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CS 445 / 645 Introduction to Computer Graphics Lecture 24 Final Exam Prep Final Exam Thursday, December 12th from 7 – 10 p.m. • Room OLS 011 You may use one sheet of notes (8.5 x 11’’) • You can write on both sides of paper Not everything from semester will be on test Pre-Midterm Material Angel • Chapter 4 • Chapter 5 • Appendix B • Appendix C OpenGL Red Book • Chapter 1 - 4 Material Since Midterm Angel • Color: 1.4, 2.5, 7.4.5, 8.13 • Lighting: 6 (all), 13.1 – 13.5 • Texture Maps and Antialiasing: 7.6 – 7.11, 8.12 • Visibility: 5.6, 8.8, 9.10.3 – 9.10.4 • Rotations: 4.10 – 4.11 • Curves: 10.1 – 10.10 Red Book • pp. 233 - 242 • Chapter 9 Class Material • Antialiasing Hardware • Morphing • Making Movies Review – Vector Arithmatic Add, subtract Dot (to determine angle between and length of projection (when normalized vectors) • Do math to understand why normalization required Cross product (Right-hand rule) Equations of lines / Equations of planes Distance from line to plane • Point of intersection Review – Coordinate Space Coordinate space • Right-handed coordinate system • openGL camera initialized to look down –z axis Review - OpenGL No significant coding required I might ask you to tell me what a function does • One 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 texturing Review Rendering Pipeline (model, light, view, clip, project) Review Homogeneous Coordinate System • What does w do? Modeling Transformations • Rotate, translate, scale, rotate about arbitrary axis Viewing Transformations • Orthographic (parallel) and Perspective Understand how matrix formed by composing many modeling and viewing transformations effects the vertices of a model and its rendering Review - Color • Metamers • Relative changes versus absolute values • Ability to represent all colors • RGB sensitivity • Color spaces – Intuitive spaces, distance between similar colors Review – Lighting Equations • Dependent on what factors • Calculate the reflection vector • Know how parameters affect images • The Rendering Equation Review - Shading Flat, Gouraud, Phong • Improvements versus cost Indirect lighting • Ray tracing, radiosity – Viewer dependent/independent – Costs/benefits – Hemicube • Form Factors – Understand geometry of how they are computed – Understand simultaneous solution of all factors Review - Antialiasing Sampling and Quantization Area Sampling (Weighted and unweighted) What is a filter? Super Sampling / Multisampling • Stochastic Supersampling Nyquist Rate How is antialiasing done in hardware? Review – Textures Filtering Mip Map • Construction • Switching between layers • Advantages and disadvantages Bump Map Displacement Map Alpha Blending Repeating vs. Clamping Review - Visibility Back-face culling Manifolds Occlusion (Painter’s Algorithm) Fragments (Analytic Visibility Algorithm) BSP Tree • Multiple polygons aligned on same plane • Construction of tree / traversal of tree • Pros and cons Review - Visibility Quadtree / Octree Warnock’s Algorithm Z-buffer • What is its depth • Pros and cons 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 3 Quaternion • Why better than Euler? • How is it similar to axis-angle • When is it better than axis-angle? Interpolation for animation with different representations? Review Splines Know how to build M matrix • Hermite, Bezier, B-spline Understand each spline’s G matrix Continuity terms What’s a duck? Uniform vs. non-uniform b-splines Review - Morphing How does the Beier and Neely algorithm work Review – Making Movies What is compositing? What is matchmoving? • How can we automate this? What is a story board? How can we preserve real-world lighting when compositing digital characters?