2. CSC418 Computer Graphics n Aliasing n Texture mapping

3. Aliasing The physical world is continuous… Computer representations of the physical world are often a discrete sampling of the continuous… “A pixel is a discrete sample of a continuous image” The question is : How densely do we need to sample something continuous to capture its essence accurately?

4. Aliasing

5. Nyquist Theorem: Acontinuous signal can be completely recovered from its samples iff the sampling rate is greater than twice the maximum frequency present in the signal.

6. Aliasing(examples)

9. Aliasing In order to have any hope of accurately reconstructing a function from a periodically sampled version of it, two conditions must be satisfied: n The function must be bandlimited. n The sampling frequency must be at least twice the maximum frequency of the function. Satisfying these conditions will eliminate aliasing.

10. Antialiasing n Prefiltering. n Postfiltering (supersampling).

11. Antialiasing(prefiltering) What is prefiltering?

12. Antialiasing(prefiltering) Prefiltering example

13. Antialiasing(postfiltering) What is postfiltering? Given a sample frequency prefiltering computes a lower frequency signal from the continuous representation. Postfiltering first supersamples the signal in its unfiltered form and then filters out the high frequency from the supersamples.

14. Antialiasing(postfiltering)

16. How should one combine samples? Simply add? Weight average is better! Filter shape = weight values.

17. Antialiasing(postfiltering) Filter shapes Gaussian Wide Gaussian

18. Antialiasing(postfiltering) Is there an ideal filter shape? Box Sinc

19. Antialiasing(postfiltering) How should one supersample?

20. Texture mapping Photographic Textures

21. Texture mapping Photographic Textures

22. Texture mapping How does one establish correspondence? (UV mapping)

23. Texture mapping Projective Textures

24. Texture mapping 3D Textures

25. Texture mapping Bump mapping

26. Texture mapping Reflection mapping

27. Next Lecture Putting it all back together….