3D Translation

In Computer graphics, 3D Translation is a process of moving an object from one position to another in a three dimensional plane.

Consider a point object O has to be moved from one position to another in a 3D plane.

Let

• Initial coordinates of the object O = (X_old, Y_old, Z_old)
• New coordinates of the objectO after translation = (X_new, Y_new, Z_old)
• Translation vector or Shift vector = (T_x, T_y, T_z)

Given a Translation vector (Tx, Ty, Tz)-

• T_x defines the distance the X_old coordinate has to be moved.
• T_y defines the distance the Y_old coordinate has to be moved.
• T_z defines the distance the Z_old coordinate has to be moved.

This translation is achieved by adding the translation coordinates to the old coordinates of the object as-

• X_new= X_old +T_x (This denotes translation towards X axis)
• Y_new= Y_old +T_y (This denotes translation towards Y axis)
• Z_new= Z_old +T_z (This denotes translation towards z axis)

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