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

February 16-17, 2003

1. Suppose you have a "horrible" polygon of 400 vertices which needs to be transformed by a translation matrix, a scaling matrix, a second translation matrix, a third translation matrix, a rotation matrix and a fourth translation matrix. All in all, seven matrices need to be composed. Which of these seven matrices are candidates for the first composition if the objective is to avoid a needlessly excessive workload?
   • all seven
   • only six of the seven
   • the "3 x 400" matrix plus its immediate neighbor must be composed first
   • the "3 x 400" matrix plus any of the other six matrices can be composed first
   (b)


2. The inverse of a translation matrix can be realized by negating ___ of its values.
   • all
   • four
   • two
   • none (i.e. it takes more/other than negation)
   (c)


3. The inverse of a scaling matrix can be realized by negating ___ of its values.
   • all
   • four
   • two
   • none (i.e. it takes more/other than negation)
   (d)


4. The inverse of a rotation matrix can be realized by negating ___ of its values.
   • all
   • four
   • two
   • none (i.e. it takes more/other than negation)
   (c)


5. Suppose seven matrices have been composed to produce a transformation. The inverse of this matrix can be realized by
   • multiplying the same matrices together in the opposite order
   • inverting the individual matrices and multiplying them together in the same order
   • inverting the individual matrices and multiplying them together in the opposite order
   • (in general, a composed transformation matrix cannot be inverted)
   (c)


6. If the minus sign is in row 2 column 1, the rotation is
   • clockwise
   • counterclockwise
   • (it depends)
   (a)


7. When composing even a very large number of translation, scaling, and rotation matrices (possibly including some inverses of these kinds of matrices), the bottom row of the composed matrix ALWAYS contains 0, 0, and 1. Therefore, these values NEVER need to be computed in order to compose the matrices.
   • true
   • false
   (a)


8. Suppose a matrix contains -1 in column 1, row 2 and in column 2, row 1. All other values are 0 except the value in row 3, column 3, which contains 1. This transformation represents
   • a rotation
   • a scaling
   • remarkably, it represents both a rotation and a scaling
   (c)


9. A hypercube (specifically a four-dimensional cube) is bounded by ___ cubes of equal size.
   • four
   • six
   • eight
   • twelve
   • sixteen
   (c)


10. When an object is to be rotated efficiently about one of its vertices which is not at the origin, the object first is translated so the vertex (for rotation) is at the origin, then the object is rotated, then it is translated so the vertex returns to its original position. Thus, the object is in up to four unique positions/orientations as a consequence of the process.
    • true
    • false; it is in only three positions/orientations
    • false; it is in only two positions/orientations
    • false; it never changes
    (c)


11. All of the following 2D reflections can be represented by a 3x3 matrix EXCEPT
    • reflection across a principal axis
    • reflection across the origin
    • reflection across a line parallel to a principal axis
    • reflection across a line through the origin and NOT parallel to a principal axis
    • reflection across a line NOT through the origin and NOT parallel to a principal axis
    • (no exceptions here)
    (f)


12. A shear is best characterized as a form of
    • translation
    • scaling
    • rotation
    • reflection
    (b)


13. Suppose several objects are defined relative to coordinate system I, but we would like them defined relative to coordinate system II, where II is displaced and rotated with respect to I, and different scales are used for the axes. By what are these objects transformed so that they are defined relative to coordinate system II?
    • by a transformation which superimposes coordinate system I onto coordinate system II
    • by a transformation which superimposes coordinate system II onto coordinate system I
    • neither (a) nor (b)
    (b)


14. Suppose you have a rectangle with one of its vertices at the origin and the edges aligned with the principal axes. The rectangle can be scaled in x and/or y, but CANNOT be scaled along an axis 29 degrees above vertical, for example.
    • true
    • false
    (b)


15. Suppose you wish to translate the contents of one rectangular region of the frame buffer to another region of the frame buffer with identical shape and dimensions. This can be done "in the frame buffer" only if the regions do NOT overlap.
    • true
    • false
    (b)


16. The window-to-viewport transformation requires the window and viewport to be
    • of the same dimensions
    • of the same aspect ratio
    • proportionately displaced from their respective origins
    • (all of the above)
    • (none of the above)
    (e)


17. Which of the following is less useful?
    • a rotated window
    • a rotated viewport
    • (both (a) and (b) are essentially useless)
    (b)


18. Changes to the window affect the image _____; changes to the viewport affect the image _____.
    • directly, directly
    • directly, inversely
    • inversely, directly
    • inversely, inversely
    (c)


19. The window-to-viewport transformation (derived by two different means in class) can be expressed in matrix form with up to ____ elements having values other than 0 or 1.
    • 2
    • 4
    • 6
    • 8
    (b)


20. Assuming the clipping process to be equivalently difficult relative to the window and to the viewport, clipping should be done relative to the
    • window
    • viewport
    (b)


21. Point clipping requires a point to satisfy ____ of four conditions.
    • at least one
    • at least two
    • at least three
    • all four
    (d)


22. Given the Cohen & Sutherland endpoint codes for the two endpoints of a line segment, you can always determine
    • whether or not the line segment can be trivially accepted
    • whether or not the line segment can be trivially rejected
    • neither (a) nor (b)
    (a)


23. Suppose you are doing midpoint subdivision, and the greatest change in the value of a variable is 1000. What is the maximum number of subdivisions that must be made to find the intersection of a line segment with either an x or y clipping boundary.
    • 10 or less
    • 11 to 100
    • 101 to 999
    • 1000
    • more than 1000
    (a)


24. Suppose you are doing midpoint subdivision, and the greatest change in the value of a variable is 1000. What is the maximum number of subdivisions that must be made to find the intersection of a line segment with both an x or y clipping boundary.
    • 10 or less
    • 11 to 100
    • 101 to 999
    • 1000
    • more than 1000
    (a)


25. The parametric form of a line equation uses ____ as the parameter.
    • x
    • y
    • either x or y
    • neither x nor y
    (d)


26. If you "mind your p's and q's", the Liang and Barsky algorithm will permit you to determine all of the following EXCEPT
    • if a line segment is parallel to a clipping region boundary
    • if a "parallel" line segment is inside or outside a clipping region boundary
    • if a "nonparallel" line segment (when extended) crosses a(n extended) boundary from inside to outside or vice versa
    • the point of intersection of any such crossing
    • (no exceptions here)
    (e)


27. Nicholl Lee Nicholl is "cool" because
    • it uses simple arithmetic operations to find intersection points
    • it determines which clipping region boundaries (if any) are intersected by a line segment
    • it works for clipping regions of arbitrary orientations
    • it works for clipping regions of arbitrary shapes and orientations
    (b)


28. In Nicholl Lee Nicholl, an endpoint is characterized as being in one of ___ types of regions.
    • two
    • three
    • eight
    • nine
    (b)


29. Most clipping algorithms discussed in class are inapplicable if the clipping region is rotated.
    • true
    • false
    (b)


30. A geometric entity (such as a point, line segment, polygon) should remain a geometric entity of the same kind as a consequence of the clipping operation. In other words, the type of the input should match the type of its output.
    • true
    • false
    (a)


31. The cardinality (or one or more geometric types) can remain the same or can decrease, but it cannot increase as a consequence of clipping.
    • true
    • false
    (b)


32. Which of the following algorithms can produce geometric entities which were not part of the original polygon?
    • Cohen Sutherland
    • Weiler Atherton
    • both
    • neither
    (a)


33. Which of the following is likely to make multiple passes (one for each edge of the clipping region) to produce a correctly clipped polygon?
    • Cohen Sutherland
    • Weiler Atherton
    • both
    • neither
    (a)


34. A clipped polygon never has more vertices than the original polygon.
    • true
    • false
    (b)


35. The most simple test for "all or nothing" text clipping is to determine if ______ of the bounding box cannot be trivially accepted.
    • the four vertices
    • both diagonals
    • the minor diagonal
    (c)