Translation moves an object from one position to another in 3D space by adding a translation vector (Tx, Ty, Tz) to the original coordinates (Xold, Yold, Zold). The new coordinates (Xnew, Ynew, Znew) are calculated by adding the corresponding component of the translation vector to each original coordinate. Translation can also be represented using matrix multiplication, where a translation matrix T is multiplied by the original position vector P to yield the new position P'.

1. TRANSLATION

2. TRANSLATION:-
▪ Initial coordinates of the object O =
(Xold, Yold, Zold)
▪ New coordinates of the object O after
translation = (Xnew, Ynew, Znew)
▪ 3D Translation is a process moving
an object from one position to another in a
three dimensional plane

3. ▪ Translation vector or Shift vector = (Tx,
Ty, Tz)
Translation vector (Tx, Ty, Tz)
▪ Tx defines the distance the X old
coordinate has to be moved.
▪ Ty defines the distance the Y old
coordinate has to be moved.

4. ▪ Tz defines the distance the Z old
coordinate has to be moved.

5. This translation is achieved by adding the
translation coordinates to the old coordinates of
the object as
▪ X new = Xold + Tx (This denotes
translation towards X axis)
▪ Y new = Yold + Ty (This denotes
translation towards Y axis)
▪ Z new = Zold + Tz (This denotes
translation towards Z axis)

6. ▪ In Matrix form, the above translation
equations may be represented as
X New = X old + Tx
Y new = Y old + Ty
Z new = Z old + Tz

7. ▪ In a three-dimensional homogeneous
coordinate representation, a point is translated
from position P = (x, y, z) to position P' = (x', y', z')
with the matrix operation
Formula:-
P' = P.T