This document discusses two-dimensional geometry transformations using shear. It defines shear as a transformation that distorts the shape of an object. There are two types of shear transformations: X shear, which preserves Y coordinates but changes X coordinates, and Y shear, which preserves X coordinates but changes Y coordinates. The document provides an example of applying both X and Y shear to transform the coordinates of a rectangle.

1. SUBJECT : COMPUTERAIDED DESIGN
(2161903 )
Active Learning assignment on:-
“Two-Dimensional Geometry
Transformation In Shear ”
Prepared by:-Savsani Happy (150123119045)
1

2. Shear
Transformation that distorts the shape of an object
is called shear transformation.
Two shearing transformation used:
Shift X co-ordinates values
Shift Y co-ordinates values
2

3. X shear
y
x
(0,1) (1,1)
(1,0)(0,0)
y
x
(2,1) (3,1)
(1,0)(0,0)
shx=2










100
010
01 xsh
yy
yshxx x


'
'
 Preserve Y coordinates but change the X coordinates values
3

4. Y shear
 Preserve X coordinates but change the Y coordinates values
x’ = x
y’ = y + Shy . x
y
x
(0,1) (1,1)
(1,0)(0,0)
y
x
(0,1)
(1,2)
(1,1)
(0,0)










100
01
001
ysh
4

5. Example :-
A rectangle is formed by four points: A(25,25), B(25,15),
C(75,125), and D(75,25). Calculate the coordinates of
transformed rectangle if:
(i) It is changed by shear and2xsh 3ysh
1. Shear factor 2xsh
•The shear matrix is,














100
010
0
x
sh1
5

6. The sheared points are :










1111
''''
''''
4321
4321
yyyy
xxxx
    PshP x .' 



































1
.
100
010
0
x
sh1
1
'
'
y
x
y
x
*



































1111
2512512525
75752525
.
100
010
021
1
'
'
y
x
*
6

7. 




















1111
2512512525
12532527575
1
'
'
y
x
*
 The transformed coordinates are :
 A(75,25)
 B(275,125)
 C(325,125)
 D(125,25)
7

8. 2. Shear factor
•The shear matrix is,














100
01sh
001
y
3ysh
The sheared points are :










1111
''''
''''
4321
4321
yyyy
xxxx
    PshP y .' 
8

9. 


































1
.
100
01sh
001
1
'
'
y y
x
y
x
*



































1111
2512512525
75752525
.
100
013
001
1
'
'
y
x
*





















1111
250350200100
12532527575
1
'
'
y
x
*
 The transformed coordinates are :
 A(75,100)
 B(275,200)
 C(325,350)
 D(125,250)
9

10. 10