Computer Science 455
Instructor: R. P. Burton
Third Quiz
Name
_________________________________________ Score
____________/xx
1.
Suppose [M] = [A] [B] [C]. What
is [M]-1?
a.
[A]-1[B]-1[C]-1
b.
[C]-1[B]-1[A]-1
c.
both (a) and (b)
d.
neither (a) nor (b)
(b)
2.
Which if the following is preferred for inverting a matrix M whose
contents are known, but whose derivation is not known?
a.
Cramer’s rule
b.
Gauss elimination with partial pivoting
c.
Gauss elimination with full pivoting
(b)
3.
Suppose you wish to scale a polygon about an arbitrary point and then
rotate the same polygon about a (possibly different) arbitrary point. How many 3 x 3 matrices are composed to
produce a transformation matrix that will do the job?
a.
2
b.
3
c.
5
d.
6
e.
8
(d)
4.
Suppose you wish to reflect across an arbitrary line in the plane,
described by two points which lie along the line. How many 3 x 3 matrices are
composed to produce a transformation matrix that will do the job?
a.
2
b.
3
c.
5
d.
6
e.
8
f.
(you can’t reflect across an arbitrary line in the plane)
(c)
5.
Which of the following accurately describes the following
transformation matrix?
|-1 0 0|
|0 -1 0|
|0 0 1|
a.
scaling by –1 in x and y
b.
rotation through 180 degrees
c.
reflection through the origin
d.
(any all of
the above)
e.
(none of the above)
(d)
6.
Suppose you wish to find the inverse of M, which represents rotation
about the origin through some angle theta.
How many of the values in M-1 will be identical to the
corresponding entries in M?
a.
none
b.
1 or 2
c.
3 or 4
d.
5 or 6
e.
7 or 8
f.
all nine
(e
- 7)
7.
Suppose you have a matrix T which represents rotation about an
arbitrary point, scaling relative to an arbitrary point, reflection across an
arbitrary point, and shearing in both x and y.
How many elements in T might be different from the corresponding
elements in the identity matrix?
a. none
b.
1 or 2
c.
3 or 4
d.
5 or 6
e.
7 or 8
f.
all nine
(d
- 6)
8.
Suppose rotating about an arbitrary point and scaling relative to an
arbitrary point are expected to be very common activities. In a well-written graphics package, how many
matrices need to be multiplied together at execution time to transform the
vertices of an arbitrary polygon (stored in matrix form) to accomplish one
either of these activities? (Include the
polygon matrix in your count.)
a.
none
b.
two
c.
three
d.
four
(b
– compose algebraically in advance)
9.
Suppose a particular matrix is the same as the identity matrix except
that it has a value V in position (1,2). What is the inverse of this matrix?
a.
The identity matrix except that it has a –V in position (1,2)
b.
The identity matrix except that it has a –V in position (2,1)
c.
The identity matrix except that it has a 1/V in position (1,2)
d.
The identity matrix except that it has a 1/V in position (2,1)
e.
(none of the above)
(a)
10.
Suppose polygon P is defined relative to coordinate frame C1, but we
would like to define it relative to coordinate frame C2. Coordinate frame C2 is not coincident with
coordinate frame C1, nor is it aligned with coordinate frame C1, nor is the
scale of C2 the same as C1. To define
polygon P relative to C2,
a.
Find a transformation which maps coordinate frame C1 to coordinate
frame C2 and apply this transformation to coordinate frame C1
b.
Find a transformation which maps coordinate frame C2 to coordinate
frame C1 and apply this transformation to coordinate frame C2
c.
Find a transformation which maps coordinate frame C1 to coordinate
frame C2 and apply this transformation to polygon P
d.
Find a transformation which maps coordinate frame C2 to coordinate
frame C1 and apply this transformation to polygon P
(d)
11.
Suppose the contents of a rectangular region of the frame buffer need
to be moved to another region of the frame buffer of the same size and
orientation. Unfortunately, the two
rectangular regions overlap. Suppose
that you will be moving one pixel at a time (instead of all of the pixels on a
common scan line or the entire rectangular region at one time). Which corner should you start with?
a.
An overlapped corner of the source rectangle
b.
A corner of the source rectangle that is not overlapped, but is on the
same scan line as an overlapped corner.
c.
A corner of the source rectangle that is not overlapped, and is not on
the same scan line as an overlapped corner
d.
Either (a) or (b)
e.
(It can’t be done by any of these techniques; it must be possible to
move all the pixels on a common scan line.)
(a)
12.
Which of the following is least likely to be required by an
application?
a.
a rotated window
b.
a rotated viewport
c.
a viewport with a size different from the size of the window
d.
a viewport with an aspect ratio different from the aspect of the window
(b)
13.
Changing the position, size, or aspect ratio of the window (or
viewport), ______________ changes the contents of the window (or viewport).
a.
directly (or directly)
b.
directly (or inversely)
c.
inversely (or directly)
d.
inversely (or inversely)
(c)
14.
The window-to-viewport transformation can be expressed in matrix form
(i.e. with a 3 x 3 matrix) using constant scaling factors and constant
translation factors.
a.
true
b.
true except that the scaling factors are not constants
c.
true except that the translation factors are not constants
d.
false because neither the scaling factors nor the translation factors
are constants
e.
false because the window-to-viewport transformation involves more than
scaling and translation
(a)
15.
Where, in general, is the most efficient place to clip?
a.
in world coordinates
b.
after transformation beyond world coordinates
(b)
16.
1500 points need to be point clipped.
What is the minimum number of comparisons that could be
requiredneeded?
a.
1500
b.
1500 x 2
c.
1500 x 3
d.
1500 x 4
(a)
17.
Continuing the previous question, what is the maximum number of
comparisons?
a.
1500
b.
1500 x 2
c.
1500 x 3
d.
1500 x 4
(d)
18.
For the Cohen Sutherland algorithm, the end point codes indicate,
unambiguously, that a line segment is 1) trivially acceptable, 2) trivially
rejectable, or 3) partially acceptable.
a.
true
b.
false
(b)
19.
When a line segment intersects a (rectangular, aligned) clipping region
boundary, one of the coordinates of that intersection point always is known.
a.
true
b.
only in your dreams (i.e. “false”)
(a)
20.
Cohen Sutherland trivial acceptance and trivial rejection each
both
involve
a.
the ANDing of endpoint codes
b.
the ORing of endpoint codes
c.
(either (a) or (b) works for both)
d.
(neither (a) nor (b) works for both)
(d)
21.
Suppose your are doing Cohen Sutherland with
midpoint subdivision on a line segment that is 500 pixels long. What is the maximum number of subdivisions
required to find the intersections with all
intersected boundaries?
a.
0-10
b.
11-100
c.
101-500
(b)
22.
Which of the following cannot
be determined given only the Liang & Barsky “p’s & q’s” (followed by
any needed processing), the description of the clipping region, and the
coordinates of the endpoints of the line segment? (think carefully)
a.
if a line segment is parallel to a particular boundary
b.
if a line segment is completely outside the window boundary
c.
if a line segment is completely inside the window boundary
d.
exactly what part of the line segment is inside the window boundary
e.
which (nonextended) window boundaries the line segment intersects
f.
(no exceptions here)
(f)
23.
Nicholl, Lee, Nicholl is
a.
an alternative to traditional line clipping algorithms like Cohen &
Sutherland
b.
an enhancement to traditional line clipping algorithms
c.
an area clipping algorithm
(b)
24. Using Nicholl Lee Nicholl, if one endpoint P1 is inside the (rectangular) clipping region, determining boundary crossings requires the consideration of ___ other line(s).
a. one
b. two
c. four
d. six
e. eight
(c)
25. Using Nicholl Lee Nicholl, if one endpoint P1 is in a corner region, determining boundary crossings requires consideration of ___ other line(s).
a. one
b. two
c. four
d. six
e. eight
(e)
26. No meaningful clipping can be done relative to an arbitrarily rotated window unless all entities which might be clipped are rotated so as to effectively align the rotated window with the x and y axes.
a. true
b. false
(b)
27. As a general rule, clipping a homogeneous set of entities (points, lines, or areas, for example) should result in a homogeneous set of the same kind of entities.
a. true
b. false
(a)
28. Suppose a polygon of n vertices (and hence n edges) is clipped using the Sutherland Hodgman algorithm. The resulting polygon will have
a. not more than n vertices (and edges)
b. exactly n vertices (and edges)
c. at least n vertices (and edges)
d. m vertices, where the relationship between n and m cannot be stated in general
(d)
29.
During any one of the four passes of Sutherland Hodgman
clipping of a polygon of n vertices, what is the maximum number of vertices
that will may result?
a. less than n
b. n
c. more than n
d.a.can’t
say in general
(c)
30. Does the following algorithm perform clipping correctly for a non self-intersecting polygon?
·
Trace
around the border of the subject polygon counterclockwise until an intersection
with the clip polygon is encountered
·
If the
edge enters the clip polygon:
·
,
Proceed along the
subject polygon
·
Else:
·
Make
a left turn and follow the clip polygon Ifuntil
the subject polygon is encountered, then make
a left turn and follow the subject polygon
·
Remember
intersections so that all paths are traced exactly once
a. yes
b. no
(a)
31. For all-or-nothing string or character clipping, a trivial acceptance test of either diagonal is a sufficient test.
a. true
b. false
(a)
32. Curve clipping can be done by
a. point and line clipping techniques
b. only by techniques which are beyond the scope of CS 455
(a)
33. Which of the following conditions is least desirable in terms of efficiency?
a. posted and painted
b. posted but not painted
c. painted but not posted
d. neither posted nor painted
(c)
34. When additional primitives need to be added to a structure
a. the location of the (representation of the) structure is determined and additional primitives are appended
b. the location of the (representation of the) structure is determined and primitives are inserted based on relative priorities
c. the (representation of the) structure likely will require relocation
(c)
35. The “representation” of a model (such as a logic circuit), for the purposes of computer graphics, consists of
a. data structures
b. procedures
c. both data structures and procedures
(c)
36. Suppose the highest level of a hierarchy is called “physical device coordinates,” the next highest is called “normalized device coordinates,” the next highest is called “world coordinates,” ... and the lowest is called “master coordinates.” What is an appropriate name for the levels between world coordinates and the lowest level?
a. also “world coordinates”
b. also “master coordinates”
c. something other than “world coordinates” or “master coordinates”
d. (there are no layers between world coordinates and the lowest level)
(b)
37. Suppose a chair is part of an office which is part of a group which is part of a department which is part of an area which is part of a facility. Suppose that seven 3x3 transformations needed to be composed to transform the representation of the chair from master coordinates to physical device coordinates. Suppose that a desk is part of the same office, albeit at a different location in the office. In a well-designed system, how many 3x3 matrices need to be composed to transform the desk from master coordinates to physical device coordinates?
a. none; use the same composed transformation matrix
b. just two
c. seven
(b)
38. In general, a graphical user interface is designed to
a. accommodate users at all skill levels, from novice to expert
b. target just one specific skill level (for example, novice, ordinary skill, or expert)
c. optimize the ratio of resources expended to profit realized
(c)
39.
Who initiates data input in “sample mode”?
a.
the application program
b.
the input device
c.
neither the application program nor the input device
(c)
40.
Suppose that two clicks of the mouse are intended to produce a
horizontal line. How many scalar values are
need to be extracted from the mouse
clicks to determine the line? (An
example of a scalar value would be the y-coordinate associated with the first
click.)
a.
two
b.
three
c.
four
(b)