# Computer Graphics – 3D Scaling Transformation

**Prerequisite: **Computer Graphics – 3D Translation Transformation

**Scaling Transformation :**

It is performed to resize the 3D-object that is the dimension of the object can be scaled(alter) in any of the x, y, z direction through S_{x}, S_{y}, S_{z} scaling factors.

**Matrix representation of Scaling transformation Condition :**

The following kind of sequences occur while performing the scaling transformations on a fixed point –

- The fixed point is translated to the origin.
- The object is scaled.
- The fixed point is translated to its original position.

Let a point in 3D space is P(x, y, z) over which we want to apply Scaling Transformation operation and we are given with Scaling factor [S_{x}, S_{y}, S_{z}] So, the new position of the point after applying Scaling operation would be –

**Note : **If Scaling factor (S_{x}, S_{y}, S_{z}), then, in this case, the 3D object will be Scaled up uniformly in all X, Y, Z direction.

**Problem :**

Consider the above problem where a cube” OABCDEFG” is given O(0, 0, 0, ), A(0, 4, 0), B(0, 4, 4), C(4, 4, 0), D(4, 4, 4), E(4, 0, 0), F(0, 0, 4), G (4, 0, 4) and we are given with Scaling factor S_{x}, S_{y}, S_{z}. Perform Scaling operation operation over the cube.

**Solution :**

We are asked to perform the **Scaling transformation** over the given below 3D object **Fig.1:**

Now, applying the Matrix Scaling transformation condition we get –

After performing the Scaling Transformation successfully the Fig.1 will look like as below Fig.2 –