CS372

2006 Exam Answers

1 a

2 b

3 b

4 d

5 b

6 c

jtho153

The line and the plane are parallel ( The planes normal and the line vector are orthagonal ). 
So we can just find the distance from point on the line to the plane.

Easiest point = (2,1,0).

Distance = |n.p| / |n|
 = 4 / √21

7 c

8 d

9 d

jtho153

| y^2 + 3*e^(xz)*z |
|      2xy         |
|  3*e^(xz)*x - 1  |

10 arob136: B -> I subsituted (1, 0) for (s, t)

jtho153: A

jtho153

I can only find in the notes how to get the tangent of a parametric equation with 1 parameter. But because its multi-choice you can figure it out :P.
s'= (1,0,2s) = (1,0,2)
t'= (0,1,-e^t) =(0,1,-1)
n = s' x t' = (-2,1,1) 

Cross the tangents of both parameters, at the point, and you should get the normal. 

11 c

12 a

13 b

14 a

jtho153

Cross product gives you an othagonal vector, dotted with either u or v will give you 0.

15 d

16 ezur001 a. texture coords of (10,10) is (1,1)

17 d None of the above, should be over √14

18 c

19 a

jtho153

                *     
                ^ Q    ^
                |      |
            ^   |      |
            |n  | h    |
      ______|___|_     | H
     /      |   | \    |
    |       *c  *a |   |
     \____________/    |
            ^          |
            |          |
            |d         |
            |          |
   (origin) o ----------
           
|a-c| < r
a = Q - c
a = Q - h
h = H - d
H = (Q.n) * n
d = (n.c) * n
h = (Q.n - n.c) * n
|Q - (Q.n - n.c) * n - c| < r

20 b

21 bcar066: d Stunt him is C - clai049

arob136: B -> translate by 1, then scale and rotate

22 jtho153: b (jtho153 could be (a) not 100% sure )

aols010: d

jtho153

(i)
Don't even know if we're meant to know about extents but its like the view volume.
If you use them but all your objects end up inside it anyway then you've just wasted time checking it.

So yeah it can slow it down.

(ii)
False, just examine the square of the distances. Square root is too expensive.

(iii)
I'm not 100% sure but like it makes sense. There may be some exception.

aols010

Extents sounds like a way of only testing if rays hit complex objects by first testing if the ray is within a simple extent, 
eg a sphere or a cube. That sounds faster. You can look it up and tell me how good a guesser I am sometime. 

23 ? [inside sets? not even in the notes]

24 aols010: guess=b?

25 [no longer examinable]

26 [no longer examinable]

27 d

28 a

29 c

30 aols010: a or c (are surface normals affected at all by translations (or crazy transposes of translations)? if not then c).

31 ?

32 b

33 b

34 a

35 ? [whats image precision?]

36 a

37 d

38 d

39 c

40 a

41 ? ["dir"?]

42 d

43 c

44 b

45 b (or d if "positive" == "non negative")

46 [no longer examinable]

47 [no longer examinable]

48 [no longer examinable]

49 D

50 D object gets brighter as more blue is added, bringing it closer to white.