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

March 17-18, 2003

1. Suppose an open quadrilateral "tube" is generated by sweeping a quadrilateral translationally in x so that the midpoint of the "tube" changes by 100 pixels in x. Assume that y of the midpoint does not change, nor does the quadrilateral transform in any other fashion. How many polygons should be used to describe the resulting open tube?
   • 4
   • 4 x 100
   • 4 x (s + 1) where s (>0) is the number of intermediate steps along the translational path
   (a)


2. A path along which a 2D shape is swept can be any of the following EXCEPT
   • a straight line segment
   • a full circle
   • a Bezier curve
   • a self-intersecting curve
   • (no exceptions here)
   (e)


3. Which of the following constructive solid geometry operations is least likely to have a (nonvacuous) real world counterpart in a typical shop?
   • union
   • intersection
   • difference
   • (all have common real world counterparts in a typical shop)
   (b)


4. Suppose that the intersection of two polygons (not "two intersecting polygons") is to be written to the frame buffer. Which of the following should occur first?
   • intersecting the two polygons
   • writing one of the two polygons to the frame buffer
   (a)


5. Suppose that a quadtree is produced to represent a scene measuring 700 units x 700 units. What is the maximum depth/height of the quadtree?
   • somewhere between 1 and 10
   • somewhere between 11 and 100
   • somewhere between 101 and 700
   (a)


6. How does the storage space for an octree compare to the storage space for a 1000 x 1000 quadtree representing the frame buffer image of the same scene? Assume that the octree is 1000 deep and that information is distributed equivalently in all directions.
   • About the same
   • 10 times as much
   • 100 times as much
   • 1000 times as much
   (d)


7. Octants in an octree typically are
   • cube-shaped and of uniform size
   • cube-shaped, but of different sizes
   • shaped like elongated cubes and of uniform size
   • shaped like elongated cubes, but of different face sizes
   (b)


8. Which approach would be best for determining detail on Mount Timpanogos for presentation as background to "virtual BYU?"
   • aerial photographs (or x,y,z surface samples obtained with a GPS) from which approximating polygons can be determined
   • constructive solid geometry techniques
   • fractals
   • particle systems
   (c)


9. Suppose you have a matrix for translating vertices in d-dimensional space. How many non-zero entries can be in the matrix? Be careful.
   • d or less
   • more than d, but not more than 2d
   • more than 2d, but less than d2
   • d2 or more
   (c)


10. Suppose you have a matrix for scaling vertices relative to an arbitrary point in d-dimensional space. How many non-zero entries are in the matrix?
    • d or less
    • more than d, but not more than 2d
    • more than 2d, but less than d2
    • d2 or more
    (b)


11. Counterclockwise rotation in 3-dimensional space "about an axis" always involves 2 sines and two cosines, with the "minus" sign on the sine in the lower-left corner.
    • true
    • false
    (b)


12. Suppose you have a matrix for rotating "in an arbitrary plane" in d-dimensional space. The combined number of sines and cosines is _____.
    • 4
    • 2(d-1)
    • 2d
    • 2(d+1)
    (a)


13. All of the following rotations are reasonable and unambiguous (and can be represented in matrix form, given the angle and its sign) in 3-dimensional space EXCEPT
    • rotation about a point
    • rotation about a principal axis
    • rotation about an axis parallel to a principal axis
    • rotation about an axis (not a principal axis) through the origin
    • rotation about an axis not parallel to a principal axis and not through the origin
    • (no exceptions here)
    (a)


14. Suppose you are given two points (in three-dimensional space) on an axis about which you want to rotate theta degrees. How many matrices need to be composed to produce the desired transformation matrix?
    • two or three
    • four or five
    • six or seven
    • eight or nine
    • (there is no guarantee that even an unlimited number of matrices can be composed to produce the desired results)
    (c)


15. The x axis points down, the y axis points out, and the z axis points left. You wish to rotate counterclockwise about the y axis. Where does the minus sign go in the rotation matrix? Assume that the element in the upper-left corner is at (1,1).
    • (1,2)
    • (1,3)
    • (2,1)
    • (2,3)
    • (3,1)
    • (3,2)
    (e)


16. Reflection in 3D can be defined unambiguously as being
    • across (and perpendicular to) a plane
    • across (and perpendicular to) a line
    • through a point
    • (any of the above)
    (d)


17. In order to reflect across a plane, the plane must
    • be a principal plane
    • be parallel to a principal plane
    • pass through the origin
    • (none of the above)
    (d)


18. What is the maximum number of 4x4 transformation matrices that must be composed to produce a transformation which maps one right-handed coordinate system onto another right-handed coordinate system?
    • 2 or 3
    • 4 or 5
    • 6 or 7
    • 8 or 9
    • 10 or more (i.e. it could be unlimited)
    (b)


19. An orthographic projection is
    • a parallel projection
    • a perspective projection
    • either a parallel or perspective projection
    • neither a parallel nor perspective projection
    (c)


20. A parallel projection is so called because
    • points are projected to the display surface along lines which are parallel
    • typically multiple projections are provided "in parallel" to provide all relevant views of an object
    • projection lines are parallel to the display surface
    (a)


21. An axonometric projection, as stated in the class notes and in the text, is __________ projection.
    • an orthographic
    • an oblique projection
    • neither an orthographic nor an oblique
    (a)


22. Cavalier and cabinet projections are __________ projections.
    • orthographic
    • oblique
    • neither orthographic nor oblique
    (b)


23. To do a perspective projection to a planar viewing surface which is perpendicular to the user's direction of vision
    • ignore z coordinates
    • divide each x and y coordinate by its depth z
    • divide each x and y coordinate by its distance (square root of the sum of the squares) from the eye
    (b)


24. The perspective transformation can be represented in a 4 x 4 matrix in a manner which permits it to be composed with other 4 x 4 matrices for transforming an arbitrary collection of points in a 3D scene to their counterparts in a 2D image.
    • true
    • false
    (b)


25. When the viewing transformation is applied to a collection of points in 3-dimensional space, a collection of points in ___ space results.
    • 2-dimensional
    • 3-dimensional
    (b)


26. What is the primary purpose of a view volume?
    • To define a bounding box to contain all the objects in the scene.
    • To provide a volume within which all objects in the scene must be placed.
    • To select a volume/subset of the scene for presentation on the display surface.
    (c)


27. Which of the following lends itself most easily (in terms of computation) to projection?
    • parallel orthographic
    • parallel oblique
    • perspective orthographic
    • perspective oblique
    (a)


28. Which of the following lends itself LEAST easily to projection?
    • parallel orthographic
    • parallel oblique
    • perspective orthographic
    • perspective oblique
    (d)