Computer Science 455

Instructor: R. P. Burton

Fifth Quiz

March 17-18, 2008 

Name _________________________________________ Score ____________/48 

1. A(n) ______ projection is a specific kind of _______ projection.

1. axonometric, isometric
2. isometric, axonometric
3. axonometric, oblique
4. perspective, oblique

 

(b) 

2. A perspective projection is as simple as a divison of x and y by depth z.

1. True
2. False

 

(a) 

3. In _________ projection, lines perpendicular to the projection plane are preserved in length.

1. a cavalier
2. a cabinet
3. both a cavalier and a cabinet
4. neither a cavalier nor cabinet

 

(a) 

4. _______ projections can be represented in a useful, composable matrix form.

1. Parallel
2. Perspective
3. Both parallel and perspective
4. Neither parallel nor perspective

 

(a)
Note: perspective can be put in a matrix, but that matrix cannot be freely composed; this is why OpenGL has a separate Projection matrix. — Luther 

5. In a perspective projection, all parallel lines converge to a vanishing point on the (infinite extension of the) display.

1. True
2. False

 

(b) 

6. A center of projection on the view plane causes all points to project perspectively to a common point.

1. True
2. False

 

(a) 

7. Transforming to viewing coordinates is as simple as transforming from one coordinate system to another coordinate system.

1. True
2. False

 

(a) 

8. Ease of clipping is a primary advantage of transforming to a view volume which is a regular parallelpiped with its edges parallel or perpendicular to the view plane.

1. True
2. False

 

(a) 

9. Shearing is sufficient to transform an oblique projection into an equivalent orthographic projection.

1. True
2. False

 

(a) 

10. An oblique projection can be transformed to an equivalent orthographic projection, but a perspective projection cannot be transformed to an equivalent parallel projection.

1. True
2. False

 

(b) 

11. All of the following are advantages of near and far planes EXCEPT

1. being able to take cross sections of arbitrary thickness
2. more accurate hidden element determination
3. facilitating clipping to a view volume
4. (no exceptions here)

 

(d) 

12. Suppose you have a self-intersecting curve in the 2D plane.  The curve should be represented

1. with y as a function of x
2. with x as a function of y
3. sometimes (a) and sometimes (b), depending on slope
4. explicitly
5. parametrically

 

(e) 

13. Two curve sections have a common end point.  The most than can be said with confidence is that the curves exhibit

1. no continuity
2. zero-order continuity
3. first-order continuity
4. more than first-order continuity

 

(b) 

14. It could be said, that, in Texas, the large metropolitan areas are distributed randomly across the 2D plane (or is that “plain”?) .  If the federal government were to build the first freeway, the freeway should ________ the major metropolitan areas.

1. accommodate (but not necessarily pass through)
2. actually pass through

 

(a) 

15. Like the Bresenham line and circle algorithms, the Bezier coordinate function “works” but offers little by way of intuitive insight as to why it works.

1. true
2. false

 

(b) 

16. To plot five Bezier curves with four control points each, ____ blending functions need to be determined.

1. three
2. four
3. five
4. six
5. 20

 

(b) 

 

17. The convex hull for a Bezier curve is determined by

1. something other than the control points
2. some or all of the control points
3. always all of the control points

 

(b) 

18. A Bezier curve passes through at least _____ of the control points.

1. none
2. one
3. two
4. half
5. most
6. all

 

(c) 

19. From the following list, the greatest disadvantage of Bezier curves is that

1. they cannot be made to close upon themselves
2. they can be made to close, but the continuity at the point of closure cannot be retained
3. they are limited to at most four control points
4. the greater the number of control points, the higher the degree of the polynomial
5. (none of the above is characteristic of Bezier curves)

 

(d) 

20. From the following list, the greatest disadvantage of B-spline curves is that

1. they cannot be made to close upon themselves
2. they can be made to close, but the continuity at the point of closure cannot be retained
3. they are limited to at most four control points
4. the greater the number of control points, the higher the degree of the polynomial
5. (none of the above is a disadvantage of B-spline curves)

 

(e) 

21. You get interpolation or you get the convex hull and variation diminishing properties, but not both.

1. true
2. false

 

(a) 

22. There are Bezier curves and B-spline curves,

1. but only Bezier surfaces
2. but only B-spline surfaces
3. as well as Bezier surfaces and B-spline surfaces

 

(c) 

23. The edges of a Bezier surface determined by a mesh of 4 x 5 control points are Bezier curves.

1. true
2. false

 

(a) 

24. Given than quadrics include spheres, ellipsoids, tori, parabolids, and hyperboloids, what are superquadrics?

1. the hyperdimensional counterparts of these objects
2. these same objects (same dimensionality, too), with additional parameters for altering their shapes
3. mathematical objects not suitable for graphic presentation

 

(b) 

25. In a typical machine shop, the set operation least likely to have a counterpart is

1. union
2. intersection
3. difference
4. (all are likely to have counterparts)

 

(b) 

26. Suppose a triangle is swept translationally and not in its plane.  The resulting solid likely will be described by _____ polygons.

1. 3
2. 4 to 6
3. 7 to 10
4. more than 10

(b – 5) 

27. While being swept, a shape can undergo any of the following EXCEPT

1. translation along a linear path
2. translation along a Bezier curve
3. rotation
4. scaling
5. (no exceptions here)

 

(e) 

28. A circle can be “swept” to produce any of the following shapes EXCEPT

1. a sphere
2. a torus
3. a cylinder
4. an ellipsoid
5. (no exceptions here)

 

(e) 

29. Approximately how many levels does a quadtree have?

1. just one
2. log₂(the resolution of the display)
3. log₂(the maximum dimensionality – in screen coordinates - of the object represented by the quadtree)
4. it depends on the homogeneity/heterogeneity of the scene

 

(d) 

30. What is most likely to remain constant in a blobby object?

1. shape
2. surface area
3. volume

 

(c) 

31. Which of the following techniques would be suitable (or most appropriate if multiple options are suitable) for producing a representation of a recognizable individual?

1. polygonal approximation
2. (the application of) constructive solid geometry
3. sweeping
4. (the application of) fractal techniques
5. quadtrees or octrees
6. (none of the above would be suitable)

 

(a) 

 

32. Assume a matrix M with which to premultiply a collection of coordinates to produce a new collection of coordinates relative to a different coordinate system (probably consisting of translations, rotations, scalings, etc.).  Suppose a plane Ax + By +Cz + D has been determined in the original coordinate system.  What, if anything, can be done to A, B, C, and D to obtain A’, B’, C’, and D’ in the new coordinate system.

1. nothing; A’, B’, C’, and D’ must be calculated using vertices transformed to the new coordinate system
2. premultiply A, B, C, and D by M
3. postmultiply A, B, C, and D by M
4. premultiply A, B, C, and D by M-inverse
5. postmultiply A, B, C, and D by M-inverse

 

(e) 

33. “Hidden” lines and surfaces are not rendered in any fashion.

1. true
2. false

 

(b) 

34. Which group of algorithms is likely to have higher precision, and hence be amenable to zooming?

1. image space
2. object space
3. both have similar precision

 

(b) 

35. The Roberts’ hidden line algorithm is an _____-space algorithm.

1. image
2. object
3. image/object hybrid

 

(b) 

36. The first hidden-line algorithm for higher-dimensional spaces (n>3) was an _____-space algorithm.

1. image
2. object
3. image/object hybrid

 

(b) 

 

37. Which of the following can (and has been) exploited to enhance the efficiency of visible element algorithms?

1. sorting
2. coherence
3. both sorting and coherence
4. neither sorting nor coherence

 

(c) 

38. Back faces are most efficiently detected by

1. Substituting the coordinates of the eye into the equation of the plane containing the potential back face, then looking at the sign of the result
2. Looking at the normal for the potential back face (in viewing coordinates)
3. Looking at just one of the coefficients of the normal for the potential back face (in viewing coordinates)

 

(c) 

39. The depth-buffer is so called because

1. It treats the frame buffer as a depth buffer
2. It has a depth buffer in addition to the frame buffer
3. It stores the polygons in a buffer in sorted order

 

(b) 

40. Finding the depth of a planar surface at screen-position (x,y) requires two subtractions and a division.  Finding the depth of the same planar surface at an adjacent screen position requires

1. Two subtractions (or additions) and a division
2. Just a division
3. Just two subtractions (or additions)
4. Just one subtraction (or addition)

 

(d) 

41. The depth-buffer algorithm is able to handle all of the following EXCEPT

1. multiple polygons
2. convex polygons
3. interpenetrating polygons
4. transparent polygons
5. (no exceptions here)

 

(d) 

42. The scan-line algorithm (for visible surface determination is able to handle all of the following EXCEPT

1. multiple polygons
2. convex polygons
3. interpenetrating polygons
4. transparent polygons
5. (no exceptions here)

 

(e) 

43. The depth-sorting method also is known as

1. painter’s algorithm
2. the Newell-Newell-Sancha algorithm
3. both (a) and (b)
4. neither (a) nor (B)

 

(c) 

44. Because polygons can extend in x, y, and z, it is not reasonable to “sort” them preliminarily based on x, y, or z.

1. true
2. false

 

(b) 

45. Suppose two polygons (the “far candidate” and its “neighbor”) overlap in x, y, and z, all the vertices of the far candidate are not farther away than the plane of the neighbor, and all the vertices of the neighbor are not closer than the plane of the far candidate.  What can you conclude?

1. that the surfaces may be in the wrong order
2. that something has gone awry; this is not possible

 

(a) 

46. When does the area subdivision visible surface algorithm stop recursion?

1. only when not more than one polygon intersects a quadrant
2. sometimes when two polygons intersect a quadrant
3. only when pixel level is reached (unless coarser resolution is acceptable)

 

(b) 

47. Computation time for the area subdivision algorithm is more related to

1. number of levels of subdivision
2. visual complexity

 

(b) 

48. All of the following algorithms can be used or adapted for hidden line removal EXCEPT

1. Roberts
2. z-buffer
3. scan-line
4. painters
5. Warnock
6. (no exceptions here)

 

(f)