Computer Science 455

Instructor: R. P. Burton

Fifth Quiz

March 19-20, 2007

Name _________________________________________ Score ____________/47

1. Suppose three different Bézier curves are needed – two of which are defined by four different control points each, and one of which is defined by 5 control points. How many different blending functions are needed?

   1. four

   2. five

   3. nine

   4. thirteen

(c)

2. In the context of Bézier curves, what is a convex hull?

   1. a curve (such as along the hull of a ship), without concavities

   2. a bounding polygon without concavities

   3. a bounding box, always consisting of four edges and four right angles, that encloses the control points

   4. a bounding box, always consisting of four edges and four right angles, that encloses the Bézier curve

(b)

3. Pick the most complete, true statement:

   1. a Bézier curve cannot close.

   2. a Bézier curve can close, but the tangents generally cannot be made to match at the point of connection.

   3. a Bézier curve can close, and the tangents can be made to match at the point of connection.

(c)

4. What is the (maximum) degree of the polynomial for a Bézier curve determined by 6 control points?

   1. 3

   2. 4

   3. 5

   4. 6

   5. 7

(c)

5. When a control point of the previous question is moved, how much of the curve is affected?

   1. 1/6

   2. 1/3

   3. ½

   4. all of it

(d)

6. The degree of the polynomial for a B-spline curve is always the same as the degree of the polynomial for the Bézier curve determined by the same control points.

   1. true

   2. false

(b)

7. Pick the most complete, true statement:

   1. a B-spline curve cannot close.

   2. a B-spline curve can close, but the tangents generally cannot be made to match at the point of connection.

   3. a B-spline curve can close, and the tangents can be made to match at the point of connection.

(c)

8. In general, you can have the convex hull property and the variation diminishing property, or you can have interpolation, but not both.

   1. true

   2. false

(a)

9. A Bézier surface can be determined by a 3 x 4 mesh of control points. How many quadrilaterals make up the resulting surface?

   1. 2 x 3

   2. 3 x 4

   3. 4 x 5

   4. whatever you choose

(d)

10. In general, when Bézier surfaces are pieced together, continuity beyond zero order must be sacrificed.

    1. true

    2. false

(b)

11. Suppose A, B, C, and D have been determined for a plane, after which the coordinates of the vertices which determined the plane are transformed using matrix M. Can A’, B’, C’, and D’ be determined for the vertices in their new positions and, if so, how?

    1. they must be derived from the new coordinates

    2. they can be derived by postmultiplying the original A,B, C, and D with M

    3. the can be derived by premultiplying the original A, B, C, and D with M

    4. they can be derived by postmultiplying the original A,B, C, and D with M inverse

    5. the can be derived by premultiplying the original A, B, C, and D with M inverse

(e)

12. The equation of a plane, Ax + By + Cz + D can be used to determine

    1. if a point (x,y,z) is in the plane

    2. if a point (x,y,z) is on the front side or on the back side of a plane

    3. (all of the above)

(c)

13. Quadric surfaces include spheres, ellipsoids, tori, paraboloids, and hyperboloids. Superquadrics include

    1. their hyperdimensional (n>3) counterparts

    2. parameters for adjusting the shapes of quadric surfaces

(b)

14. If your bicep muscle is to be depicted as it expands and contracts, it should be modeled as

    1. an ellipsoid with changing radii

    2. a quadric surface

    3. a superquadric

    4. a blobby object

    5. a collection of particles which can move independent of each other

(d)

15. Fire and grass both can (and possibly should) be modeled using

    1. superquadrics

    2. blobby objects

    3. particle systems

(c)

16. Sweeping anticipates movement along

    1. a straight line with arbitrary orientation

    2. a Bézier or B-spline curve

    3. either (a) or (b)

(c)

17. A surface being swept is required to

    1. retain its orientation

    2. retain its shape

    3. retain its orientation and its shape

    4. do none of the above

(d)

18. Constructive solid geometry methods allow all of the following EXCEPT

    1. union

    2. intersection

    3. difference

    4. (no exceptions here)

(d)

19. For graphic presentation “the removal of hidden elements” means that these elements will NOT be presented in the final display.

    1. always

    2. sometimes

    3. never

(b)

20. Generally, what is the fundamental difference between object-space visible surface methods and image-space visible surface methods?

    1. The dimensionality of the space in which the problem is solved.

    2. Whether or not an OOP approach is taken

(a)

21. “Hidden”

    1. is applicable only to a 3D world

    2. extends downward in dimensionality

    3. extends upward in dimensionality

    4. extends both upward and downward in dimensionality

(d)

22. The Roberts hidden-line algorithm lends itself to extension to four-dimensions.

    1. true

    2. false

(a)

23. A back-face removal algorithm can be expected to remove approximately ____ of the surfaces in a typical scene.

    1. 10%

    2. 25%

    3. 50%

    4. 75%

(c)

24. Back-face removal requires, at a minimum,

    1. substitution of the eye coordinates into the equation of the plane in which the back face lies, with consideration of the resulting sign

    2. consideration of the normal vector (in viewing coordinates) of the back face

    3. consideration of only one of the elements of the normal vector (in viewing coordinates) of the back face

(c)

25. The depth-buffer algorithm processes surfaces

    1. in order of increasing depth

    2. in order of decreasing depth

    3. in any order

(c)

26. A separate buffer (i.e. the depth buffer) with the same dimensions as the frame buffer is needed for the depth-buffer algorithm; reducing the size of the depth buffer renders the algorithm as best partially operable.

    1. true

    2. false

(b)

27. In the z-buffer algorithm, the depth of each point on each polygon must be calculated independent of the depths of other points on the same polygon.

    1. true

    2. false

(b)

28. The traditional z-buffer algorithm _______ transparent polygons correctly.

    1. processes

    2. does not process

(b)

29. 29. The traditional scan-line algorithm _______ transparent polygons correctly.

    1. processes

    2. does not process

(c)

30. Suppose the scan-line algorithm is used to process a scene consisting of 100 polygons. What is the minimum number of “spans” potentially associated with any particular scan line?

    1. approximately 1

    2. approximately 100

    3. significantly more than 100

(a)

31. Continuing the previous question, what is the maximum number of “spans” potentially associated with any particular scan line?

    1. approximately 1

    2. approximately 100

    3. significantly more than 100

(c)

32. Since surfaces can have dimensional extension in any or all three dimensions, it is not possible to do a meaningful presort of surfaces, on z for example.

    1. true

    2. false

(b)

33. For purposes of painter’s algorithm, suppose 1) two surfaces overlap in x, y, and z, 2) all the vertices of the surface of greatest depth are NOT further away that the plane of the surface of greatest dept, 3) all the vertices of the surface of next greatest depth are NOT closer than the plane of the surface of greatest depth, and 4) the full overlap test fails. The next step is to subdivide one of the surfaces.

    1. true

    2. false

(b)

34. Which of the following warrants further subdivision in the area subdivision algorithm?

    1. all surfaces are outside an area

    2. only one surface intersects the area

    3. multiple surfaces intersect the area, but a surrounder is closest

    4. (none warrant further subdivision)

(d)

35. All of the following algorithms lend themselves to hidden-line elimination EXCEPT

    1. the depth-buffer algorithm

    2. the scan-line algorithm

    3. painter’s algorithm

    4. the area subdivision algorithm

    5. (no exceptions here)

(e)

36. Octree methods lend themselves, with minimal adaptation, to

    1. “plan” and “elevation” projection

    2. any form of parallel projection

    3. parallel and perspective projection, parallel to a principal axis

    4. any form of parallel, perspective, orthographic, and oblique projection

(a)

37. For graphics purposes, all of the following can be treated as sources of light EXCEPT

    1. light-emitting sources

    2. light-reflecting sources

    3. light-transmitting sources

    4. (no exceptions here)

(d)

38. Diffuse reflections results from

    1. point source light

    2. ambient light

    3. both (a) and (b)

(c)

39. Specular reflection results from

    1. point source light

    2. ambient light

    3. both (a) and (b)

(a)

40. The intensity of diffuse reflection ____ affected by the orientation of the surface relative to the light source(s).

    1. is

    2. is not

    3. (point light sources do not produce diffuse reflection)

(a)

41. Specular reflection calculations consider all of the following EXCEPT

    1. the direction to the light source

    2. the direction to the viewer

    3. the intensity of the light source

    4. the distance to the viewer

    5. the material reflecting the light source

    6. (no exceptions here)

(d)

42. When light moves through the air, passes through a thick, rectangular block of glass, and exits the panel back into the air. The final direction of the light is

    1. coincident with the initial direction

    2. parallel to the initial direction

    3. neither (a) nor (b)

(b)

43. Meaningful real-world texture contemplates variations in surface geometry.

    1. true

    2. false

(a)

44. Texture and surface patterns are two ways of referring to the same phenomenon.

    1. true

    2. false

(b)

45. All of the following can be communicated by using surface patterns EXCEPT

    1. texture

    2. marbling (“the look of marble”)

    3. shadows

    4. shading

    5. transparency

    6. (no exceptions here)

(f)

46. A surface “in the shadow” can be treated as a “hidden surface,” at least for computational purposes.

    1. true

    2. false

(a)

47. Halftoning (for computer graphics) _______ halftoning as used for newspapers.

    1. duplicates

    2. mimics (i.e. approximates)

(b)