Computer Science 455

Instructor: R. P. Burton

Third Quiz

February 14-15, 2005

Name _________________________________________ Score ____________/39

1. How many points in homogeneous space map (correspond) to a single point in two-dimensional space?

   1. just one

   2. exactly two

   3. infinitely many

(c)

2. If you have a matrix that is the composition of several individual two-dimensional affine transformations, it’s inverse should be computed using

   1. Cramer’s rule

   2. Gauss elimination with partial pivoting

   3. Gauss elimination with full pivoting

   4. any of the above – none had advantages over any of the others

(b)

3. Suppose you know the individual affine transformations used to produce a composite matrix. The inverse of the composite matrix can be determined by

   1. multiplying the matrices together in the opposite order

   2. inverting the individual matrices and multiplying them together in the same order

   3. inverting the individual matrices and multiplying them together in the opposite order

(c)

4. Reflection through the origin is the equivalent of

   1. scaling by -1 in x and -1 in y

   2. rotating through 180 degrees

   3. both (a) and (b)

(c)

5. It is meaningful to speak of, and reasonable to program, all of the following except

   1. reflection across a principal axis

   2. reflection across a line parallel to a principal axis

   3. reflection across an arbitrary line

   4. reflection through the origin

   5. reflection through an arbitrary point

   6. (no exceptions here)

(f)

6. The inverse of a shearing transformation is realized by

   1. negating the shearing factor

   2. inverting the shearing factor

   3. negating and inverting the shearing factor

   4. (none of the above)

(a)

7. Shearing first in x and then in y produces the same results as shearing first in y and then in x, with the same shearing factors.

   1. true

   2. false

(b)

8. The inverse of a composite shearing matrix (which shears in both x and y) is realized by _____ in the composite matrix.

   1. negating the shearing factors

   2. inverting the shearing factor

   3. negating and inverting the shearing factors

   4. (none of the above)

(d)

9. If you have a unit square with vertices at (1,0), (2,0), (2,1), and (2,2) and you shear y based on x, how many vertices remain in their original positions? (NOTE: these points do not actually form a square, but that doesn’t change the answer)

   1. none

   2. one

   3. two

(a)

10. How many nonzero elements would be in a matrix for translating data involving 6 variables (what you and I would refer to as six-dimensional data)?

    1. 6

    2. 7

    3. 12

    4. 13

    5. 14

(d)

11. A single rule could be provided which would suffice for inverting a scaling matrix for data with 2, 3, …, 100 variables. (Assume no scaling factors with the value 0.)

    1. true

    2. false

(a – invert all the elements on the diagonal)

12. As expressed in a single, easily-writable matrix, translation in nD involves up to n translation factors; scaling in nD involves up to n scaling factors; rotation in nD involves ___ sines and ___ cosines.

    1. 2

    2. n/2

    3. n

(a)

13. What is the most consistent way to speak about rotation, independent of the dimensionality of the space?

    1. “about a point”

    2. “about a line”

    3. “about an entity of dimension one less than the dimension of the space in which the rotation is taking place”

    4. “as keeping the coordinates in the something-something plane”

(d)

14. Why is the minus sign on the sine in a “funny” place for “rotation about the y-axis (to use the common parlance)”

    1. because computer graphics uses left-handed coordinates

    2. because computer graphics uses a y axis which points downward

    3. because rotation “about the y-axis” is clockwise whereas other rotations are counterclockwise

    4. because the sines and cosines migrate down and to the right as you advance from rotation about x to rotations about y to rotations about z

(d)

15. For rotation about an axis not parallel to a principal axis, it is appropriate (and usually necessary) to find an arctangent (or an arccotangent).

    1. true

    2. false

(b)

16. Suppose you have an arbitrary line segment with one end at the origin. Rotation of this arbitrary line segment about the z-axis changes the _____ coordinates of the other end of the line segment.

    1. x and y

    2. x and z

    3. y and z

    4. x, y, and z

(a)

17. In order for rotation to occur about an arbitrary line segment, the (extended) arbitrary line segment MUST pass through the origin.

    1. true

    2. false

(b)

18. x points in, y points up, and z points left. Where is the minus sign for clockwise rotation about z?

    1. first row

    2. second row

    3. third row

(a)

19. Reflection in 3D can take place relative to all of the following EXCEPT

    1. an arbitrary point

    2. an arbitrary line

    3. an arbitrary plane

    4. (no exceptions here)

(d)

20. Two reflection transformations A and B are commutative (i.e. AB = BA).

    1. true

    2. false

(a)

21. In 3D it possible to shear x with respect to all of the following EXCEPT

    1. x

    2. y

    3. z

    4. y and z

    5. (no exceptions here)

(e)

22. In general, to rotate about an arbitrary line segment, two “preparatory” rotations precede the intended rotation. In these two “preparatory” rotations, the hypotenuse(s) (determined by the arbitrary line segment) used to calculate sines and cosines is/are

    1. the same

    2. different

(b)

23. Suppose an object J is defined in a coordinate system C which is defined relative to the origin of world coordinates W. To represent J relative to W

    1. find a transformation which maps C onto W and apply it to J

    2. find a transformation which maps W on to C and apply it to J

    3. find a transformation which maps C onto W and apply it to C

    4. find a transformation which maps W on to C and apply it to C

(b)

24. Suppose you want to rotate the little flag on the mail box to indicate there is mail to be picked up. The little flag is to be rotated about its origin, which, conveniently, is precisely where the nut and bolt are. But, the flag’s position is described relative to the mailbox whose position is described related to the farm whose position is described relative to the county whose position is described relative to the state, …. relative to the sun. To rotate the flag, find a transformation which maps

    1. the flag coordinate system to the sun coordinate system

    2. the sun coordinate system to the flag coordinate system

(b)

25. Traditionally (i.e. as graphics was being developed), a window was a region of

    1. the world

    2. the display surface

(a)

26. Changes to the window _____ affect the contents of the scene (as presented to the user); changes to the viewport _____ affect the contents of the scene (as presented to the user).

    1. directly, directly

    2. directly, inversely

    3. inversely, directly

    4. inversely, inversely

(c)

27. The window-to-viewport transformation can be expressed as one or more affine transformations.

    1. true

    2. false

(a)

28. A rotated window _____; a rotated viewport _____.

    1. makes sense, makes sense

    2. makes sense, doesn’t make much sense

    3. doesn’t make much sense, makes sense

    4. doesn’t make much sense, doesn’t make much sense

(b)

29. All things considered, clipping should take place relative to the _____ rather than relative to the ______.

    1. window, viewport

    2. viewport, window

(b)

30. For whom is the standard point-clipping algorithm named?

    1. Sutherland

    2. Hodgman

    3. Weiler

    4. Atherton

    5. nobody – it hardly took much thought to develop it

(e)

31. Given the endpoint codes for Cohen Sutherland clipping, it is possible to determine all of the following EXCEPT

    1. trivial acceptance

    2. trivial rejection

    3. exactly which actual clipping region boundaries are crossed

    4. (no exceptions here)

(c)

32. Cohen Sutherland with midpoint subdivision is computationally efficient whether endpoint codes are represented as integers or as floating point values.

    1. true

    2. false

(b)

33. The “p’s and q’s” of Liang and Barsky communicate (or facilitate the easy calculation of) all of the following EXCEPT

    1. lines parallel to a window boundary

    2. the direction from which the (extended) line crosses the (extended) boundary

    3. the point at which the (extended) line crosses the (extended) boundary

    4. Whether or not the actual line crosses the actual boundary

    5. (no exceptions here)

(d)

34. For Nicholl Lee Nicholl, the slope of a line segment needs to be compared against the slope of _____ other line(s) to determine which boundaries it crosses.

    1. one

    2. two

    3. four

    4. nine

(c)

35. Sutherland Hodgman can produce lines which were never part of the original polygon, but only for concave subject polygons.

    1. true

    2. false

(a)

36. The clip polygon for Weiler Atherton must be rectangular, but need not be a rectangle aligned with the coordinate axes.

    1. true

    2. false

(b)

37. For “all or nothing” string clipping, it is sufficient to clip a diagonal of the bounding box for the string, but the diagonal must be upper-left-to-lower right diagonal if the bounding box intersects the upper-left or lower-right corner of the clipping rectangle.

    1. true

    2. false

(b)

38. As discussed in class, techniques for clipping curves are beyond the scope of the course.

    1. true

    2. false

(b)

39. All of the clipping algorithms discussed in class lend themselves to blanking.

    1. true

    2. false

    3. what’s blanking?

(a)