Translate a square - 2-d and 3-d transformations, Computer Graphics

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Example1: Translate a square ABCD along with the coordinates as: A(0,0),B(5,0),C(5,5),D(0,5) via 2 units in x-direction and 3 units in y-direction.

Solution: We can show the square here, in matrix form, by using homogeneous coordinates of vertices as:

1628_Translate a square 1.png

The translation factors are, tx=2, ty=3

The transformation matrix for translation:

T_v=

2344_Translate a square 2.png

So new object point coordinates are:

[A'B'C'D'] = [ABCD].T_v

1270_Translate a square 3.png

Hence, A'(x'1,y'1)=(2,3)

B'(x'2,y'2)=(7,3)

C'(x'3,y'3)=(7,8) and

D'(x'4,y'4)=(2,8)

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