Page 81 - DCAP504_Computer Graphics

Computer Graphics

Consider a point coordinate (x, y), represented in the matrix form as,
 x 
P=    
 y 

Let, P’ be the coordinate after shear transformation,
P’=Sh.P
Here, Sh can be either X or Y-shear.
If it is X-shear then,
1  a  x 
P’=      
 
 0 1   y 
 + ayx 
P’=   

 y 
If it is Y-shear then
 1  0  x 
P’=      
 
 b 1   y 
 x 
P’=    
 bx + y 
Consider a rectangle object with point coordinates (0, 0), (2, 0), (2, 2) and (0, 2).
The rectangle undergoes X-shear with the shear factor value 1.
The shear transform matrix for X-shear is given as,

1  a 1  1
=
Sh x    =    

 0 1   0 1 
Here, the value of the shear factor, a=1.
After multiplying the point coordinates of the rectangle with the X-shear
transform matrix individually we obtain the following coordinate points that
define the rectangle after X-shear transform are (0, 0), (2, 0), (4, 2) and (2, 2).
If the value of a=-1, then the X-shear transform matrix is given as,
1 −1 
Sh x    
=
 0 1 
Then the value of the rectangle after X-shear transform are (0, 0), (2, 0), (0, 2)
and (-2, 2).

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