Computer Graphics

Trivial Quiz 2

For each question circle ONE answer.

1. The two end-points of a line segment in 3D are (1,2,1) and (2,5,8). P(t) = (x(t),y(t),z(t)) is the parametric equation of the line segment, for parameter t in the range 0 to 1. In this case
:
(a) P(t) = (2+t, 5+2t, 8+t)
(b) P(t) = (1+t,2+3t,1+7t)
(c) P(t) = (8+3t,2+5t,1+t)
(d) P(t) = (1+2t,2+t,5+8t)
(e) P(t) = (1+8t,2+5t,1+2t)

2. The following sequence of points are given describing a polygon in 3D: (0,2,0), (1,2,0), (1,2,1). What is the "front facing normal vector" for the plane on which this polygon lies?

(a) (1,0,1)
(b) (0,0,1)
(c) (0,0,-1)
(d) (0,-1,0)
(e) (0,1,0)

3. The Centre of Projection is at point (0,0,-1) and the viewplane is the XY plane (i.e., the View Plane Distance is 0). What is the projection of the point (16,8,7) on the viewplane?

(a) (2,1,7)
(b) (16,8,0)
(c) (2,1,0)
(d) (1,2,1)
(e) (8,7,0)

4. The wedge shape pictured in Figure below is centred at the origin, with the axes aligned shown in the diagram, which is a right-handed coordinate system with Y going into the page. The sides of (1) that cannot be seen are coloured white. For each of the cases (2), (3) and (4) give viewing parameters sufficient to obtain the view shown.

View number	VRP	VPN	VUV	COP
(2)				
(a)		(0,0,0)	(0,1,0)	(0,0,1)	(0,0,-1)
(b)		(0,0,0)	(1,0,0)	(1,1,1)	(1,0,-2)
(c)		(0,0,1)	(0,0,0)	(0,1,0)	(0,0,-1)
(d)		(0,0,-1)(0,0,1)	(0,1,0)	(0,0,0)
(e)		(0,0,0)	(0,1,1)	(1,0,-1)(-1,0,0)
				
(3)				
(a)		(0,0,0)	(1,0,0)	(1,1,1)	(0,1,-1)
(b)		(0,0,0)	(0,0,-1)(-1,0,0)(0,0,-1)
(c)		(0,0,0)	(0,-1,0)(1,0,1)	(0,1,1)
(d)		(0,1,0)	(0,-1,0)(1,0,1)	(0,1,1)
(e)		(1,0,0)	(1,0,0)	(0,1,0)	(0,0,-1.5)
				
(4)				
(a)		(0,1,1)	(1,1,1)	(1,0,2.8)(0,0,-1)
(b)		(0,1,1)	(1,0.5,2)(0,-1,1.8)(1,1,1)
(c)		(0,0,0)	(1,0,0)	(1,1,1)	(0,1,-1)
(d)		(0,0,0)	(1,0,0)	(1,0,1)	(0,0,-1)
(e)		(0,0,0)	(-1,0,0)(0,1,0)	(0,0,-1)

5. The following camera parameters are given: VRP = (0,0,0), VPN = (0,2,0), VUV = (0,0,4). The point (1,1,1) in World Coordinates is which point when described in Viewing Coordinates?

(a) (-1,0,1)
(b) (1,1,1)
(c) (-1,-1,-1)
(d) (0,0,0)
(e) (0,1,1)

6. The clipping region in canonical viewing space is defined by the boundaries: x = (z+1), x = -(z+1), y = (z+1), y = -(z+1), z = 1, z = 5. Which one of the following lines can be trivially rejected?

(a) (3,1,1) to (5,1,3)
(b) (3,1,1) to (1,5,3)
(c) (1,2,3) to (3,2,1)
(d) (-1,-4,-3) to (-1,-4,-1)
(e) (0,0,0) to (0,0,10)

7. Clipping must generally be done before projection, because:

(a) It is arithmetically easier.
(b) Otherwise there can be a divide by zero.
(c) An object that is too far away from the COP would be projected upside down.
(d) An object that is behind the viewport would be larger than the COP behind the window boundaries.
(e) An object that is behind and in front of the COP would otherwise be projected incorrectly.