Computer Science 455
Instructor: R. P. Burton
Second Quiz

February 2-3, 2003

1. Suppose you wish to draw a line from (100, 200) to (52, 27) using the simple DDA algorithm. How many distinct x values are plotted? Pick the range in which the answer lies.
   • between 0 and 25
   • between 26 and 50
   • between 51 and 75
   • between 76 and 100
   • between 101 and 150
   • between 151 and 200
   (b)


2. What is the answer if, instead, the symmetric DDA is used?
   • between 0 and 25
   • between 26 and 50
   • between 51 and 75
   • between 76 and 100
   • between 101 and 150
   • between 151 and 200
   (b)


3. For the line of the previous two questions, how much does x change with each iteration (presumably of a for loop) of the simple DDA?
   • by less than one quarter
   • by more than one quarter, but less than one half
   • more than one half, but less than one
   • exactly one
   • more than one
   (b)


4. For the line of the previous three questions, how much does x change with each iteration (presumably of a for loop) of the symmetric DDA?
   • by less than one quarter
   • by more than one quarter, but less than one half
   • more than one half, but less than one
   • exactly one
   • more than one
   (a)


5. The simple DDA algorithm can be either more efficient (by using trunc instead of round) or more accurate by selecting pixels with midpoints as close as possible to the true line (as opposed to pixels all of which lie on or below the true line), but not both.
   • true
   • false
   (b)


6. What's so cool about the Bresenham algorithm?
   • It became famous in conjunction with IBM's "first out of the gate" graphics systems.
   • It minimizes the overhead required before beginning to plot the line
   • It overcomes the constraints of DDA lines which cause them to be either accurate or efficient, but not both
   • Once it gets started on a line, it really "hauls" (goes quickly)
   • It's simple derivation makes its behavior almost intuitive
   • It produces the most accurate lines
   (d)


7. Suppose time t is required to compute the location in the frame buffer (a 2D array) of the first pixel of a DDA or Bresenham line. About how much time is required to compute the location in the frame buffer of the second pixel of a DDA or Bresenham line?
   • much less than time t
   • time t once again; all locations in the frame buffer being pretty much equal
   • usually more than time t due in part to the accumulating overhead
   (a)


8. Both the implicit form of a circle and the polar parametric form of a circle suffer from
   • unequal spacing on points along the circumference
   • avoidable, time-consuming computation problems
   • both (a) and (b)
   (b)


9. The circle-generating DDA algorithm, as discussed in class and without the efficiency enhancements facilitated by the symmetry of a circle, produces
   • an accurate circle
   • a circle which doesn't close
   • an ellipse instead of a circle
   (c)


10. In most cases, calculating the coordinates of one point on the circumference of a circle centered at the origin permits ___ other point(s) to be calculated using only simple operations such as compliments and swaps.
    • one
    • three
    • seven
    • fifteen
    (c)


11. In most cases, calculating the coordinates of one point on the circumference of an ellipse centered at the origin permits ___ other point(s) to be calculated using only simple operations such as compliments and swaps.
    • one
    • three
    • seven
    • fifteen
    (b)


12. Simple addition (or subtraction) is sufficient to calculate points on the circumference of a circle/ellipse even if the circle/ellipse
    • is not centered at the origin
    • is rotated
    • both (a) and (b)
    (a)


13. The most accurate line between (x1,y1) and (x2,y2) is produced if these coordinates refer to
    • pixel centers
    • pixel corners
    • (it doesn't make any difference; the invisible grid is arbitrary)
    (b)


14. Geometric properties of a circle are maintained by displaying only those pixels which are
    • exterior to the circle
    • interior to the circle
    • centered on (or as close as possible to) the circumference of the circle
    (b)


15. Suppose you have the following polygon which you hope to fill using the scan-line algorithm:
        A
            B
            C    D         J
                 E    F
                      G    H
    Assume vertices are connected in alphabetical order, with J connected to H. Assume, too, that vertices E & F are on the same scan line, as are vertices G and H. How many intersection points are determined at point F?
    • one
    • two
    (b)


16. Continuing the previous question, how many intersection points are at point H?
    • one
    • two
    (a)


17. Continuing the previous questions, intersection points are generated by using the DDA algorithm and always stepping in
    • x
    • y
    • the axis of greatest excursion
    (b)


18. Which of the following is the LEAST important consideration for determining edge position in the active edge list?
    • max y (for an edge)
    • leftmost (as opposed to rightmost) from a local maximum (I suppose it should be "leftmore" and "rightmore," but these sound corny.)
    • change in y (for an edge)
    (b)


19. Using the "odd-even" rule, is an inflexion point (a vertex on the boundary which is neither a local maximum nor a local minimum) in or out?
    • out, because an even number of subsequent edge intersections are encountered
    • in, because an odd number of subsequent edge intersections are encountered
    • It depends on whether the boundary is considered to be "in" the polygon or "outside" the polygon
    (c)


20. A nonzero winding number for a point and a nonselfintersecting polygon means the point is
    • in
    • out
    • (it depends on the sign of the number)
    (a)


21. For selfintersecting polygons, the "odd-even" rule and the "nonzero winding number" rule
    • always produce identical results
    • always produce different results
    • sometimes produce different results
    (c)


22. Which of the following works for nonselfintersecting polygons with one or more holes?
    • boundary-fill
    • flood-fill
    • both
    • neither
    (c)


23. Which of the following can be expected to produce the (significantly) larger stack during the filling process?
    • boundary-fill
    • flood-fill
    • neither; their behaviors are roughly equivalent
    (c)


24. When filling a polygon with cells ("tiles") which of the following constraints MUST be observed?
    • the start point (a "corner" of the "tile") must be interior to the polygon
    • the start point must not be in a hole
    • all of the "tiles" must be placed in the same orientation (i.e. no rotations of 90, 180, or 270 degrees)
    • the "tile" must not be larger than the polygon (i.e. it must not be able to bound it)
    • (none of the above MUST be observed)
    (e)


25. By tradition (in the printing industry) if the width of a stroke is 15% of the width of the character, this ratio is preserved independent of the size of the character.
    • true
    • false
    (b)


26. What's a marker symbol?
    • an invisible symbol used as a reference point
    • an indicator to either the top or bottom of the active edge list
    • a logo, such as "EXPO2" that often appears on whiteboard pens
    • a symbol with a position, but usually without connections to other symbols
    • (none of the above)
    (d)


27. The number of pixels required to draw a line from (0,0) to (p,0) is p. The number of pixels required to draw a line from (0,0) to (0,p) is p. What is the number of pixels required to draw a line from (0,0) to (p,p)?
    • p
    • the square root of 2 times p
    • 2 times p
    (a)


28. The DDA line drawing algorithm can be used or modified easily to draw lines of
    • thickness e where e is an even, positive integer
    • thickness o where o is an odd, positive integer
    • thickness e or o, as defined above
    (c)


29. Suppose a particular system is capable of presenting any (or all) of 8192 colors (from a pallet of 224) on a 480 x 525 display. How many bits are required for the color look-up table?
    • (the "numbers" do not call for a color look-up table)
    • 480
    • 525
    • log28192 times 24
    • 8192 times 24
    • 480 x 525 x 224
    (e)


30. Which of the following is most likely to result from using a linear soft-fill algorithm?
    • an object of a uniform color
    • an object with nonlinear or "flowing" boundaries
    • an object consisting of tints (pastels)
    • an apparent double exposure
    • a recursive flood-fill with an unnecessarily large stack
    (d)


31. Pick the best statement:
    • text alignment need not be specified since it is virtually always perpendicular to the text path
    • text path can be specified, but text alignment is virtually always preset
    • text path and text alignment can be specified independent of one another
    (c)


32. What is the purpose of bundling attributes?
    • to make certain that no attribute is unintentionally omitted
    • to define the meanings of attributes for various output devices
    • to provide visually pleasing collections of attributes
    • to achieve economies of scale
    (b)


33. The primary purpose of an inquiry function is to "leave things the way you found them."
    • true
    • false
    (a)


34. Computing intensities at subpixel grid positions and then combining them to obtain pixel intensities is known as
    • the jaggies
    • supersampling
    • area sampling
    • prefiltering
    • pixel phasing
    (b)


35. When supersampling is used to draw a one-pixel-wide line with a positive slope of less than 45 degrees, all of the following are possible EXCEPT
    • the pixel may be set to the color of the line
    • the pixel may be set to the color of the line, but with the intensity diminished
    • two adjacent pixels (with a common x value, but different y values) may be set to the color of the line
    • two adjacent pixels (with a common x value, but different y values) may be set to the color of the line, but with the intensity diminished
    • (no exceptions here)
    (c)


36. Which is likely to give higher precision?
    • supersampling
    • area sampling
    • (they yield indistinguishable results)
    (b)


37. Suppose some of the boundary pixels between a red polygon and a blue polygon are represented in the frame buffer using purple. What is the best potential visual effect?
    • the polygons look like they have a border (or at least a partial border) along this shared edge
    • the shared edge looks like it is sprinkled with purple dots
    • the border looks straighter and the resolution seems higher
    (c)


38. Relative to the needs of other antialiasing techniques, pixel-phasing's most critical need is
    • substantial additional memory
    • a relatively fast processor
    • specialized integration hardware for achieving weighted average intensities
    • other special hardware characteristics
    (d)


39. An adaptation of the Bresenham algorithm by Pitteway and Watkinson is used for
    • supersampling
    • area sampling
    • pixel phasing
    (b)


40. All of the following transformations can be done conveniently using matrix techniques without homogeneous coordinates EXCEPT
    • translation
    • scaling
    • rotation
    • (no exceptions here)
    (a)


41. After doing scaling (with a scaling factor other than 1) or rotation (by other than a multiple of 360 degrees), discretionarily preceded or followed by other transformatin(s), a single point can remain fixed
    • only if that point was at the origin prior to beginning the transformation process
    • only if that point is a vertex of the entity being transformed
    • and that point can be any point on or interior to the entity being transformed
    • (none of the above)
    (c)


42. When an entity described by its vertices is transformed (translated, rotated, and/or scaled), an identical transformation is applied to all its vertices.
    • true
    • false
    (a)
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