Page 92 - DCAP504_Computer Graphics

Unit 6: 2-D Transformation

6.7 Self Assessment

1. State whether the following statements are true or false:
(a) Translation transformation is used to move the object in the X and Y directions of the 2-D
space.
(b) The object is scaled in the X direction of the 2-D graph, by adding all the X coordinate points
of the object by a scaling factor Sx.

cos θ − sin θ  0
 
 sin θ cos θ  0
 0 0 1 
(c) The counterclockwise rotation matrix used for rotation transformation is   .
(d) The shear transformation makes the object to slant either in X direction or Y direction and it
is called Y-shear and X-shear respectively.
(e) The basic transformations in 2-D matrices can be converted into matrices of size 3 x 3 using
homogeneous coordinate system.
(f) Scaling and shearing transformation can be combined using homogeneous coordinate
system.
2. Fill in the blanks:
(a) The translation matrix is ............. to the point coordinate matrix of the object.
(b) ..............transformation is done to resize the object.
(c) The X-shear transformation matrix is represented in matrix form as..................
(d) If (x, y) is a point coordinate then it is represented in homogeneous coordinate system
as.................
(e) The inverse transformation matrix of scaling is....................
3. Select a suitable choice for every question:
(a) Identify the translation matrix.

0 x d 
   
(i)  0 y d 

 0 0 
   
(ii)  x d y d 
d x 0 
   
(iii)  0 y d 

dy dx 
   
(iv)  0 0 

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