Computer Science 455

Instructor: R. P. Burton

Third Quiz

February 21-22, 2006

Name _________________________________________ Score ____________/31

1. Suppose x points up, y points right, and the rotation is counterclockwise. Where is the minus sign?

   1. (1,2)

   2. (2,1)

(a)

2. Suppose you are solving a problem in 4D space (x, y, z, and w) and you wish to do rotation involving the y and w planes. Which position does not have a 1 in it?

   1. (1,1)

   2. (2,2)

   3. (3,3)

(b)

3. To rotate a 6-sided polygon “about” an arbitrary point in 2D using a well-written graphics package, how many 3x3 matrices are composed at runtime?

   1. none

   2. one

   3. two

   4. three

   5. more than three

1. they should be composed algebraically in advance)

4. A 3x3 matrix can scale a 2D shape only in x and/or y, but not in some arbitrary direction in the plane.

   1. true

   2. false

(b)

5. Shearing is most like

   1. translation

   2. scaling

   3. rotation

(b)

6. The inverse of a shearing matrix is formed by

   1. negating the shearing value

   2. inverting the shearing value

   3. negating and inverting the shearing value

   4. transposing the shearing value across the diagonal

(a)

7. Two shearing matrices – one involving x and the other involving y – are commutative.

   1. true

   2. false

(b)

8. In 2D, reflection occurs

   1. across a principal axis

   2. across an arbitrary line

   3. through a point

   4. (any of the above)

(d)

9. Suppose the transformation matrix has 0s everywhere except along the diagonal, which has -1 in positions (1,1) and (2,2), and a 1 in (3,3). This represents

   1. scaling

   2. rotation

   3. reflection

   4. (any of the above)

(d)

10. If the geometry is described relative to coordinate system A, but we would like it to be described relative to coordinate system B, we should

    1. find a transformation which maps A to B and apply it to the data

    2. find a transformation which maps A to B and apply it to A

    3. find a transformation which maps B to A and apply it to the data

    4. find a transformation which maps B to A and apply it to B

(c)

11. A bit-block transfer (or a pix-block transfer) can take place

    1. unless the two blocks overlap at all

    2. unless the two blocks overlap in both x and y

    3. even if the two blocks overlap in both x and y

(c)

12. Rotation in 3D can take place “about an arbitrary axis” even if (pick the most inclusive answer)

    1. the arbitrary axis is not a principal axis

    2. the arbitrary axis is not parallel to a principal axis

    3. the arbitrary axis does not pass through the origin

    4. all of the above (a, b, and c) are true

(d)

13. The composed matrix which represents 3D rotation “about an arbitrary axis” (to the extent this is possible) consists of ____ rotation matrix/matrices.

    1. 1

    2. 2

    3. 3

    4. 4

    5. 5

(e)

14. If it can refer to only one of the following, a “window” refers to a region of the_______.

    1. display

    2. world

(b)

15. A change to the window produces a(n) ___________ change in the display; a change to the viewport produces a(n) ___________ change in the display.

    1. corresponding, corresponding

    2. corresponding, inverse

    3. inverse, corresponding

    4. inverse, inverse

(c)

16. The window-to-viewport transformation represents a mapping of one coordinate system onto another coordinate system.

    1. true

    2. false

(a)

17. For a point to be clipped against a rectangular clipping window, it must fail _____ of four tests.

    1. any one

    2. at least two

    3. all four

(a)

18. A line segment that is completely outside a clipping region is always trivially rejected by the Cohen-Sutherland algorithm.

    1. true

    2. false

(b)

19. A line segment which is not trivially rejected by the Cohen-Sutherland algorithm has at least one visible subsegment (possibly even a proper subsegment).

    1. true

    2. false

(b)

20. The principal advantage of the Liang-Barsky algorithm is

    1. the simplicity of the instructions it must execute

    2. the detection of cases which obviate the need for further processing

    3. its adaptability to geometric entities besides lines

(b)

21. Nicholl Lee Nicholl can detect line segments which do not intersect any clipping region boundaries.

    1. true

    2. false

(a)

22. Nicholl Lee Nicholl places the first endpoint of a line segment into one of ____ general categories.

    1. 2

    2. 3

    3. 4

    4. 8

    5. 9

(b)

23. Clipping (to axis-aligned) boundaries is not meaningful for rotated clipping regions. The (contents of the) clipping region must first be rotated to align with the axes before any meaningful clipping can be done.

    1. true

    2. false

(b)

24. Sutherland-Hodgman does the same basic task ____ times to clip an area against an aligned, rectangular clipping region.

    1. 2

    2. 4

    3. 8

(b)

25. Which lends itself more to clipping regions which have arbitrary (and possibly concave) polygonal shapes?

    1. Sutherland-Hodgman

    2. Weiler-Atherton

    3. Neither lends itself better than the other

(c)

26. Algorithms for reverse clipping (aka “blanking”) are conceptually ________ algorithms for clipping.

    1. the same as

    2. different from

(a)

27. All things considered, the better place to clip is in _______ coordinates.

    1. device

    2. world

(a)

28. Curve clipping is fundamentally ______ point and line clipping.

    1. the same as

    2. different from

(a)

29. If a clipping algorithm processes entities of dimension n, it should produce (zero or more) entities of dimension ____.

    1. n+1

    2. n

    3. <= n

    4. n-1

(b)

30. In order to transform from one 3D coordinate system to another 3D coordinate system,

    1. both systems must be either left-handed or right handed

    2. both systems must use the same units of measurement

    3. corresponding axes must be parallel to one another

    4. (none of these restrictions applies)

(d)

31. Mice are not suitable for graphics input if the mouse “slides” (i.e. the mouse is moved, but the cursor does not respond).

    1. true

    2. false

(b)