CS 284: CAGD 
Lecture #1 -- Tu 8/29, 2006.

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 ...
• Course Content:
  see information on home page... (and below)
  

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
• T-Splines
• Point Clouds
• Implicit Surfaces
  --- content will be tailored somewhat to interests of course participants.
• Background Questionnaire:
  Please fill in !

Course Goal

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

• Where does CS 284 fit in ?
  Should have had some computer graphics or CAD course; (e.g. cs 184).
  
• Teaching Style:
  Application oriented; learning by doing;  (even the chosen textbook has an interactive component).
  Intuitive introduction first; hands-on experience; math later.
  Interactive lectures, Q&A;
  Many small homework assignments initially, to deepen understanding, "close feedback loop".
  
• The Key Problem of CAGD:
  Handout: Experiment -- connect the dots ...
  What do the result tell us ?
• Reading Assignments:
  Important; --> you get much more out of class discussions.
• Thinking/Experimenting/Programming  Assignments:
  Equally important; --> to make sure you can apply the discussed material.
• Quizzes/Exams:
  Probably just one quiz, somewhere in the middle of the semester,
  to check whether the key concepts have sunk in.
• Course Projects:   (sorry no links -- just titles)
  Reimplement the key algorithm from some (siggraph?) paper;
  Create some utility that solves a particular task (possibly for your own use);
  Design an interesting virtual or real object (possibly build it on our FDM machine).
  

Expected Math Foundations

• Parametric Curves and Surfaces
  -- not just single valued height fields, can handle infinite slope, can be subjected to transformations ...
  
• Derivatives; Tangents; Normals
-- "velocity vector, vector of all component derivatives; -- if <>0, normalize to 1; -- normal on all tangent vectors

• Linear Interpolation
• Basis Vectors

Some Possibly New Concepts

• Hodograph
  -- plot of parameterized derivative vector
  
• Winding Number of a (closed, oriented) Curve around a Point
  -- how many times does it loop around that point ?
  
• Turning Number of a (closed) Curve
  -- if v<>0 it is equal to winding numper of hodograph around origin.
  
• Parametric Continuity
  -- all component functions are differentiable
  
• Geometric Continuity
  -- visual appearance is smooth, ignore parametrization!
  
• Basis Functions
  -- see definition 14, page 29 ...
  

New Homework Assignment:

DUE: WED 8/31/06, 2:10pm.
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: