Final Review Zhicheng Yan

Over Operator  Two formulas  Alpha Slides  C A over B = a A C A + (1 – a A ) a B C B and a A over B = a A + (1 – a A ) a B  Know each parameter  Simple 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.

Curves  Curves 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:

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 question  Read 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 slides  Past 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 question  May 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 2  Make sure you read them and understand  Other material always have the probability of appearing on the exam, so be prepared for a high level question