Computer Graphics

1. Computer Graphics Lecture 9 Antialiasing, Texture Mapping

2. Today • Texture mapping • Common texture coordinates mapping • Texture coordinates • Antialiasing • Antialiasing-textures 2

3. Texture Mapping : Why needed? • We don't want to represent all this detail with colour / geometry

4. Texture mapping. • Method of improving surface appearance by adding details on surface. • Done at the rasterization stage 4

5. Photo-textures

6. Interpolating the uv coordinates u1 v1 Again, we use baricentric Coordinates u= α u1 + β u2 + γ u3 v = α v1 + β v2 + γ v3 Or scan conversion u3 v3 u2 v2 u1 v1 u2 v2

7. What will the textured triangle look like?

8. Interpolation - What Goes Wrong? • Linear interpolation in screen space: texture source what we get| what we want

9. Why does it happen? • Uniform steps on the image plane does not correspond to uniform steps along the edge

10. How do we deal with it? • Use hyperbolic interpolation • (u,v) cannot be linearly interpolated, but 1/w and (u/w, v/w) can • w is the last component after the canonical view transformation • A w is computed for every 3D point

11. Texture Mapping Examples • Linear interpolation vs. Hyperbolic interpolation • Two triangles per square

12. In what case hyperbolic interpolation is essential? 1. ? 2. ?

13. Common Texture Coordinate Mappings • Orthogonal • Cylindrical • Spherical

14. Texture Mapping & Illumination Texture mapping can be used to alter some or allof the constants in the illumination equation: – pixel color, diffuse color

15. Today • Texture mapping • Common texture coordinates mapping • Texture coordinates • Antialiasing • Antialiasing textures 15

16. Anti-aliasing • Aliasing: distortion artifacts produced when representing a high-resolution signal at a lower resolution. • Anti-aliasing : techniques to remove aliasing Aliased polygons (jagged edges)‏ Anti-aliased polygons 16

17. Nyquist Limit • The signal frequency (fsignal) should be no greater than half the sample frequency (fsample) • fsignal < 0.5 fsample • In the top, fsignal = 0.8 fsample -> cannot reconstruct the original signal • In the bottom fsignal =0.5 fsample -> the original signal can be reconstructed by slightly increasing the sampling rate

18. Screen-based Anti-aliasing • Each pixel is subdivided (sub-sampled) into n regions, and each sub-pixel has a color; • Compute the average color value 18

19. Accumulation Buffer (A-Buffer)‏ • Use a buffer that has the same resolution as the original image • To obtain a 2x2 sampling of a scene, 4 images are made by shifting the buffer horizontally/vertically for half a pixel • The results are accumulated and the final results are obtained by averaging • Various sampling schemes are available Pixel center Subsampled point

20. Different Sampling Schemes

22. Accumulation Buffer (A-Buffer)‏ • The lighting computation is usually done only once per vertex • Not doing the lighting computation at each sample point • The A-buffer’s focus is on the edge anti-aliasing • Also useful for rendering transparent objects, motion blur (will be covered later in the course) Edges

23. Stochastic Sampling • A scene can be produced of objects that are arbitrarily small • A regular pattern of sampling will always exhibit some sort of aliasing • By irregular sampling, the higher frequencies appear in the image as noise rather than aliases • Humans are more sensitive to aliases than noise

24. Stochastic Sampling • One approach to solve this is to randomly sample over the pixels • Jittering : subdivide into n regions of equal size and randomly sample inside each region • Compute the colour at the sample and average • Can precompute a table and recycle it or simply jitter on the fly

25. Comparison

26. Today • Texture mapping • Common texture coordinates mapping • Texture coordinates • Antialiasing • Antialiasing textures 26

27. Aliasing of textures Happens when the camera is zoomed too much into the textured surface (magnification)‏ Several texels (pixels of the texture) covering a pixel’s cell (minification)‏ 27

28. Texture Magnification • Zooming too much into a surface with a texture • One texel covering many pixels 28

29. Bilinear Interpolation • Mapping the pixel centre to the uv coordinates • Computing the pixel colour by interpolating the surrounding texel values 29

30. Bilinear Interpolation - 2 • For (pu, pv), compute its (u,v) coordinates by barycentric coordinates • u = pu – (int)pu, v = pv - (int)pv • xl= pu, xr = pu +1, yb= pv, yt= pv +1, • (pu, pv) : the pixel centre mapped into the texture space • b(pu,pv) : the colour at point pu, pv • t(x,y) : the texel colour at (x,y) • u = pu – (int)pu, v = pv - (int)pv

31. Texture MinificationWhich texture will cause more aliasing when mapped onto the floor?

32. Texture Minification • Many texels covering a pixel’s cell • Results in aliasing (remember Nyquist limit)‏ • The artifacts are even more noticeable when the surface moves • Solution • Mipmapping 32

33. MIP map Multum In Parvo = Many things in a small place Produce a texture of multiple resolutions Switch the resolution according to the number of texels in one pixel Select a level that the ratio of the texture and the pixel is 1:1 33

34. Selecting the resolution in Mipmap Map the pixel corners to the texture space Find the resolution that roughly covers the mapped quadrilateral Apply a bilinear interpolation in that resolution, Or find the two surrounding resolutions and apply a trilinear interpolation (also along the resolution axis)‏ 34

35. Texture Minification • Multiple textures in a single pixel • Solution: • Nearest neighbour Bilinear blending Mipmapping 35

36. Readings • Chapter 5.1-2 of Real-Time Rendering Second edition • http://books.google.co.uk/books?id=mOKEfBTw4x0C&printsec=frontcover&source=gbs_v2_summary_r&cad=0#v=onepage&q=&f=false • “Hyperbolic Interpolation” IEEE Computer Graphics and Applications, vol12, no.4, 89-94, 1992