Computer Graphics Presentation Engg.pptx

Computer Graphics PPT

1. Coordinate Transformation in Computer Graphics Understanding Coordinate Systems and Transformations Presenter: Ayan Ali Khan B.Tech Information Technology, 3rd Year

2. Introduction to Coordinate Transformation Definition: Coordinate transformation refers to changing the position, orientation, or scale of objects in a 2D/3D space. Importance: Used in computer graphics for rendering, animation, simulations, and game development. Types of Coordinate Transformations: Translation Rotation Scaling Shearing Reflection

3. Translation Transformation A translation moves an object to a different position on the screen. You can translate a point in 2D by adding translation coordinate ( tx , ty) to the original coordinate X,Y to get the new coordinate X′,Y′.

4. Rotation Transformation In rotation, we rotate the object at particular angle θ theta from its origin. From the following figure, we can see that the point PX,Y is located at angle φ from the horizontal X coordinate with distance r from the origin.

5. Scaling Transformation To change the size of an object, scaling transformation is used. In the scaling process, you either expand or compress the dimensions of the object. Scaling can be achieved by multiplying the original coordinates of the object with the scaling factor to get the desired result.

6. Shearing Transformation A transformation that slants the shape of an object is called the shear transformation. There are two shear transformations  X-Shear  and  Y-Shear . One shifts X coordinates values and other shifts Y coordinate values. However; in both the cases only one coordinate changes its coordinates and other preserves its values. Shearing is also termed as  Skewing .

7. Reflection Transformation

8. Matrix Representation for Combination Transformation Matrix: Each transformation (translation, rotation, scaling) can be represented as a matrix. Translation: T Rotation: R Scaling: S Composite Transformation Formula: M=T × R × S where M is the final transformation matrix.

9. Example: Rotation Followed by Translation

10. Real-World Applications Gaming: Rotating and moving objects in virtual environments. Animation: Scaling and transforming characters or objects. Augmented Reality (AR): Mapping transformations onto real-world surfaces.

11. THANK YOU