Asst. Prof / CA
Transactions are helpful in changing the
object. There are three basic rigid
The derived geometrical transformation is:
The translation is repositioning an object along a straight-line path
from one coordinate location to another coordinate location.
The translation is the rigid body transformation that saves an object
without deformation. A translation moves to a different position on the
X’=X + tx
Y’=Y + ty
we can also write as:
It is the transformation that is used to
reposition one object along the circular path in
the XY plane. We specify a rotation angle TITA
and the portion of the rotation point A and B
about which the object is being rotated to
generate a rotation.
Where R is the rotation matrix
Scaling is the transformation that is used to change the
object’s size. The Operation is carried out by multiplying
the coordinate value(X,Y)with Sx and Sy scaling factors.
X’=X. Sx and Y’=Y. Sy
P’=P . S
Shearing is the transformation used to change the
shape of an existing object in the 2D plane. The size of
the object changes along the x direction as well as the
Reflection is the mirror image of the original object.
In other words, we will say that it is the rotation
operation with 180 degree. In reflection
transformation, the object’s size does not change.
Matrix representation is a method used by
a computer language to store matrices of
more than one dimension in memory. Fortran
and C use different schemes for their native
arrays. Fortran uses “Column Major”, in
which all the elements for a given column are
stored contiguously in memory.
P’=M1 +P +M2
Homogeneous coordinates have a natural
application to computer graphics ; they form a
basis for the projective geometry used
extensively to project a three dimensional
scene onto a two dimensional image plane.
They also unify the treatment of common
graphical transformation and operations.
A number of transformation or sequence of
transformation can be combined into single
one called as composition. The process of
combining is called as concatenation.
Suppose we want to perform rotation about an
arbitrary point, then we can perform it by the
sequence of three transformation.
3. Reverse Translation