JUNE 2012 – PAPER III
47. The colour of an object is largely determined by
its diffuse reflection coefficient. If Kd = (0.8,
0.4, 0), then what shall be the colour of the object, if the light used is blue
and magenta ?
(A) White and Red
(B) Red and Blue
(C) Black and White
(D) Black and Red
Ans:- D
Explanation:-
The color of an object is
largely determined by its diffuse reflection coefficient(kd). Kd is assigned a value between 0.0 and 1.0.
0.0 – for dull surface that absorbs
almost all light
1.0 – for shiny
surface that reflects almost all light.
You
should understand the range of kd
and its meaning very clearly. For colored surfaces,
there are three kd values,
one for red, green and blue.
Let
us consider a polygon with diffuse color(1,0,0). It reflects
all of the red light it is hit with, and absorbs all of the blue and green(because red has a value 1, and green and blue has a
0).
If
this red polygon is hit with a white light it will appear red. If it is hit
with a blue light, or
a green light, or an aqua light it will appear black(as those
lights have no red component). If it is hit with a yellow light or a purple
light it will appear red(as the polygon will reflect
the red component of the light).
The
kd value given in the equation is kd=(0.8,0.4,0)
What
shall be the color of the object if the light used is
blue and magenta?. That is the question.
Let
us consider the first color. Blue light falls on the
object. But the blue component of kd
is 0. It means that color is going to be completely
absorbed by the object and it will appear black. So, when blue light falls on
the object, the object will appear black.
Let
us consider the next color. Magenta light falls on
the object. Magents is a violet-red or purplish-red color. It is midway between red and blue. Since red has a
high kd value, it will get
reflected more and so the color of the object will be
Red.
So,
the color of the object will be Black and Red. The
correct option is D.
59.
The perspective projection matrix, on the view plane z = d where the centre of
projection is the origin (0, 0, 0) shall be
(A) 0 0 0 d
0 0 d 0
0 d 0 0
d 0 0 1
(B) d 0 0 0
0 d 0 0
0 0 d 0
0 0 1 0
(C)
0 0 0 d
0 0 d 0
0 d 0 0
1 0 0 0
(D)
d 0 0 0
0 d 0 0
0 0 d 0
0 0 0 1
Ans:- B
Explanation:-
A
perspective transformation is determined by prescribing a center
of projection and a view plane. The view plane is determined by its view
reference point R0 and view plane normal N.
The
projection transformation as a matrix
PerN,R0 = d0 0 0 0
0 d0 0 0
0 0 d0 0
n1 n2 n3 0
The
plance z = d is parallel, to the xy
plane. Thus the view plane normal vector N is the same as the normal vector K
to the xy plance, that is
N=K. Choosing the view reference
point as R0(0,0,d), we can identify the
parameters
N(n1,n2,n3)
= (0,0,1)
R0(x0,y0,z0)=(0,0,d)
So,
d0
= n1x0 + n2y0 + n3z0 = d
and
so the projection matrix is
PerK,R0 = d 0 0 0
0 d 0 0
0 0 d 0
0 0 1 0
So,
the correct answer is option B. The same problem is solved in the Schaum’s outlines, Computer Graphics book(pg.
no. 138).