Numerical Examples of 2d Geometric Transformation- Translation

Problem Statement:

An object is placed with respect to origin on (2,1). Now move the object away from the origin by 2 steps in x and 3 steps in y. What would be new coordinates to the moved object.

S-1 : The old coordinates of the object are x=2 and y =1. Translation coordinate in x direction (tx) = 2 and Translation coordinate in y direction (ty) =3. Lets call the new coordinates as x’ and y’.  

S-2: Since the translated object is moving away from origin , Hence it is a positive translation and new coordinates could be obtained in simple arithmetic as x’=x+tx and y’=y+ty.

S-3: Computer Graphics only deal with matrix calculations because all the transformation would not be as simple as in translation. Translation transformation of a single element at (x,y) coordinate is displayed as follows.

S-4: Just substitute the values of x, y as (2,1) with tx=2 and ty=1. Multiply all the matrices to get the result. This will give you new coordinates (x’,y’) of point (x,y).

S-5: After Multiplication we would get the new element x’=2+2 = 4 and y’=1+3=4. The new element is also displayed in last figure.