Computer Science 455

Instructor: R. P. Burton

Third Quiz

February 17-18, 2004

Name _________________________________________ Score ____________/36

1. The point at position (x,y) is just that – a point. The notion of attributes other than location is meaningless.

a. true

b. false

(b)

2. Suppose the line from (0,0) to (x,0) consist of 500 pixels, and the line from (0,0) to (0,y) consists of 500 pixels. The line from (0,0) to (x,y) consists of roughly ____ pixels.

a. 500

b. 707

c. 1000

(a)

3. A “double thickness” line of positive slope < > 1 can be produced using the DDA algorithm and (a) not rounding the y value and (b) always plotting the pixel above. Further, the plotted “line” will be centered (to the extent possible) on the true line.

a. true

b. false

(a)

4. Suppose a vendor advertises that its 500 x 500 monitor can display 4096 of 16,384 colors. How big is the frame buffer (in bits)?

a. 500 x 500

b. 500 x 500 x 12

c. 500 x 500 x 4096

d. 500 x 500 x 14

e. 500 x 500 x 16,384

(b)

5. If a polygon is “soft filled,”

a. it is likely to be painted with a single color

b. its borders likely will appear “fuzzy”

c. it likely will appear transparent

d. it likely will look “grainy,” as if the pixels have been “supersized”

(c)

6. What is the primary purpose of bundling attributes?

a. to provide compatible combinations (perhaps compensating for a lack of taste among users)

b. to permit an entire group of attribute selections to be made in one step

c. to provide an interpretation of an attribute for each of several output devices

(c)

7. What is the primary purpose of an inquiry function?

a. to learn a current attribute setting, with the anticipation of changing it temporarily

b. to discover the attribute settings used to achieve a particular effect (typically of a selected item)

c. to discover the available settings for a particular attribute

(a)

8. What constitutes an “alias?”

a. distorted (and hence misleading) information

b. an inaccurate representation (in the frame buffer) processed to yield a more pleasing or more realistic image for the viewer

c. an original image from which a subsequent image is produced to compensate for the aspect ratio

d. a youthful female alien.

(a)

9. To accommodate the intensity range of a typical contemporary monitor, which approach is likely more efficient?

a. postfiltering (supersampling)

b. prefiltering (area sampling)

c. pixel phasing

(b)

10. Techniques such as postfiltering and prefiltering for antialiasing lines tend to

a. spread the line to other pixels

b. concentrate the line on a smaller number of pixels

c. have no effect on the pixels that are selected to help present the line

(a)

11. The decision variable from the Bresenham line drawing technique can be adapted to indicate the extent to which a pixel is “overlapped” by a line.

a. true

b. false

(a)

12. Suppose a polygon is represented by the absolute coordinates of one of its vertices, and by the relative coordinates of the remaining vertices. This representation simplifies subsequent ________ of the polygon.

a. translation

b. scaling

c. rotation

d. translation and scaling

e. scaling and rotation

f. translation, scaling, and rotation

(a)

13. When a polygon is scaled, as discussed in class

a. its size is scaled

b. its position relative to the origin is scaled

c. (both (a) and (b))

(c)

14. When a polygon is rotated, as discussed in class

a. its orientation can be changed

b. its position relative to the origin can be changed

c. (both (a) and (b))

(c)

15. Suppose the rotation of a polygon with a large number of vertices is derived by moving its center of rotation to the origin, rotating it, and moving its center of rotation back to its original position. Suppose the polygon and each of these activities are represented in matrix form. Which matrix should NOT participate in the first composition?

a. the matrix which represents the polygon

b. the matrix which moves the center of rotation to the origin

c. the matrix which performs the rotation

d. the matrix which restores the center of rotation to its original position

e. (it is acceptable for any of these matrices to participate in the first composition)

(a)

16. Without homogeneous coordinates, _____ cannot be represented in composable matrix form.

a. translation

b. scaling

c. rotation

d. translation, scaling, rotation (individually and collectively)

(a)

17. To invert the composition of five transformations, all represented in composable matrix form,

a. multiply the five matrices together in the opposite order

b. invert each matrix and multiply the five matrices together in the same order

c. invert each matrix and multiply the five matrices together in the opposite order

d. give up; composed transformation matrices generally are not invertible

(c)

18. When a composite transformation matrix is built using an individual transformation matrix which takes the “fixed point” to the origin, what is done to protect against the overwriting of another object already at the origin (in the frame buffer)?

a. a bounding box is determined for the object being transformed, and that much of the frame buffer, at the origin, is saved

b. the origin is moved to the “fixed point” so that objects at the true origin are not overwritten

c. (either (a) or (b))

d. nothing is done

(d)

19. Matrix multiplication is commutative in general, i.e. M1 x M2 x M3 == M3 x M2 x M1.

a. true

b. false

(b)

20. A composite transformation is best inverted by using

a. Gauss elimination with partial pivoting

b. Gauss elimination with full pivoting

c. Cramer’s rule

(a)

21. What kind of transformation is suggested by the following matrix:

-1 0 0

0 -1 0

0 0 1

a. scaling

b. rotation

c. reflection

d. (all of the above)

(d)

22. At ~~most~~best, a single 3 x 3 transformation matrix can be produced which represents

a. reflection across a principal axis

b. reflection across a line parallel to a principal axis

c. reflection across an arbitrary line passing through the origin

d. reflection across an arbitrary line

(d)

23. At ~~most~~best, a single 3 x 3 transformation matrix can be produced which represents

a. reflection through the origin

b. reflection through an arbitrary point

(b)

24. If you wish to invert a shearing transformation, use the same matrix, but

a. invert the shearing factor

b. negate the shearing factor

c. invert and negate the shearing factor

d. “reflect” the shearing factor across the principal diagonal

e. (wish again; it can’t be done)

(b)

25. How many nonzero entries are in a 3 x 3 matrix which represents reflection across a the line through the origin with a slope of 1?

a. three

b. four

c. five

d. more than five

e. (there is no 3 x 3 matrix which represents such a reflection)

(a)

26. Suppose you have a large number of objects defined relative to a 2-dimensional coordinate system in which x points to the right and y points up. Suppose you would like these same objects to be defined relative to a new coordinate system whose origin is at (100,200), in which x points at 35 degrees, y points at 125 degrees, and whose units are twice as dense as in the original coordinate system. To do so:

a. find a transformation which maps the original coordinate system onto the new coordinate system and apply it to the original coordinate system

b. find a transformation which maps the original coordinate system onto the new coordinate system and apply it to the “large number of objects”

c. find a transformation which maps the new coordinate system onto the original coordinate system and apply it to the new coordinate system

d. find a transformation which maps the new coordinate system onto the original coordinate system and apply it to the “large number of objects”

(d)

27. How many 3 x 3 (translation, rotation, scaling, reflection, or shearing) matrices need to be composed to produce the transformation needed for the previous problem?

a. three

b. four

c. six

d. seven

(a)

28. Suppose you wish to move the contents of a rectangular, aligned-with-the-axes region of the frame buffer to another identically shaped and oriented region of the frame buffer. Suppose you can move only one scan-line at a time. What scan-line do you begin ~~with~~to copy from?

a. a scan-line which contains a corner unique to the source rectangle

b. a scan-line which contains a corner unique to the destination rectangle

c. a scan-line which contains a corner common to both rectangles

d. it doesn’t matter; (a), (b), and (c) all can be made to work

e. it can’t be done if the rectangles overlap

(c)

29. Suppose you wish to move the contents of a rectangular, aligned-with-the-axes region of the frame buffer to another identically shaped and oriented region of the frame buffer which is rotated 180 degrees relative to the first. Suppose you can move only one scan-line at a time. What scan-line do you begin with?

a. a scan-line which contains a corner unique to the source rectangle

b. a scan-line which contains a corner unique to the destination rectangle

c. a scan-line which contains a corner common to both rectangles

d. it doesn’t matter; (a), (b), and (c) all can be made to work

e. it can’t be done if the rectangles overlap

(e)

30. To map from window to viewport coordinates,

a. find a transformation which maps the window to the viewport, and apply it to the window

b. find a transformation which maps from the viewport to the window, and apply it to the window

c. find a transformation which maps from the window to the viewport and apply it to the contents of the window

d. find a transformation which maps the viewport to the window and apply it to the contents of the window

(d)

31. Which has greater utility?

a. a rotated window

b. a rotated viewport

c. both have equivalently utility

(a)

32. Suppose an object is inside the window. What happens to the image of the object as the window is enlarged?

a. it enlarges, too

b. it shrinks

(b)

33. Continuing the previous question, what happens when the viewport is shifted to the right?

a. the object shifts right

b. the object shifts left

c. the object’s position is unchanged

(a)

34. For rectangular, aligned viewports and windows, the window-to-viewport transformation can be represented in matrix form as a scaling and a translation.

a. false

b. true, but only if their width:height ratios match

c. true

(c)

35. All things considered, where is the more efficient place to clip?

a. to the window

b. to the viewport

c. (both are equivalently efficient; clipping is clipping)

(b)

36. Data typically resides in master coordinates. Most everything else is transformations except for the frame buffer representation.

a. true

b. false

(a)