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Computer Graphics
To move a point P that is located at (3, 4, 5) to a new location with distance (2, 4,
6) units.
Given, P= [3, 4, 5, 1]
Dx=2, Dy=4, Dy=6
We apply the translation transformation and obtain the result as
Hence the result is the point P being shifted to a new position P’.
8.2.2 Scaling
The scaling in the x, y and z directions can be obtained by using the transformation matrix:
Sx 0 0 0
S[x,y,z] = 0 Sy 0 0
0 0 Sz 0
0 0 0 1
In the x, y and z directions the scaling factors S x, S y and S z are applied as shown in the figure 8.9. The
letter S denotes the basic scaling matrix.
Figure 8.9 : 3-D Scaling
The following sequences of transformations occur in the scaling process for a fixed point:
1. The fixed point is translated to origin
2. The object is scaled
3. The fixed point is translated to its original position
8.2.3 Rotation
The rotation transformations in 3-D plane can be designated around any line in space. This is not true in
the case of 2-D rotations. So, an axis of rotation is specified for a 3-D rotation. The object rotates along
the angle of rotation.
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