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TRANSLATION
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
▪ 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.
▪ Tz 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 = 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)
▪ 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
▪ 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
 Cg   3 d translation
 Cg   3 d translation
 Cg   3 d translation
 Cg   3 d translation

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Cg 3 d 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