CS 284: CAGD 
Lecture #1 -- Mo 8/25, 2003.

Preparation:

Lecture Topics

Introduction to CAGD

• What is CAGD ?

Subset of CAD; originally mostly shipbuilding, automotive, aeroplanes; mostly smooth, curved shapes.
• Motivation for COE Students:

CS: smooth motions for movies, ME: freeform parts; Math: data fitting ...
• Issues Addressed in This Course:

see below.
• Course Overview:

see topic list on home page.
• Method of Attack:

Intuitive introduction first; hands-on experience; math later.
• Where does CS 284 fit in ?

Should have had some computer graphics or CAD course;
Graduate CG course can be taken concurrently.
• The Key Problem of CAGD:

Handout: Experiment -- connect the dots ...
What do the result tell us ?

Key Course Topics

• Interpolation
• Subdivision (more than in the past)
• Splines (less than in the past)
•  all on 1, 2, (and 3)-manifolds
• Curve and surface optimization

Course Goal

• How to make smooth curves and surfaces that fit certain constraints.
• Optimization will play an ever bigger role (compute power is available).
• Make it easier on the user (even though underlying formulation may get more complex).
• The key common concept:

Use a simple (piecewise linear) shape, with the fewest degrees of freedom (DoF) necessary,
to define and control an associated (smooth, continuous) design shape.

Course Administration

• Teaching Style:

Application oriented; learning by doing;
even the chosen textbooks have an interactive component.
• Reading Assignments:

Important; --> you get much more out of class discussions.
• Thinking/Experimenting/Programming Assignments
• Quizzes/Exams:

Probably just one quiz, somewhere in the middle of the semester,
to check whether key concepts have sunk in.
• Course Projects:

Create some utility that solves a particular task,
possibly in the context of some special shape that you want to design.
• Background Questionnaire:

Please fill in !

Expected Math Foundations

• Parametric Curves
• Parametric Surfaces
• Derivatives, Tangents, Normals
• Linear Interpolation
• Basis Vectors

Some Possibly New Concepts

• Hodograph
• Turning Number of a (closed) Curve
• Parametric Continuity
• Geometric Continuity
• Basis Functions

New Homework Assignment:

DUE: WED 8/27/03, 9:10am.
You don't actually have to build a CAD model for this shape,
but think through all the steps that you would have to go through,
and estimate how long it might take you.
In a couple of paragraphs, write down your thoughts on how you would do this
and bring that write-up to class on Wednesday;
also be prepared to explain your approach in a few sentences.

Next Reading Assignment: