Computer Science 455
Instructor: R. P. Burton
Fifth Quiz
March 15-16, 2004
Name _________________________________________ Score ____________/35
1. Two curves meeting at a common point with matching tangents at that point exhibit ____ order continuity.
a. zero
b. first
c. second
(b)
2. As a general rule, a curve which _____ a set of control points is more advantageous.
a. approximates
b. interpolates
(a)
3. You need ____ blending functions in order to produce Bezier curves for 10 sets of four control points.
a. four
b. ten
c. forty
(a)
4. The “convex hull” for a set of five (ordered) control points is equivalent to a polygon drawn from each vertex to its successor, with the polygon closed by including a line segment from the last vertex back to the first vertex.
a. true
b. false
(b)
5. Bezier curves can be (pick the most inclusive answer)
a. closed
b. closed with matching tangents at the point of closure
(b)
6. The maximum degree of the polynomial for a Bezier curve
a. is constant
b. grows linearly with the number of control points
c. grows as the square of the number of control points
(b)
7. The maximum degree of the polynomial for a B-spline curve
a. is constant
b. grows linearly with the number of control points
c. grows as the square of the number of control points
(a)
8. A B-spline or Bezier surface has ______ parameter(s).
a. one
b. two dependent
c. two independent
d. three dependent
e. three independent
(c)
9. How does the number of patches in a Bezier or B-spline surface relate to the n x m grid of control points?
a. there are n x m patches
b. there are (n - 1) x (m - 1) patches
c. there are (n + 1) x (m+1) patches
d. there is no relationship
(d)
10. Parallel projection can be as simple as dropping the z-coordinate.
a. true
b. false
(a)
11. Perspective projection can be as simple as dividing (the x- and y-coordinates) by their depth.
a. true
b. false
(a)
12. In a parallel projection, the direction of projection is always perpendicular to the display surface.
a. true
b. false
(b)
13. In a ____ projection, lines perpendicular to the projection plane are preserved in length.
a. cabinet
b. cavalier
(a)
14. “d”, the distance from the eye to the screen, should be measured in
a. (computer) room coordinates (for example, 2222 TMCB)
b. screen coordinates
c. world coordinates
d. master coordinates
e. (it doesn’t matter; just pick some value for “d”)
(c)
15. Parallel projection can be represented with a composable matrix, for all the points in the scene.
a. true
b. false
(a)
16. Perspective projection can be represented with a composable matrix, for all the points in the scene.
a. true
b. false
(b)
17. Polyhedra can have _______ vanishing point(s).
a. one
b. two
c. three
d. a theoretically unlimited number of
(d)
18. For a perspective projection, where is the center of projection relative to the view plane?
a. always on the view plane
b. always on the view plane and centered on the view plane
c. always centered relative to the view plane, but usually displaced in z
d. anywhere
(d)
19. Whether the projection is parallel or perspective, orthographic or oblique, it is always possible to transform the contents of the scene so that a parallel orthographic projection produces a correct collection of x- and y-coordinates.
a. true
b. false
(a)
20. (continuing the previous questions). It is always possible to produce a view volume measuring 1 x 1 x 1 and then to produce a correct collection of x- and y-coordinates simply by dropping the z-coordinates of the elements in this view volume.
a. true
b. false
(a)
21. When a frustum, with the viewpoint at the apex, is transformed into a parallelepiped, the viewpoint
a. becomes centered in the parallelepiped
b. becomes centered on the end cap of the parallelepiped
c. moves off to infinity (and beyond!)
(c)
22. What is the distance from the plane Ax + By + Cz + D = 0 to the origin of coordinates?
a. D
b. D divided by the length of the normal vector (A, B, C)
c. D divided by the length of the normalized normal vector.
d. None of the above – the plane has no fixed position in space – only an orientation
(c)
23. What “something” does the Roberts’ hidden-line algorithm use to determine if that “something” is inside a convex hull?
a. nothing
b. each edge of each surface
c. each point along each edge of each surface
d. each point along the projection toward the eye of each point on each edge of each surface
(d)
24. The approach of the Roberts’ algorithm could be applied to surfaces, not just to edges of convex hulls.
a. true
b. false
(a)
25. The simplest algorithm for identifying a back face (with the vertices of the associated polyhedron being defined in viewing coordinates)
a. substitutes the coordinates of the eye into the coordinates of the plane in which the back face lies
b. considers only the normal to the plane in which the back face lies
c. considers only one of the coefficients of the equation of the plane in which the back face lies
(c)
26. The depth buffer algorithm
a. must process all surfaces simultaneously
b. must process the surfaces in order, front to back
c. must process the surfaces in order, back to front
d. can process surfaces in any order
(d)
27. Once a surface qualifies to be written into the frame buffer (using the depth buffer method), it “owns” the associated pixels, and prevents them from being overwritten by any other surface, at least for the current frame.
a. true
b. false
(b)
28. If you know the depth of some planar surface at (x,y), its depth at (x+1,y), (x-1,y), (x, y+1) or (x, y-1) can be determined by a simple addition or subtraction.
a. true
b. false
(a)
29. Two surfaces, S1 and S2, overlap in x, so that each is “on”. S1 begins first and ends first. Using the scan-line method, which surface is drawn where the two surfaces overlap?
a. S1
b. S2
c. (can’t say for sure)
(c)
30. Continuing the previous question, once S2 starts “claiming pixels,” S1 is finished claiming pixels for that scan line.
a. true
b. false
(b)
31. Several polygons are partially drawn before any polygon is completely drawn. The hidden surface method is the ______ method.
a. z-buffer
b. scan-line
c. depth-sorting
d. (can’t say for sure)
(b)
32. When the sorting/rearranging of surfaces is finished for the painter’s algorithm, they can be written into the frame buffer, starting with the farthest surface and working toward the nearest surface, resulting in a scene with the hidden surfaces properly overwritten.
a. true
b. false
c. false unless additional “hidden surface” processing is done.
(a)
33. Suppose surfaces are originally ordered according to the “z-max” of each. Suppose two surfaces, A (the “far” surface) & B (the “near” surface), overlap in x, y, and z. Suppose the vertices of A are not on the far side of the plane of B, and the vertices of B are not on the near side of the plane of A. Suppose the projections overlap. Suppose A & B are interchanged, and all the tests still fail. What do you conclude?
a. the surfaces were originally in the correct order
b. the scenario described above is impossible
c. further processing is needed
(c)
34. Transparency is likely to be most difficult to provide with the ____ hidden-surface algorithm.
a. depth-buffer
b. scan-line
c. Newell, Newell, Sancha
(a)
35. Suppose a quadtree is built, representing the subdivision of an area (for the area subdivision algorithm). If the output device consists of 1000 x 1000 pixels, what is the maximum height of the quadtree? Assume a quadtree of one node has height 1.
a. 1-10
b. 11-100
c. 101-1000
d. more than 1000
(b- 11)