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 Sx, Sy, Sz scaling factors.
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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 [Sx, Sy, Sz] So, the new position of the point after applying Scaling operation would be –
Note : If Scaling factor (Sx, Sy, Sz), then, in this case, the 3D object will be Scaled up uniformly in all X, Y, Z direction.
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 Sx, Sy, Sz. Perform Scaling operation operation over the cube.
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 –