1. CS148: Introduction to Computer Graphics Final Review Session

2. CS148 Final Review Winter 2008 Outline Final Info Review of Topics Mattes and Compositing Sampling and Filtering Compression Programmable Shading Cameras Rendering Modeling

3. CS148 Final Review Winter 2008 Final Exam Info Time: Thursday March 20, 12:15 Location: Meyer Forum 112 Duration: 3 hours Closed book Consists of a few (4 or 5) multi-part questions Emphasis on the second half of the course, but don’t forget the first half

4. CS148 Final Review Winter 2008 Mattes and Compositing α = Coverage = Area = Opacity = 1 – Transparency Standard Compositing Equation C = α * C F + (1 – α) * C B Premultiplied α: C’ = αC = (αr, αg, αb, α) α

5. CS148 Final Review Winter 2008 Porter-Duff Compositing Algebra

6. CS148 Final Review Winter 2008 Green Screen Matte Extraction Given: C – Observed color C B – Backing color Compute: C F = (α F R F, α F G F, α F B F, α F ) Compositing Equation: C = C F + (1 – α F )C B 3 Equations, 4 Unknowns – must make some assumptions

7. CS148 Final Review Winter 2008 The Horrors of Poor Sampling

8. CS148 Final Review Winter 2008 The Horrors of Poor Sampling Retort sequence by Don Mitchell

9. CS148 Final Review Winter 2008 Nyquist Frequency Nyquist Frequency – ½ the sampling frequency A periodic signal with a frequency above the Nyquist frequency cannot be distinguished from a periodic signal below the Nyquist frequency These indistinguishable signals are called aliases

10. CS148 Final Review Winter 2008 Fourier Transform You can express any (periodic) signal as a sum of sinusoids

11. CS148 Final Review Winter 2008 Fourier Transform Spatial Domain f(x,y) Frequency Domain F(ω x, ω y ) Fourier Transform Inverse Fourier Transform ConvolutionMultiplication MultiplicationConvolution SincBox

12. CS148 Final Review Winter 2008 Convolution Convolution – integration/summation of translated filter with signal

13. CS148 Final Review Winter 2008 Fourier Transform

14. CS148 Final Review Winter 2008 Low Pass Filter

15. CS148 Final Review Winter 2008 High Pass Filter

16. CS148 Final Review Winter 2008 Band Pass Filter

17. CS148 Final Review Winter 2008 Sampling – Spatial Domain

18. CS148 Final Review Winter 2008 Sampling – Frequency Domain

19. CS148 Final Review Winter 2008 Reconstruction – Frequency Domain

20. CS148 Final Review Winter 2008 Reconstruction – Spatial Domain

21. CS148 Final Review Winter 2008 Undersampling – Frequency Domain

22. CS148 Final Review Winter 2008 Compression Kolmogorov Complexity – smallest program to generate data Lossless Coding Run length coding – exploit obvious redundancy Huffman Coding – variable length code, highly probable characters -> shorter codes Transform Coding – perform invertible transform on data to make it more amenable to compression (applies to lossless and lossy!)

23. CS148 Final Review Winter 2008 Lossy Image Compression (JPEG) Image Discrete Cosine Transform Transformed Image Quantization (Lossy Step) Reorder + Coding Compressed Data Stream JPEG2000 is similar but uses the wavelet transform. Exploit human perception – quantize high frequencies more heavily since we are less sensitive to them.

24. CS148 Final Review Winter 2008 Wavelet Transform Just another invertible transform (expresses signal in different basis) Generated in steps by calculating smoothed (approximate) values and detail (corrective) values Resulting basis functions have compact support – they are only non-zero over a limited range – error in coefficient causes localized error

25. CS148 Final Review Winter 2008 Wavelet Transform 68595566 6.250-200 Full Transform High Resolution Details Medium Resolution Details Low Resolution Details Average Value -.5.75

26. CS148 Final Review Winter 2008 Rendering Pipeline Vertex Data Primitive Data Tessellation Vertex Processing Geometry Processing Pixel Processing Texture Sampler Textured Surface Pixel Rendering

27. CS148 Final Review Winter 2008 Example Vertex Shader Vertex Shader

28. CS148 Final Review Winter 2008 Example Pixel Shader Pixel Shader

29. CS148 Final Review Winter 2008 GPGPU CPU Thread synchronization Bandwidth limitations Scheduling overhead Small number of cores GPU All threads independent Message passing is not allowed Resource allocation is done by GPU Many cores available (12 to 48 typical)

30. CS148 Final Review Winter 2008 GPGPU Applications Beyond triangle rendering Collision detection Fluid simulation Physics Raytracing Video compression Beyond graphics Folding@Home Speech Recognition Partial differential equation solvers Fourier transform

31. CS148 Final Review Winter 2008 Pinhole Camera film f x’ (x,z) pinhole Field of view

32. CS148 Final Review Winter 2008 Pinhole Camera film f x’ (x,z) pinhole Field of view

33. CS148 Final Review Winter 2008 Homogeneous Coordinates

34. CS148 Final Review Winter 2008 Perspective Transform

35. CS148 Final Review Winter 2008 Orthographic Projection

36. CS148 Final Review Winter 2008 Field of View and Focal Length

37. CS148 Final Review Winter 2008 Depth of Field

38. CS148 Final Review Winter 2008 Circle of Confusion

39. CS148 Final Review Winter 2008 Types of Reflection Mirror Ideal reflection Reflection law Diffuse Matte Lambert’s Law Specular Highlights and gloss Microfacet model

40. CS148 Final Review Winter 2008 Lambert’s Law

41. CS148 Final Review Winter 2008 Ideal Reflection

42. CS148 Final Review Winter 2008 Microfacets

43. CS148 Final Review Winter 2008 Modeling Representations Dense Polygonal Meshes Bicubic surfaces Subdivision Surfaces Operations Instancing Transformation – linear and non-linear Compression, simplification Deform, skin, morph, animate Smooth Set operations

44. CS148 Final Review Winter 2008 Bezier Curve

45. CS148 Final Review Winter 2008 Subdivision Surfaces Loop subdivision algorithm Extraordinary points