## Transformation

The process of changing of sizes, orientations or positions of objects by mathematical operation is called

Transformations are of two types:

- Geometric Transformation
- Coordinate Transformation

### Geometric Transformation:

It is a type of transformation in which an object itself is transformed relative to stationary coordinate system.

### Coordinate Transformation:

It is a type of transformation in which the object is held stationary while the coordinate system is transformed relative to the object.

### Translation:

Translation is a process of changing the position of an object.

Let P be an object point with the co-ordinate(x, y). We wish to move this point P to new position say P' having the coordinate (x', y').

Notice here that, P has been moved by some quantity in x direction as well as y direction. Let t_{x}, t_{y } be the quantities by which we have moved in x and y directions respectively.

Thus we can write,

x'=x+t_{x}

y'=y+t_{y}

The quantities tx, ty are called as translation vectors. We can represent the equation in the matrix form.

### Column Major Matrix:

New Object Matrix = Translation Matrix * Previously Object Matrix

### Row Major Matrix:

New Object Matrix = Previously Object Matrix * Translation Matrix