CIS881 Midterm Notes

Main notes on the exam format:

The midterm will be closed book
The midterm will cover the lectures, readings from the book, and papers handed out in class. Of primary importance will be the things we covered in class (including the papers I handed out).
I give partial credit
Often, When I ask you to comment on an issue or problem, I'm not looking for a specific answer but rather I'm just looking for you to say something 'intelligent' about the matter.
An answer without reasons or supporting evidence receives much less partial credit than an answer with.

The main types of things that you should be concerned with:

Terms: definitions, uses, comparisons, etc.
Techniques: how to use them, what their restrictions are, what are the tradeoffs in using one technique over another, modify a technique to work on a similar class of problem, etc.
Analysis: mathematical analysis equations we've covered in class such as calcuating tangents, curvature, proving continuity, discuss complexity, etc.

Sample Terms

Solid Modeling
Constructive Solid Geometry (CSG)
Boundary Representation (B-Rep)
Wireframe
Euler Formula
Basis Function (Blending Function)
Algebraic v. Geometric Form
Explicit, Implicit, Parametric Equations
Local Control v. Global Control
Continuity: C¹ v. G¹

Sample Techniques you should be familiar with

Solid of Revolution
Extrusion
Sweep Operators
Lofting: Christiansen & Sederberg, Ganapathy & Dennehy
Euler Operators
Hermite
Blended Parabolas
Bezier
B-Spline
NURBS

Sample Analysis

Deriving continuity properties of a specific point in a specific type of curve.
Converting between one curve type to another
Subdividing a curve
Reparameterizing a curve
Degree elevation
Truncating a curve
Geometric construction of a curve
Showing transformation invariance

Sample Questions

Show that colinear control points provide G1 continuity at the junction of Bezier segments. What would it take to make it C1 continuous?
How would you form a quintic Hermite curve which used curvature information at the end points?
Given a point on a Bezier curve, how could you find the parametric value associated with it?
Relate the lofting technique of Christiansen and Sederberg to either of the techniques in Ganapathy and Dennehy - give a case in which they would produce differnt choices for the next edge of the lofted surface.
In a uniform B-Spline curve, explain what happens when you make one of the internal knot values equal to an adjacent value. Give your answer in terms of the basis functions. [I would give you the recurves definition of the basis function].
Given a cubic B-Spline with four points and a knot vector of [00001111], how would you convert it to a cubic Bezier curve?
What does it mean to be valid in the Euler formula sense? What does that tell you and not tell you about the object?
How would you convert blended parabolas to a Bezier formulation?
In the Catmull-Rom formulation, are the curve segments C1 or G1 continuous? How would you make it the other type of continuity? Would it make any sense to do so?
Give the equation for N_3,4(0.2) given the recursive definitioin for the basis function.
Given the following diagram of basis functions for a curve, what can you tell me about the curve? (pick a diagram from the book and look at it).
Give an example of a wireframe representation which is ambiguous with respect to the polyhedron it represents.
What are the tradeoffs involved in using the algebraic v. geometric form of a curve equation in an implementation?
In the solid of revolution technique, how would you incorporate a second silhouette curve which is defined 180 degrees from the first if they contained the same number of points?

Richard Parent