## 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

### 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

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