HOMOGENEOUS CO-ORDINATES IN COMPUTER GRAPHICS PPT

In mathematics, homogeneous coordinates or projective coordinates. This ppt is about the use of coordinates in graphics

1. HOMOGENEOUS CO-ORDINATES Presented By: Ahtesham Ullah Khan CS-3 rd yr 1604610013

2. HOMOGENEOUS COORDINATES In mathematics,  homogeneous coordinates  or  projective coordinates , introduced by  August Ferdinand Möbius  in his 1827 . They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Homogeneous coordinates have a range of applications, including  computer graphics  and 3D  computer vision , where they allow  affine transformations  and, in general,  projective transformations  to be easily represented by a matrix.   If the homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point.

3. Why we need Homogeneous Coordinates? One of the many purposes of using homogeneous coordinates is to capture the concept of infinity.  If we don’t use homogeneous coordinates, it would be difficult to design certain classes of very useful curves and surfaces. These curves and surfaces are very crucial in developing algorithms in computer vision, graphics, CAD, etc. We have seen that basic transformations can be expressed in matrix form. But many graphic application involve sequences of geometric transformations. Hence we need a general form of matrix to represent such  transformations.

4. OPERATIONS:- Translation Shearing Rotation Reflection

5. TRANSLATION

6. X Y Z TRANSLATION

7. ROTATION

8. COORDINATE AXIS ROTATION

9. X-AXIS ROTATION

10. X-AXIS ROTATION Y Z X

11. Y-AXIS ROTATION

12. Y-AXIS ROTATION Y Z X

13. Z-AXIS ROTATION

14. Z-AXIS ROTATION Y Z X

15. SCALING

16. SCALING

17. SCALING Y Z X

18. REFLECTION

19. REFLECTION

20. REFLECTION

21. SHEARING

22. SHEARING

23. SHEARING

24. THANK YOU