Computer Science 455

Instructor: R. P. Burton

Third Quiz

May 27-28, 2003

Name _________________________________________ Score ____________/32

1. What most likely has taken place when an object is “reoriented?”

a. It has a new location, but has not been rotated.

b. It’s been rotated.

c. It has a different size.

d. It has a new location and/or it’s been rotated.

(b)

2. Which of the following transformations can be represented in composable (i.e. supports multiplication, for example of multiple n x n matrices resulting in a single n x n matrix) matrix form only when homogeneous coordinates are used?

a. translation

b. rotation

c. scaling

(a)

3. The scaling transformation (represented by a matrix with scaling factors down the diagonal) scales

a. the dimensions of lines and polygons to which it is applied

b. the offset (relative to the origin) of lines and polygons to which is it applied

c. both (a) and (b)

(c)

4. What results when a transformation matrix and its inverse are composed?

a. twice the transformation

b. the identity matrix

c. a matrix which invites problems at execution time

(b)

5. Suppose you have a collection of symbols representing a rotation matrix. How many symbols need to be moved to new locations to produce the inverse of the rotation matrix?

a. none

b. just one

c. exactly two

d. exactly four

e. exactly eight

f. exactly nine

(b)

6. For scaling which holds a single point fixed, John derives a matrix which represents translation so that the fixed point moves to the origin where the object is scaled, and then is translated so that the fixed point returns to its original location. Marsha derives a matrix which represents scaling and then a single translation so that the fixed point returns to its original location. How does the single matrix derived by John compare with the single matrix composed by Marsha?

a. they are identical

b. John’s is more complex than Marsha’s

c. Marsha’s is more complex than John’s

d. No general comparison statement can be made

(a)

7. Igor has composed several transformation matrices M1, M2, M3, …, M9 resulting in matrix MT. When applied to his arbitrary polygon, it looks just terrible. What does Igor need to do to transform the data back to its original form? Fortunately, Igor didn’t do any scaling by zero.

a. Compose the matrices in the opposite order

b. Compose the inverses of the matrices in the original order

c. Compose the inverses of the matrices in the opposite order

d. Apply Cramer’s rule to matrix MT

e. Do Gauss elimination with full pivoting

(c)

8. Igor’s original arbitrary polygon had five vertices stored in a matrix AP. Which two matrices should Igor NOT have composed first?

a. M1 & M2

b. M8 & M9

c. M9 & AP

(c)

9. To what point in two-dimensional space does the point (10, 5, 5) in homogeneous coordinate space correspond?

a. none

b. (10,5)

c. (5, 10)

d. (2,1)

e. (5,0)

(d)

10. Suppose you have a transformation matrix with zeros everywhere except down the diagonal. The values at (1,1), (2,2), and (3,3) are –1, -1, and 1, respectively. What does the transformation matrix represent? (pick the most inclusive answer)

a. scaling

b. rotation

c. scaling and rotation

d. reflection

e. scaling and reflection

f. (all of the above)

(f)

11. Which of the following can NOT be represented with a 3x3 transformation matrix?

a. rotation about an arbitrary point

b. scaling with one point remaining fixed

c. scaling in other than the x and/or y direction

d. reflection across an arbitrary line

e. reflection through an arbitrary point

f. (no exceptions here)

(f)

12. Suppose an arbitrary polygon is represented in coordinate system A. Suppose we wish to represent the polygon relative to coordinate system B. What should we do?

a. Find the transformation that superimposes A onto B, and apply it to A.

b. Find the transformation that superimposes A onto B, and apply it to B

c. Find the transformation that superimposes A onto B, and apply it to the polygon.

d. Find the transformation that superimposes B onto A, and apply it to A.

e. Find the transformation that superimposes B onto A, and apply it to B.

f. Find the transformation that superimposes B onto A, and apply it to the polygon.

(f)

13. Suppose you wish to transfer a region of the frame buffer to an overlapping region of the frame buffer.

a. It is necessary to store the region first to auxiliary memory.

b. The transfer can be made by starting with a nonoverlapped corner.

c. The transfer can be made by starting with an overlapped corner.

(c)

14. Suppose you wish to rotate a region of the frame buffer to an overlapping region of the frame buffer.

a. It is necessary to store the region first to auxiliary memory.

b. The transfer can be made by starting with a nonoverlapped corner.

c. The transfer can be made by starting with an overlapped corner.

(a)

15. The window-to-viewport transformation can be done by 1) placing a point in the viewport in the same relative position as the corresponding point in the window or 2) translating the lower left corner of the window to the origin, scaling the window to the unit square, scaling the window to the viewport size, and translating the lower left corner of the resulting figure to the lower left corner of the viewport’s intended position. Pick the best of the following statements:

a. Both can be represented as a matrix with identical scaling and translation values

b. Approach (1) can be represented as a matrix with scaling and translation values, but approach (2) cannot

c. Approach (2) can be represented as a matrix with scaling and translation values, but approach (1) cannot

(a)

16. Pick the best statement:

a. a rotated window makes sense, but a rotated viewport makes almost no sense

b. a rotated viewport makes sense, but a rotated window makes almost no sense

c. neither a rotated window nor a rotated viewport makes sense

d. both a rotated window and a rotated window make sense

(a)

17. The window-to-viewport transformation can be done by

a. finding a transformation which maps the window onto the viewport

b. finding a transformation which maps the viewport onto the window

c. (neither (a) nor (b))

(a)

18. Changing the position, rotation angle, or size of the window causes the view on the screen to change

a. correspondingly

b. inversely

(b)

19. Changing the position, rotation angle, or size of the viewport causes the view on the screen to change

a. correspondingly

b. inversely

(a)

20. Where is the most efficient place to clip?

a. in the world (i.e. in world coordinates)

b. before or after the world, but not in the world (Sounds almost scriptural, don’t you agree?!)

(b)

21. 1000 points need to be point-clipped. What is the maximum number of comparisons needed to clip these points? Assume that the boundaries of the rectangular clipping region, and the two-dimensional coordinates of each point are known.

a. two

b. four

c. log 1000

d. 1000

e. 2000

f. 4000

(f)

22. To determine if a line segment can be trivially accepted using Cohen & Sutherland, the endpoint codes should be

a. ANDed

b. ORed

c. Clipped

(b)

23. To determine if a line segment can be trivially rejected using Cohen & Sutherland, the endpoint codes should be

a. ANDed

b. ORed

c. Clipped

(a)

24. For a line segment which cannot be trivially accepted or trivially rejected by Cohen & Sutherland,

a. the window boundaries it crosses are immediately apparent from the endpoint codes

b. the extended window boundaries it crosses are immediately apparent from the endpoint codes

c. neither (a) nor (b) is true

(b)

25. Finding the intersection of a line segment with a rectangular window boundary parallel to the x or y axis involves solving

a. one equation for one unknown

b. two equations for two unknowns (namely, x and y)

(a)

26. Suppose a line segment has length 500 pixels and crosses a window boundary. If midpoint subdivision is used, what is the maximum number of required subdivisions?

a. 1

b. more than one but less than 11

c. more than 10 but less than 101

d. more than 100 but less than 500

e. 500

(b – 9)

27. What can Liang & Barsky’s “Ps and Qs” be used to tell us?

a. if a line segment is parallel to a window boundary

b. if an extended line segment crosses an extended boundary from inside to outside, or outside to inside

c. where an extended line segment crosses an extended boundary (if there is such a crossing)

d. (all of the above)

(d)

28. What information is provided by the Nicholl Lee Nicholl algorithm?

a. if an extended line segment crosses an extended boundary

b. where an extended line segment crosses an extended boundary (if it does)

c. which actual window boundaries a line segment crosses

d. (all of the above)

(c)

29. If a clipping region is rotated (but still rectangular), clipping provides no advantage.

a. true

b. false

(b)

30. When you clip a set of (points, lines, polygons), the result should be a set of (points, lines, polygons), i.e. clipping should produce a collection of zero or more of the same kinds of things.

a. true

b. false

(a)

31. Suppose a polygon of n vertices is clipped using Sutherland Hodgman. What is the maximum number of vertices of the resulting polygon?

a. more than n

b. n

c. less than n

d. n/2

(a)

32. The Sutherland Hodgman algorithm is a ____-pass algorithm.

a. one

b. two

c. four

d. eight

(c)