Types of Transformations in Computer Graphics

Transformation

Transformation can be defined as repositioning of coordinates, size or orientation of an object. There are various types of transformations namely translation, rotation scaling, etc. A transformation can be 2D and 3D. In this, We will study about 2D transformation that forms using (x,y) coordinates

Types of Transformations

In computer graphics, there are various types of transformation :

Translation
Rotation
Scaling
Reflection
Shearing

Translation

A translation is a repositioning of an object along a straight line by adding a translation factor to the original coordinates of the given object.
A translation factor is also known as the translation vector.
Suppose, (x,y) is a position of an object. (t_x,t_y) is a translation vector that to be added to the given coordinate (x,y). After adding them, the object would be placed at a new coordinate.

x’=x+t_x ,

y’=y+t_y

Rotation

Rotation can be defined as moving an object in a circular path at a given angle theta. if there is a positive angle, it would rotate in anticlockwise whereas if it appears to a negative angle, the object would rotate in clockwise. The point at which an object about to rotate is known as a pivot point.

x’= x cosθ – y sinθ

y’= x sinθ + y cosθ

Scaling

Scaling is a redefining the size of an object or changing the size of an object by multiplying scaling factor to it.
x’ = x*S_{x ,}

y’=y.S_y

Reflection

Reflection has nothing to do with size, it is a repositioning of an object relative to xy quadrants that produce a mirror image.

Shear

Shearing is a process of slanting the edges of an object. it can be of two types x shear and y shear
In x-shear, we don’t touch y-coordinates, but changes are made to x coordinate which produces a  right or left tilted object
In y shear, we don’t touch x coordinate, instead, changes are made to x coordinate which produces a right or left tilted object