Computer Science 455
Instructor: R. P. Burton
Seventh Quiz
April 11-12, 2005

Name _________________________________________ Score ____________/27


1.What is the relationship between mathematical elegance and computational efficiency (in ray tracing algorithms)
a.linear
b.none in general

(b)

2.In the algebraic solution for the intersection of a ray and a sphere, the ray is represented ______ and the sphere is represented ______.
a.parametrically, parametrically
b.parametrically, explicitly
c.parametrically, implicitly
d.implicitly, parametrically
e.explicitly, parametrically

(c)

3.The algebraic solution for the intersection of a ray and a sphere is able to determine
a.if the ray hits the sphere
b.(a) and how many times it hits the sphere
c.(b) and where it hits the sphere
d.(c) and if the ray originates inside the sphere

(d)

4.The geometric solution to the ray-sphere intersection problem includes the following, all of which could be included in the algebraic solution (discussed in class) EXCEPT
a.avoidance of square root calculations
b.using multiplicative inverses to avoid divisions
c.checks to avoid certain calculations

(a)

5.Spherical inverse mapping, as discussed in class maps texture onto a sphere
a.without distortion
b.with distortion

(b)

6.The approach taken for ray-plane intersection is _____ the approach taken for ray-sphere intersection.
a.fundamentally the same as
b.a special case of
c.fundamentally different from

(a)

7.Ray-polygon intersection is just ray-plane intersection followed by an inside-outside test.
a.true
b.false

(a)

8.Inverse mapping (from a 2D array of texture/color) works only for quadrilaterals.
a.true
b.false

(b)

9.The ray-box intersection algorithm is useful only when a scene consists of one or more "boxes."
a.true
b.false

(b)

10.For a ray to intersect a box, it must intersect ______ slabs (x-, y-, and/or z-).
a.at least one
b.at least two
c.all three

(c)

11.The characteristics of the ray-sphere intersection problem make its solution ________ the more general, ray-quadric intersection problem.
a.fundamentally different from
b.of the same form as

(b)

12.All of the following always introduce distortions EXCEPT the inverse mapping for
a.a circle
b.a cylinder
c.a cone
d.(no exceptions here)

(b)

13.Fractal geometry is about _____ years old.
a.10
b.30
c.100
d.300
e.1000
f.3000

(b)

14.Fractal geometry is useful for producing pictures of mountains, coastlines, bark, lightning, etc., but it has little application outside of computer graphics.
a.true
b.false

(b)

15.The complexity of a fractal curve is based upon
a.the length of the curve
b.the extent to which the curve fills the plane
c.the length of the shortest program which can produce the curve

(c)

16.Why are fractal curves often generated with functions in the complex plane?
a.because fractals have both real and imaginary parts
b.to separate the x values from the y values
c.to accommodate negative values of which square roots must be taken

(b)

17.Which of the following is NOT an important consideration in random displacement methods?
a.the average displacement should be zero
b.the average point should be at the middle of the "segment"
c.the shorter the segment, the less the displacement
d.even-numbered displacements should be inward; odd-numbered displacements should be outward (or vice versa)
e.(all are important considerations)

(d)

18.The Koch snowflake manifests
a.exact self-similarity
b.statistical self-similarity

(a)

19.What is the approximate fractal dimension of the Koch snowflake?
a.1
b.1.3
c.2
d.2.3
e.3
f.3.3

(b)

20.Suppose height variations are scaled with a power law. If the power is less than 1, peaks are _______; if the power is greater than one, peaks are ________, and the fractal dimensions is _______.
a.flattened, emphasized, changed
b.emphasized, flattened , changed
c.flattened, emphasized, unchanged
d.emphasized, flattened, unchanged

(c)

21.Realism in the distribution of craters upon the surface of a sphere is achieved by
a.randomly generating the number of craters of each size
b.making the number of each size of crater proportional to its size
c.making the number of each size of crater inversely proportional to its size

(c)

22.What will result if a sphere is subjected (iteratively) to 10,000 faults, where a fault consists of a plane passing through the center of the sphere, but in an arbitrary direction and a subsequent displacement of the resulting hemispheres relative to each other?
a.a random distribution of elevations, but typically without any "continents" (large land masses of relatively high elevation) being formed
b.the formation of "continents"

(b)

23.What is the source of 1/fbeta noise?
a.it's artificial, but used to create fractal forgeries
b.Mother Nature
c.Roy G. Biv
d.negative time transmissions from outer space

(b)

24.Which of the following (if any) has an unstable orbit?
a.sqrt(x)
b.sin(x)
c.cos(x)
d.sqr(x)
e.none has an unstable orbit

(d)

25.What is the inverse iteration method?
a.working the opposite direction through an orbit
b.using multiplicative inverses to avoid division during iteration
c.working from either 0 or infinity (i.e. a very large number) back toward a fractal

(a)

26.A program to calculate the Julia set by inverse iteration requires approximately ____ lines of code.
a.20
b.200
c.2000

(a)

27.What is the fundamental difference in how the Mandelbrot set is calculated, relative to the (filled-in) Julia set?
a.there is no fundamental difference
b.the Mandelbrot set always starts at (0,0)
c.the Julia set always adds in a fixed quantity, whereas the Mandelbrot set does not

(b)