# What are the various transformations possible in 2-D? Explain any 3 of them.

by Dinesh Thakur Category: Two Dimensional Transformations

1. Translation: A translation is applied to an object by repositioning it along a straight line path from one coordinate position to another. We translate a 2-D point by adding translation distances tx & ty, to the original coordinate position ( x, y) to move the point to a new position (x? , y?)
X? = x + tx , y? = y + ty.

2. Rotation: A 2-D rotation is applied to an object by repositioning it along a circular path in the xy plane. To generate a rotation, we specify a rotation angle ? and the position (xr , yr) of the rotation point about which the object is to be rotated.
P1 = R . P
Where the rotation matrix is R = cos? - sin ? sin ? cos?

3. Scaling: A scaling transformation alters the size of a.n object. This operation can be carried out for polygons by multiplying the coordinate values (x,y) of each vertex by scaling factors sx & sy to produce the transformed coordinates (x? , y?):
x1 = x.sx , y1 = y.sy

4.Reflection: It is also called as mirror or mirror image . It can be either about x axis or y axis. The object is rotated about 180 degree. Reflection can be done about line.

5. Shearing : It is change of shape of object. It can be in x or y or both directions. Dinesh Thakur holds an B.SC (Computer Science), MCSE, MCDBA, CCNA, CCNP, A+, SCJP certifications. Dinesh authors the hugely popular blog. Where he writes how-to guides around Computer fundamental , computer software, Computer programming, and web apps. For any type of query or something that you think is missing, please feel free to Contact us.

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