CPSC 453, Winter ’15, Midterm
CPSC 453, Winter 2015, Midterm Exam (Take Home)
Released: March 10th, 2015
DUE: March 19th, 2015 (Thursday) in class
Full Name: ______________________________________________
Student ID: __________________________________________
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This exam is individual work.
15% of the final grade
Print it out, fill your name and ID, carefully answer all the questions and hand it in on
March 19th, 2015 in class
Please use BLUE pen to answer your questions
Late hand-ins will NOT be accepted
Question # Points Your Points
Q1
8
Q2
8
Q3
4
Q4
5
Q5
4
Q6
2
Q7
10
Q8
7
Total
48
1
CPSC 453, Winter ’15, Midterm
Q1: Circle out Vector (V) or Raster (R) displays? (8 pts)
V
R -- lines are smooth
V
R -- only lines possible, no filled polygons, or bitmaps
V
R -- discretized version of the model
V
R -- close to the 'pure mathematics' of the model
V
R -- no flicker
V
R -- jagged edges
V
R -- constant time to redraw any number of elements
V
R -- slower with more elements to be drawn, can start to flicker
Q2: Four-Universe Paradigm – For each problem below, circle which ‘universe’ the corresponding component
belongs to. (8 pts)
Problem #1 – Virtual Camera (1 pt for each problem component)
Problem Component
Four Universes
Projective transformations
P
M
R
I
(…)
gluLookAt(10.0,15.0,10.0,3.0,5.0,-2.0,0.0,1.0,0.0)
(…)
gluPerspective(40.0,1.5,50.0,100.0)
(…)
P
M
R
I
P
M
R
I
P
M
R
I
Photographic camera
2
CPSC 453, Winter ’15, Midterm
Problem #2 – 2D Image Modeling (1 pt for each problem component)
Problem Component
Four Universes
A = [ai, j], i = 1,...,m; j = 1,...,n
P
M
R
I
Black & White photo
P
M
R
I
P
M
R
I
P
M
R
I
Point sampling
Q3: Transformations. (4 pts)
Show that the translation represented by [T] affects points but not vectors.
u1 
x 
 


Consider the 2D case. Let P  y be a point and u  u 2 be a vector.
 
 
0 
1 
(a) Fill in the blanks (2 pts)


 _______ 
1 0 tx   x  







[T ]P  0 1 ty   y  
 _______ 
0 0 1   1  



 _______ 


 _______ 
1 0 tx   u1  







[T ]u  0 1 ty  u 2  
 _______ 
0 0 1   0  



 _______ 
(b) Your justification analysis based on the results from the above two transformations (2 pts):
(b.1) what happened to point P after it is transformed by matrix [T]? (1 pt)
(b.2) what happened to vector u after it is transformed by matrix [T]? (1 pt)
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CPSC 453, Winter ’15, Midterm
Q4: Which of the following pairs of transforms can be reversed without affecting the result (that is,
applied in reverse order)? Circle out Y if they can be reversed and N if they cannot. (5 pts)
Y
N
-- Translate(1,2)* Translate (2,3)
Y
N
-- Scale(2,1) * Rotate(45)
Y
N
-- Rotate(45) * Translate(1,1)
Y
N
-- Rotate (10) * Rotate (20)
Y
N
-- Scale(2,2) * Rotate(45)
Q5: Perform a 45 degrees rotation of triangle A(0,0), B(1,1), C(5,2) – IMPORTANT: you must show the actual
numerical values for the transformation matrices and the new triangle coordinates. Fill in the blanks. (4 pts)
sine 45 degrees = 0.707 and cosine 45 degrees = 0.707
(a) About the origin (1 pt for matrix R and 1 pt for the transformed triangle coordinates)

 _______


R   _______

 _______


_______
_______
_______

_______ 

_______ 


_______ 



_____


_____


_____


_____


_____


_____

A _____
B _____
C _____
(b) About P(-1,-1) (1 pt for matrix R and 1 pt for the transformed triangle coordinates)

 _______


R   _______

 _______


_______
_______
_______

_______ 

_______ 


_______ 


A _____
B _____
C _____
4
CPSC 453, Winter ’15, Midterm
Q6: Draw house A, and house B transformed by the appropriate commands in the given order: Identity()
… drawHouseB(). The untransformed house is below. (1 pt each)
Identity();
Scale(1, .5);
Translate(-4, -2);
drawHouseA();
Rotate(180);
Translate(0, 2);
drawHouseB();
Untransformed House
House A
House B
5
CPSC 453, Winter ’15, Midterm
Q7: Use the number corresponding to a term or name below as an in the space provided answer if you
think it is the best match for one of the concepts or terms on the next page. Each term may be used once,
more than once, or not at all. (10 pts)
1.
2.
3.
4.
5.
6.
7.
8.
9.
homogeneous
point
flicker
world frame
jaggies
screen window
GLUT
reverse mapping
Breseham
10. affine
11. topology
12. virtual camera
13. sampling ratio
14. graphics pipeline
15. Weiler-Atherton
16. linear
17. modeling transformations
18. clipping
19. refresh rate
20. projection
21. object frame
22. Cohen-Sutherland
23. true color
24. alpha
25. geometry
Questions
We often add this fourth ???? coordinate in 3-D graphics to provide a uniform matrix
representation for the various transformations that are used.
Answers
A weighted sum of vectors is a ???? combination and is itself always a vector.
Use the ???? to place objeects and cameras within the scene
Once we have set up the scene (objects and virtual camera in place), we use ????.to
create a 2D image
A weighted sum of points must be ???? if the result is a point.
The ???? clipping algorithm is the most general polygon clipping algorithm of those
discussed in the textbook.
The ???? is a useful analogy or metaphor that assists in understanding various viewing
and perspective parameters.
Build complex objects by placing individual parts within the main object and overall
scene
The discrete, grid-like structure of pixels gives rise to this visual artifact when straight
lines are drawn on a raster display if the lines are not exactly vertical or horizontal.
The entire process of creating and perceiving an image on a CRT or other display device
starting with a software application program and ending with the human visual system
and brain.
6
CPSC 453, Winter ’15, Midterm
Q8: Circle either True or False about the Phong illumination Model. (7 pts)
The shinier the surface the more light is specularly reflected
True
False
Ambient component realistically models ambient lighting
True
False
The rougher the surface the less light is diffusely reflected
True
False
All of the terms used directly derive from physical laws
True
False
Specular reflection is responsible for the highlights that are visible
on shiny objects
True
False
Diffuse component depends on the viewing direction
True
False
If a blue object is illuminated by a white light source, the color of the diffuse reflection
will be blue but that of the specular reflection will be white
True
False
END OF EXAM
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