pts] Illustrate and label in a much detail as possible the components and distinguished locations on the human eye (you should label/name at least 8 components).

8)  [18pts] Draw the global Edge Table for the polygon below. Next, draw the sequence values the Active Edge Table (AET) would be assigned during the rasterization of this polygon. Also show the y coordinate of the scan-line that the rasterization algorithm is working on, when the AET has each these different assigned values.

9)  [18pts] Given the two coordinate systems A and B shown in the diagram: a) What is the matrix MB←A that transforms a point’s coordinate given in A into its coordinate in B? (From inspecting the diagram you should be able to give the exact real number values of the elements in the matrix—its ok to leave results in a form like cos 45 if you want).b) If you had to compute MB←A by concatenating together only elementary matrices (translations and rotations, scales , and shears, etc about the origin) what would the sequence of these elementary matrices be? You should leave your answer as a sequence of matrices to be concatenated and for each matrix indicate what type of elementary matrix it is.

10) [18pts] Line Clipping: a) Cohen-Sutherland and Nichol-Lee-Nichol (NLN) algorithms both start by computing region codes for the input line segment. What is a region code? b) How are they computed? c) Sketch an example clipping window and illustrate the region codes in the appropriate regions in the sketch. D) For each input line segment, the NLN algorithm further subdivides the clipping window into even more regions. Illustrate the regions in each of the 4 basic subdivision cases/subcases (Recall there are 3 basic cases, one of which has two subcases). Label the regions as done in class and describe in the general significance of these labels.

11) [18pts] A) Describe and illustrate the steps involved in the 2D viewing pipeline. Wherever a transformation is needed label what type of transformation is used and described in words what the transformation should accomplish. B) If my clipping window worlds coordinates had corners at (10,10) and (30,40) and I used the OpenGL convention of clipping in normalized device coordinates where the clipping boundaries have corners at (-1,-1) and (1,1), give the precise sequence of transformation matrices needed to map a point in world coordinates into normalized clipping coordinates.