# Computer Graphics – 3D Translation Transformation

**3-D Transformation :**

3-D Transformation is the process of manipulating the view of a three-D object with respect to its original position by modifying its physical attributes through various methods of transformation like Translation, Scaling, Rotation, Shear, etc.

**Properties of 3-D Transformation :**

- Lines are preserved,
- Parallelism is preserved,
- Proportional distances are preserved.

**Types of Transformations :**

- Translation
- Scaling
- Rotation
- Shear
- Reflection

**Translation :**

It is the process of changing the relative location of a 3-D object with respect to the original position by changing its coordinates. Translation transformation matrix in the 3-D image is shown as –

Where D_{x}, D_{y}, D_{z} are the Translation distances, let a point in 3D space is P(x, y, z) over which we want to apply Translation Transformation operation and we are given with translation distance [D_{x}, D_{y}, D_{z}] So, new position of the point after applying translation operation would be –

**Problem : **Perform translation transformation on the following figure where the given translation distances are D_{x} = 2, D_{y} = 4, D_{z} = 6.

**Solution :** On applying Translation Transformation we get corresponding points –

After performing **translation transformation** over the** Fig.1**, it will look like as below –