Page 74 - DCAP504_Computer Graphics

Unit 6: 2-D Transformation

The figure 6.3 depicts the translation transformation in a 2-D space.

Figure 6.3: Translation Transformation in a 2-D Space

(2, 5)

6.1.2 Scaling Transformation
Scaling transformation is done to resize the object, i.e. the dimension of the object is changed. The object
is scaled in the X direction of the 2-D graph, by multiplying all the X coordinate points of the object by a
scaling factor Sx. Similarly, the Y coordinates of all the points of the object are multiplied by the scaling
factor Sy. These scaling factor values define the amount by which the object has to be scaled in X and Y
direction.

You can use same or different scaling factor values for X and Y coordinates, while
scaling the object.
1. If you use same scaling factor value for X and Y coordinates, uniform scaling of the
object takes place in X and Y directions.

2. If you use different scaling factor values, then uneven scaling takes place in X and Y
directions.

The following is a simple matrix multiplication carried out to find the scaled coordinate (x’, y’).
 S x 0   x 
Equation 6.1 is the product of scaling matrix   and point coordinate matrix    


 0 y S   y 
Sx 0   x 
( x ,' y )' =        
 0 Sy   y 


=  Sx x + 0   

 0 + Sy y 

x( ) ' y , ' =  Sx x   …………………….. (Eq.6.1)


 Sy y 

LOVELY PROFESSIONAL UNIVERSITY 67