Final Review

Zhicheng Yan

Over Operator

Two formulas Alpha Slides CA over B = aA CA + (1 – aA) aB CB and aA over B = aA + (1 – aA) aB

Know each parameterSimple calculation

Given color values Given the alpha values

Past problem: Algebra questions. Given color of A and color of B find color of A over B

using the above formula. Given the alpha values of A and B find alpha A over B

using the formula.

CurvesCurves in general

Hermite Curve Linear interpolation Continuity

Bezier Curves Control points What does P(0.5) mean if P(0) is the start and P(1) is the

end?Algorithms

De Casteljau De Boor (knot vector) Blossoming game (make sure you know this!)

Past problem:Multiple choice/matching concept problems are to match curves with their properties.

Drawing problem require you understand and apply the algorithms. Mainly the BLOSSOMING procedure.

External notes: http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/

Subdivision

Half Edge Opposite End Left Next

Know halfedge data structure. Ex. What does this give you e->Next->Next in a triangle?

Subdivision

High level questionRead through the slides If you do a Catmull-Clark subdivsion on a shape what would you get as the result?Know the subdivision result. Ex. Subdivide a triangle 1 time will yield a mesh of how many triangles or quads?Past Problem:

Multiple choice/matching concept questions about the halfedge data structure and subdivision.

Quaternion's

Know how to apply a quaternion rotation

Know each parameter i,j,k’s meaning

Take a look at the Example in the slidesPast problem:

Calculation problems regarding the quaternion rules.

Skinning

High level concept

Read through it Ex. The building an elbow example in the lecture slides.Past problem:

Simple multiple choice regarding the concepts of skinning interpolation.

3D geometry

Know some common formulas Sphere Cylinder Cone Paraboloid

Ex. The expressions in Quadrics slide in the Volume Solid Modeling lecture slides.Past problem:

Matching shapes with their respective expressions.

Fractal Modeling

High level questionMay ask you to draw

Turtle Graphics L-System

Know Turtle Graphics and L-System grammar in the Fractal Modeling slides. Ex. Draw the shape given a string in the language.Past problem:

Drawing problem similar to the Ex. above.

Implicit Surfaces

Know marching cubes Know what the numbers mean Know how to draw it

In the Volume Solid Modeling lecture slides, it explains the meaning of f>0 and f<0, CSG operations, and marching cube rules. Know these concepts and especially the Marching Cubes slide. Ex. Given a matrix representing the marching cubes, draw the resulting graphics according to the rules.Past problem:

Drawing problem similar to the Ex. above.

Other material

The rest of the material since Exam 2Make sure you read them and understandOther material always have the probability of appearing on the exam, so be prepared for a high level question