1. CS 445 / 645 Introduction to Computer Graphics Lecture 24 Final Exam Prep Lecture 24 Final Exam Prep

2. Final Exam Thursday, December 12 th from 7 – 10 p.m. Room OLS 011Room OLS 011 You may use one sheet of notes (8.5 x 11’’) You can write on both sides of paperYou can write on both sides of paper Not everything from semester will be on test Thursday, December 12 th from 7 – 10 p.m. Room OLS 011Room OLS 011 You may use one sheet of notes (8.5 x 11’’) You can write on both sides of paperYou can write on both sides of paper Not everything from semester will be on test

3. Pre-Midterm Material Angel Chapter 4Chapter 4 Chapter 5Chapter 5 Appendix BAppendix B Appendix CAppendix C OpenGL Red Book Chapter 1 - 4Chapter 1 - 4Angel Chapter 4Chapter 4 Chapter 5Chapter 5 Appendix BAppendix B Appendix CAppendix C OpenGL Red Book Chapter 1 - 4Chapter 1 - 4

4. Material Since Midterm Angel Color: 1.4, 2.5, 7.4.5, 8.13Color: 1.4, 2.5, 7.4.5, 8.13 Lighting: 6 (all), 13.1 – 13.5Lighting: 6 (all), 13.1 – 13.5 Texture Maps and Antialiasing: 7.6 – 7.11, 8.12Texture Maps and Antialiasing: 7.6 – 7.11, 8.12 Visibility: 5.6, 8.8, 9.10.3 – 9.10.4Visibility: 5.6, 8.8, 9.10.3 – 9.10.4 Rotations: 4.10 – 4.11Rotations: 4.10 – 4.11 Curves: 10.1 – 10.10Curves: 10.1 – 10.10 Red Book pp. 233 - 242pp. 233 - 242 Chapter 9Chapter 9Angel Color: 1.4, 2.5, 7.4.5, 8.13Color: 1.4, 2.5, 7.4.5, 8.13 Lighting: 6 (all), 13.1 – 13.5Lighting: 6 (all), 13.1 – 13.5 Texture Maps and Antialiasing: 7.6 – 7.11, 8.12Texture Maps and Antialiasing: 7.6 – 7.11, 8.12 Visibility: 5.6, 8.8, 9.10.3 – 9.10.4Visibility: 5.6, 8.8, 9.10.3 – 9.10.4 Rotations: 4.10 – 4.11Rotations: 4.10 – 4.11 Curves: 10.1 – 10.10Curves: 10.1 – 10.10 Red Book pp. 233 - 242pp. 233 - 242 Chapter 9Chapter 9 Class Material Antialiasing HardwareAntialiasing Hardware MorphingMorphing Making MoviesMaking Movies Class Material Antialiasing HardwareAntialiasing Hardware MorphingMorphing Making MoviesMaking Movies

5. Review – Vector Arithmatic Add, subtract Dot (to determine angle between and length of projection (when normalized vectors) Do math to understand why normalization requiredDo math to understand why normalization required Cross product (Right-hand rule) Equations of lines / Equations of planes Distance from line to plane Point of intersectionPoint of intersection Add, subtract Dot (to determine angle between and length of projection (when normalized vectors) Do math to understand why normalization requiredDo math to understand why normalization required Cross product (Right-hand rule) Equations of lines / Equations of planes Distance from line to plane Point of intersectionPoint of intersection

6. Review – Coordinate Space Coordinate space Right-handed coordinate systemRight-handed coordinate system openGL camera initialized to look down –z axisopenGL camera initialized to look down –z axis Coordinate space Right-handed coordinate systemRight-handed coordinate system openGL camera initialized to look down –z axisopenGL camera initialized to look down –z axis

7. Review - OpenGL No significant coding required I might ask you to tell me what a function does One you’ve used for the projectsOne you’ve used for the projects I might ask you to tell me what order to put the transformation commands Direction of rotations Ordering of polygon vertices Back-face rendering Textures Filtering, Mipmap, Bump Map, Displacement Map, Alpha blending, Multi texturingFiltering, Mipmap, Bump Map, Displacement Map, Alpha blending, Multi texturing No significant coding required I might ask you to tell me what a function does One you’ve used for the projectsOne you’ve used for the projects I might ask you to tell me what order to put the transformation commands Direction of rotations Ordering of polygon vertices Back-face rendering Textures Filtering, Mipmap, Bump Map, Displacement Map, Alpha blending, Multi texturingFiltering, Mipmap, Bump Map, Displacement Map, Alpha blending, Multi texturing

8. Review Rendering Pipeline (model, light, view, clip, project)

9. Review Homogeneous Coordinate System What does w do?What does w do? Modeling Transformations Rotate, translate, scale, rotate about arbitrary axisRotate, translate, scale, rotate about arbitrary axis Viewing Transformations Orthographic (parallel) and PerspectiveOrthographic (parallel) and Perspective Understand how matrix formed by composing many modeling and viewing transformations effects the vertices of a model and its rendering Homogeneous Coordinate System What does w do?What does w do? Modeling Transformations Rotate, translate, scale, rotate about arbitrary axisRotate, translate, scale, rotate about arbitrary axis Viewing Transformations Orthographic (parallel) and PerspectiveOrthographic (parallel) and Perspective Understand how matrix formed by composing many modeling and viewing transformations effects the vertices of a model and its rendering

10. Review - Color MetamersMetamers Relative changes versus absolute valuesRelative changes versus absolute values Ability to represent all colorsAbility to represent all colors RGB sensitivityRGB sensitivity Color spacesColor spaces –Intuitive spaces, distance between similar colors MetamersMetamers Relative changes versus absolute valuesRelative changes versus absolute values Ability to represent all colorsAbility to represent all colors RGB sensitivityRGB sensitivity Color spacesColor spaces –Intuitive spaces, distance between similar colors

11. Review – Lighting Equations Dependent on what factorsDependent on what factors Calculate the reflection vectorCalculate the reflection vector Know how parameters affect imagesKnow how parameters affect images The Rendering EquationThe Rendering Equation Dependent on what factorsDependent on what factors Calculate the reflection vectorCalculate the reflection vector Know how parameters affect imagesKnow how parameters affect images The Rendering EquationThe Rendering Equation

12. Review - Shading Flat, Gouraud, Phong Improvements versus costImprovements versus cost Indirect lighting Ray tracing, radiosityRay tracing, radiosity –Viewer dependent/independent –Costs/benefits –Hemicube Form FactorsForm Factors –Understand geometry of how they are computed –Understand simultaneous solution of all factors Flat, Gouraud, Phong Improvements versus costImprovements versus cost Indirect lighting Ray tracing, radiosityRay tracing, radiosity –Viewer dependent/independent –Costs/benefits –Hemicube Form FactorsForm Factors –Understand geometry of how they are computed –Understand simultaneous solution of all factors

13. Review - Antialiasing Sampling and Quantization Area Sampling (Weighted and unweighted) What is a filter? Super Sampling / Multisampling Stochastic SupersamplingStochastic Supersampling Nyquist Rate How is antialiasing done in hardware? Sampling and Quantization Area Sampling (Weighted and unweighted) What is a filter? Super Sampling / Multisampling Stochastic SupersamplingStochastic Supersampling Nyquist Rate How is antialiasing done in hardware?

14. Review – Textures Filtering Mip Map ConstructionConstruction Switching between layersSwitching between layers Advantages and disadvantagesAdvantages and disadvantages Bump Map Displacement Map Alpha Blending Repeating vs. Clamping Filtering Mip Map ConstructionConstruction Switching between layersSwitching between layers Advantages and disadvantagesAdvantages and disadvantages Bump Map Displacement Map Alpha Blending Repeating vs. Clamping

15. Review - Visibility Back-face culling Manifolds Occlusion (Painter’s Algorithm) Fragments (Analytic Visibility Algorithm) BSP Tree Multiple polygons aligned on same planeMultiple polygons aligned on same plane Construction of tree / traversal of treeConstruction of tree / traversal of tree Pros and consPros and cons Back-face culling Manifolds Occlusion (Painter’s Algorithm) Fragments (Analytic Visibility Algorithm) BSP Tree Multiple polygons aligned on same planeMultiple polygons aligned on same plane Construction of tree / traversal of treeConstruction of tree / traversal of tree Pros and consPros and cons

16. Review - Visibility Quadtree / Octree Warnock’s Algorithm Z-buffer What is its depthWhat is its depth Pros and consPros and cons Quadtree / Octree Warnock’s Algorithm Z-buffer What is its depthWhat is its depth Pros and consPros and cons

17. Review - Rotations Euler Angles Gimbal Lock How many DOFs do we require Math of axis angle Why does axis angle use 4 DOFs to model 3Why does axis angle use 4 DOFs to model 3Quaternion Why better than Euler?Why better than Euler? How is it similar to axis-angleHow is it similar to axis-angle When is it better than axis-angle?When is it better than axis-angle? Interpolation for animation with different representations? Euler Angles Gimbal Lock How many DOFs do we require Math of axis angle Why does axis angle use 4 DOFs to model 3Why does axis angle use 4 DOFs to model 3Quaternion Why better than Euler?Why better than Euler? How is it similar to axis-angleHow is it similar to axis-angle When is it better than axis-angle?When is it better than axis-angle? Interpolation for animation with different representations?

18. Review Splines Know how to build M matrix Hermite, Bezier, B-splineHermite, Bezier, B-spline Understand each spline’s G matrix Continuity terms What’s a duck? Uniform vs. non-uniform b-splines Know how to build M matrix Hermite, Bezier, B-splineHermite, Bezier, B-spline Understand each spline’s G matrix Continuity terms What’s a duck? Uniform vs. non-uniform b-splines

19. Review - Morphing How does the Beier and Neely algorithm work

20. Review – Making Movies What is compositing? What is matchmoving? How can we automate this?How can we automate this? What is a story board? How can we preserve real-world lighting when compositing digital characters? What is compositing? What is matchmoving? How can we automate this?How can we automate this? What is a story board? How can we preserve real-world lighting when compositing digital characters?