Transformation

1. 909’ SENTHUR POLYTECHNIC COLLEGE
NAMDIYUR
DEPARTMENT OF MECHANICAL ENGINEERING
SEMINAR TOPIC
TRANSFORMATION
SUBMITTED BY
BALAMURUGAN. A
( 22216385 )

2. TRANSFORMATION
2D & 3D

3. TRANSLATION
1. Translation
Translation is the simplest form of transformation. It is rigid body
transformation that moves the object without any deformation.
2D translation move the object on x, y plane along straight line
By adding increments in x-axis, y-axis,
3D translation move the object on xyz coordinates
along straight line adding increments in x-axis, y-axis and z-axis,

4. The above equation can be written in matrix
From as
(X’, Y’) = (X, Y) + (tx, ty) or
(X’/Y’) = (X/Y) + (tx/ty)
The homogeneous representation of above
matrix is
X’ 1 0 tx X
Y’ = 0 1 ty Y
1 0 0 1 1

5. P’ = Tt × P
Tt = Transformation matrix for translation
Scaling
Scaling transfoation is used to enlarge or reduce
The size of the object.
Let
(X,Y) => are the initial coordinate values of the object
(X’, Y’) => final coordinate values of the object
Sx => scaling factor along the x-axis
Sy => scaling factor along the y-axis

6. Then x’ = x. Sx and Y’ = y. Sy
In matrix from
X’ Sx 0 X
=
Y’ 0 Sy Y
The above equation is written in homogenous
From as follows.

7. ROTATION
Rotation is the rigid body transformation that
Move the object along the circular path in xy plane or
In xyz coordinate without any deformation
X = r cos ∅
Y = r cos ∅
The above equation is written in homogenous form as follows
X’ = cos o - sin o 0 0 X
Y’ = sin o - cos o 0 0 Y
Z’ = 0 0 1 0 Z
1 = 0 0 0 1 1

8. 😇 THANKS YOU 😇