Computer Science 455

Instructor: R. P. Burton

Fourth Quiz

May 24-25, 2004

Name _________________________________________    Score ____________/32

1.         Coordinates represented in one coordinate system may be transformed for representation in another coordinate system

a. provided the coordinate systems have the same orientation

b. (a) and use the same units

c. independent of the orientation and units of each

(c)

2.         If object J is represented in coordinate system A and we would like to have it represented relative to coordinate system B, we should

a. find a transformation that maps A to B and apply it to J

b. find a transformation that maps B to A and apply it to J

c. find a transformation that maps A to B and apply it to A

d. find a transformation that maps B to A and apply it to B

e. accept the fact that, in general, we may not be able to achieve our objective

(b)

3.         The window to viewport transformation typically involves

a. translation only

b. translation and scaling

c. translation, scaling, and rotation

d. more than translation, scaling, and rotation and, in general, cannot be represented in matrix form

(b)

4.         An affine transformation

a. preserves lengths

b. preserves lengths and angles

c. transforms parallel lines into parallel lines

d. (all of the above)

(c)

5.         A matrix for translating points in n-dimensional space (i.e. n dimensions + the homogeneous coordinate) has at most ___ nonzero elements.

a. n

b. n+1

c. 2n-1

d. 2n

e. 2n+1

f. n²

(e)

6.         For any dimension n >= 2, it is most helping to think of rotation as

a. occurring about a point

b. occurring about an axis

c. being determined by two axes

(c)

7.         Rotation in 3D can take place relative to any of the following EXCEPT

a. an axis that is not coincident with a principal axis

b. an axis that is not parallel to a principal axis

c. an axis that does not pass through the origin

d. (no exceptions here)

(d)

8.         Using the derivation presented in class, how many matrices are composed to achieve rotation about an arbitrary axis?

a. 3

b. 5

c. 7

d. 9

e. 11

f. (none of the above)

(c)

9.         How many matrices are composed to achieve reflection through an arbitrary point?

a. 3

b. 5

c. 7

d. 9

e. 11

f. (none of the above)

(a)

10.       How many matrices are composed to achieve a transformation from one arbitrary 3D coordinate system to another (assuming different positions, orientations, “handedness,” and scales)?

a. 3 or 4

b. 5 or 6

c. 7 or 8

d. 9 or 10

e. 11 or 12

f. (none of the above)

(b – translate, rotate, rotate, rotate, swap, scale)

11.       Suppose you wish to rotate an oval-shaped doorknob about its central axis.  The doorknob has a position and orientation in door coordinates, the door has a position and orientation in room coordinates, the room has a position and orientation in building coordinates, the building has a position and orientation in city coordinates, the city has a position and orientation in state coordinates, the state has a position and orientation in country coordinates, the country has a position and orientation in world coordinates, but, fortunately, we are living at the time of Galileo, so the world is the center of everything.  How many matrices are composed to achieve the rotation of the doorknob?

a. 3

b. 5

c. 7

d. 9

e. 11

f. (none of the above)

(f)

13.       How many directions of translational freedom are there in six-dimensional space?

a. less than six

b. six

c. more than six

(b)

14.       How many degrees of rotational freedom are there in six-dimensional space?

a. less than 6

b. 6

c. more than 6 but less than 60

d. more than 60

(c – 15)

15.       Rotation through an arbitrary angle about an arbitrary axis in three-dimensional space ALWAYS requires a rotation a about each of the x, y, and z axes (at least in the derivation)?

a. true

b. false

(b)

16.       Which makes more sense?

a. a rotated viewport

b. a rotated window

c. both are reasonable and useful concepts

d. neither makes any serious sense

(b)

17.       When the position and/or size of the viewport are changed, its contents change ______; when the position and/or size of the window are changed, its contents change _______.

a. correspondingly, correspondingly

b. correspondingly, inversely

c. inversely, correspondingly

d. inversely, inversely

(b)

18.       All things considered, the more efficient place to clip is to the _______.

a. viewport

b. window

(a)

19.       The endpoint codes used in Cohen-Sutherland clipping are sufficient to determine

a. lines that can be trivially accepted

b. lines than can be trivially rejected

c. boundaries which are crossed by lines which cannot be trivially accepted or trivially rejected

d. (all of the above)

(d)

20.       When a line crosses a clipping-region boundary and the point of intersection is found using similar triangles, arithmetic is used to calculate the _____ coordinate(s) of the point of intersection.

a. x

b. y

c. x XOR y

d. x and y

(c)

21.       When a line crosses a clipping-region boundary and the point of intersection is found using midpoint subdivision, when the axis of greater excursion has length L, then not more than _____ subdivision(s) is/are needed to find the point of intersection.

a. 1

b. 2

c. L/2

d. Log L

e. L

(d)

22.       The Liang and Barsky algorithm is able to detect all of the following EXCEPT

a. lines parallel to clipping region boundaries

b. parallel lines completely inside or outside window boundaries

c. lines which cross extended clipping region boundaries

d. lines which cross actual clipping region boundaries

e. (no exceptions here)

(d)

23.       The Nicholl Lee Nicholl algorithm

a. is equivalent in performance to, but more efficient than Cohen Sutherland or Liang Barsky

b. is equivalent in performance to, but less efficient than Cohen Sutherland or Liang Barsky

c. performs a task different from Cohen Sutherland and Liang Barsky

(c)

24.       Nicholl Lee Nicholl compares the slope of a line (to be clipped) with the slope of ____ other line(s).

a. one

b. two

c. four

d. eight

e. nine

(c)

25.       The line clipping algorithms discussed in class are applicable only if the clipping region is not rotated.

a. true

b. false

(b)

26.       Suppose you have prudently and accurately determined a transformation for rotating the door knob in 120 TMCB, concatenating n matrices since the origin of world coordinates is at the Greenwich Mean and the equator.  Suppose further than you have a matrix for mapping from clock coordinates to “120 TMCB” coordinates.  How many matrices likely need to be concatenating to produce a transformation matrix for moving the second hand on the clock in 120 TMCB through 6 degrees?

a. 2 or 3

b. 4 or 5

c. n - (1, 2 or 3)

d. n

e. n + (1, 2, or 3)

(b – clock to room, room to GM/E, rotate 6 degrees, back to room or clock)

27.       A point is “saved” if it has the right relationship to _____ clipping region boundary/boundaries

a. just one

b. at least two

c. all four

(c)

28.       Exploiting symmetry, the Nicholl Lee Nicholl algorithm treats an endpoint as being in one of _____ kinds of regions.

a. 3

b. 4

c. 6

d. 9

(a)

29.       A polygon clipped by Sutherland Hodgman to a rectangular clipping region is clipped in ____ pass(es).

a. one

b. two

c. four

d. eight

(c)

30.       A polygon clipped by Weiler-Atherton to a rectangular clipping region is clipped in ____ pass(es).

a. one

b. two

c. four

d. eight

(a)

31.       If Sutherland Hodgman produces multiple polygons from a single polygon, the multiple polygons are

a. connected

b. not connected

(a)

32.       “All or nothing” string or character clipping can be done by failing to trivially accept _______ of a bounding box.

a. the main diagonal

b. either diagonal

c. both diagonals

(b)