**Introduction**

Almost all graphics systems allow the programmer to
define picture that include a variety of transformations. For example, the
programmer is able to magnify a picture so that detail appears more clearly, or
reduce it so that more of the picture is visible. The programmer is also able
to rotate the picture so that he can see it in different angles.

**Two Dimensional transformations**

In this section, we describe the general procedures for
applying translation, rotation, and scaling parameters to reposition and resize
the two dimensional objects.

**Translation**

Translation is a process of changing the position of an
object in a straight-line path from on location to another.

We can translate a two dimensional point by adding
translation distances, t

_{x}and t_{y}, to the original coordinate position (x, y) to move the point to a new position (x', y'), as shown in the figure below
x' = x + t

_{x}
y' = y + t

_{y}
The translation distance pair (t

_{x}, t_{y}) is called a translation vector or shift vector. It is possible to express the translation equations as a single matrix equation by using column vectors to represent coordinate positions and translation vector :_{x}

P = P'
= T =

y
y' t

_{y}
This allows us to write the two dimensional translation
equations in the matrix form : P' = P + T

**Example**

Translate a polygon with coordinates A (2, 5), B(7, 10)
and C(10, 2) by 3 units in x direction and 4 units in y direction.

**Rotation**

A two dimensional rotation is applied to an object by
repositioning it along a circular path in the xy plane. To generate a rotation,
we specify a rotation angle 0 and the position of the rotation point about
which the object is to be rotated.

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