Computer Science 455

Instructor: R. P. Burton

Seventh Quiz

April 17-18, 2006

Name _________________________________________ Score ____________/32

1. Making simple checks to avoid some calculations is possible in _____ solutions to the ray/sphere intersection problem.

   1. geometric but not algebraic

   2. algebraic but not geometric

   3. both the geometric and algebraic

(c)

2. What is spherical inverse mapping?

   1. determining the direction of a (reflected) ray emanating from the surface of a sphere

   2. determine the direction of a(n incident) ray striking the surface of a sphere

   3. converting a position on the surface of a sphere to a position in a 2D array

   4. turning a sphere inside out to handle rays “inside” the sphere

(c)

3. To solve the ray/plane intersection problem

   1. take the same general approach taken to solve the ray/sphere intersection problem

   2. take a fundamentally different approach which capitalizes on the relative simplicity of the explicit equation for a plane

(a)

4. “The normal of the plane points away from the ray” is synonymous with “The ray intersects the plane behind the ray’s origin.”

   1. true

   2. false

(b)

5. Suppose that a polygon and the intersection of a ray with the polygon are projected onto a principal plane. If the equation of the plane is –x + 2y – 3z + 4 =0, onto which principal plane should the projection be made?

   1. xy

   2. yz

   3. zx

   4. it makes no difference

(a)

6. For purposes of ray/box intersection, what is a slab?

   1. a region between two parallel planes

   2. a region between two parallel rectangles

   3. a region between 3 mutually perpendicular sets of 2 parallel planes each

(a)

7. It is possible for a ray to satisfy the “x” requirements and the “y” requirements for being inside a box, but not the “z” requirements for being inside a box.

   1. true

   2. false

(a)

8. A single formulation exists for finding the intersection of a ray with all of the following EXCEPT

   1. cones

   2. cylinders

   3. ellipsoids

   4. hyperboloids

   5. paraboloids

   6. (no exceptions here)

(f)

9. Inverse mapping for a circle can be as simple as converting from Cartesian to polar coordinates.

   1. true

   2. false

(a)

10. Inverse mapping for a cylinder ____ create a seam.

    1. does

    2. may

    3. does not

(b)

11. Change in direction due to refraction is ________ wavelength.

    1. dependent on

    2. independent of

(a)

12. If two pixels produce perceptibly equivalent colors, the frequency-vs-amplitude plots associated with the two pixels are identical or at least very similar.

    1. true

    2. false

(b)

13. Systematic fractal geometry was developed around the time of

    1. the reformation

    2. Joseph Smith

    3. Utah Statehood (1896)

    4. the BYU Centennial (1975)

    5. the start of the third millennium

(d)

14. Fractals were first conceived by Galileo.

    1. true

    2. false

(b)

15. The use of fractals is

    1. limited to the production of artificial shapes and artificial “worlds”

    2. applicable in several scientific disciplines

(b)

16. If the Koch snowflake is produced from an equilateral triangle with each side measuring 1 unit, what is the length of the perimeter of the Koch snowflake?

    1. 3

    2. (approaching) 6

    3. (approaching) 9

    4. ∞

(d)

17. Why are some fractals generated with functions in the complex plane?

    1. because some fractals have an inherent real component and an inherent complex component

    2. to separate the x and y values of points that constitute the fractal

    3. (they aren’t)

(b)

18. An appropriate “fractal surface” produced by the random midpoint displacement method ______ be iterated to pixel or subpixel precision.

    1. need not

    2. should always (resources permitting)

(a)

19. The Koch snowflake manifests ____ self-similarity.

    1. exact

    2. statistical

(a)

20. The fractal dimension of the Koch snowflake is

    1. 1

    2. between 1 and 2

    3. 2

    4. between 2 and 3

    5. greater than 3, but not infinite

    6. infinite

(b)

21. The Rocky Mountains exhibit _____ self-similarity.

    1. exact

    2. statistical

    3. no

(b)

22. A mountain in a painting which looks too jagged probably has a fractal dimension ____

    1. below 2.15

    2. around 2.15

    3. above 2.15

(c)

23. A plausible planet with an inconsequential atmosphere has

    1. lots more small craters than big craters

    2. about the same number of each size of crater

    3. lots more large craters than small craters

(a)

24. If an initial sphere is divided into hemispheres (which are displaced relative to each other) by an encircling fault (in a random direction) and this is done several thousand times,

    1. “continents” (i.e, conspicuous land masses) will form

    2. the surface will consist of almost uniformly distributed “island peaks”

(a)

25. What is the source of 1/f^beta noise?

    1. 60 (or 50) cycle hum

    2. solar flares

    3. the sampling rate of the human eye

    4. (none of the above)

(d)

26. LDS hymns mimic 1/f^beta noise.

    1. true

    2. false

    3. blasphemous!

(a)

27. The generation of fractals requires _____-level mathematics.

    1. high school

    2. bachelor’s

    3. doctoral

(a)

28. Which of the following does NOT have a stable orbit?

    1. sqrt(x)

    2. x²

    3. sin(x) with x measured in radians

    4. cos(x) with x measured in radians

    5. (all have stable orbits)

    6. (none have stable orbits)

(b)

29. The inverse iteration method for computing the Julia set involves

    1. beginning with a point far into the orbit (at least 30) and working toward earlier points in the orbit

    2. taking square roots instead of squaring

    3. unwinding recursive calls

(b)

30. The code to produce any of the Julia set by inverse iteration is approximately ____ lines long.

    1. 20

    2. 200

    3. 2000

(a)

31. To produce an acceptable graphic of the filled-in Julia set (on a 1000 x 1000 display), approximately ______ points must be iterated.

    1. 10

    2. 100

    3. 1000

    4. 10,000

    5. 100,000

    6. 1,000,000

(f)

32. For ________, z_k+1 = z_k² + c.

    1. only Julia

    2. only Mandelbrot

    3. both Julia and Mandelbrot

(c)