2D-3D Transformations in Computer Aided Design.

2. Transformations…
In practical problems, the components of a vector are
known in one coordinate system but it is necessary to
find them in some other coordinate system.
The relationship between the components in one
coordinate system and the components in a second
coordinate system are called the transformation
equations.

3. Transformations…
• No of Modelling software packages are available like CATIA, Uni-graphics, CREO,
Solidworks.
• All these software's are used to create part modelling.
• While designing any component alterations are needed and it can be possible with
computers easily.
• Drawings created in the software has a database.
• This database can be modified by some mathematical operations called Transformation
A geometric transformation is an operation that modifies its shape, size, position,
orientation etc. with respect to its current configuration.

4. Transformations…
Transformation is classified as-
1. Translation- Moving an object from one location to another location.
2. Rotation- To create entities arranged in circular arrays.
3. Scaling- Alters the size of object.
4. Reflection- To mirror the object.
5. Shear- This transformation causes the image to slant.
All softwares are built with matrix multiplication formats, which helps for
transformations.

5. 2D-Transformation
When this transformation is carried out in 2/3 dimensions then it is called 2D/3D
transformation.
• 2D object is represented by points and lines that join them
• Transformations can be applied only to the points defining the lines
• A point (x, y) is represented by a 2x1 column vector, so we can represent 2D
transformations by using 2x2 matrices:

6. Translation
This program is used to
shift/move any entity ie.
Point, line rectangle.

10. 3D-Transformation

11. 3D-Transformation
 Translation Transformation-
 Scaling Transformation-

12. 3D-Transformation
Rotation about X- Rotation about Y-

13. 3D-Transformation
Rotation about Z-

14. Thank You…