3D Scaling

In computer graphics, scaling is a process of modifying or altering the size of objects.

• Scaling may be used to increase or reduce the size of object.
• Scaling subjects the coordinate points of the original object to change.
• Scaling factor determines whether the object size is to be increased or reduced.
• If scaling factor > 1, then the object size is increased.
• If scaling factor < 1, then the object size is reduced.

Consider a point object O has to be scaled in a 3D plane. Let:

• Initial coordinates of the object O = (X_old, Y_old,Z_old)
• Scaling factor for X-axis = S_x
• Scaling factor for Y-axis = S_y
• Scaling factor for Z-axis = S_z
• New coordinates of the object O after scaling = (X_new, Y_new, Z_new)

This scaling is achieved by using the following scaling equations

• X_new = X_old x S_x
• Y_new = Y_old x S_y
• Z_new = Z_old x S_z

In Matrix form, the above scaling equations may be represented as-