CS 445 / 645: Introductory Computer Graphics

Review

Final Exam

Thursday, December 13th from 7 – 10 p.m.– Room Olsson 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– Class on Thursday will outline material and review

Review

If you’re going to print out all the slides from my lectures, please try to keep our costs down.– Render multiple slides to a page.– Keep the amount of black ink down

Review Slide from Midterm

Hearn and Baker– Chapter 2 (NOT ON FINAL)– Chapter 3 (84-102, 117-126) (NOT ON FINAL)– Chapter 5– Chapter 6 (225-248) (NOT ON FINAL)– Chapter 11 (No Quaternions) (FINAL WILL INCLUDE

QUATS)– Chapter 12 (432-456)– Chapter 14– Chapter 15– Appendix 1 – 4

OpenGL Red Book– Chapter 1 - 3

Review Since Midterm Hearn and Baker

– Chapter 4 (171 - 180)– Chapter 10 (315 - 355)– Chapter 11 (413 – 422)– Chapter 13– Chapter 14– Appendix (617-618)

Red Book– Chapter 5– Chapter 9

Class Material– Antialiasing– Cube Maps– Visible Surface– Making Movies– Animation

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)– Did you know the length of the cross product of two vectors

equals the area of the parallelogram formed by the two vectors?

Equations of lines 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 compositing many modeling and viewing transformations effects the vertices of a model and its rendering

Review

Color– Metamers– Relative changes versus absolute values– RGB sensitivity– Color spaces

Intuitive spaces, distance between similar colors Lighting Equations

– Dependent on what factors– Calculate the reflection vector– Know how parameters effect images

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

– Stochastic Supersampling Nyquist Rate How is this 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 – Game Consoles

How can we really compare game consoles?– Triangles/Second versus 48 Pixel Quads / Sec– Texture Bandwidth– Antialiasing– MultiTexturing

How do these things influence system performance and how do they relate to the rendering pipeline?

Review - Visibility Canonical View Volume

– Advantages?– Used for Clipping

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

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?

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 – Environment Mapping

How is environment mapping done in hardware

Understand the basic problem we discussed in class that allows us to project an intersection with one face of cube to another face of cube

Review - Animation

Keyframing– Pros/cons

Inverse Kinematics– Know what it is

Motion Capture– Pros/cons

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?