CS 284: CAGD 
Lecture #1 -- Wed 8/26, 2009.

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 (a very useful key topic)
  
• Subdivision (more than in the past)
• Splines (less than in the past)
  ... all on 1, 2, (and 3)-manifolds
• Curve and surface optimization
• Remeshing, reparametrization
• Texture (and displacement) mapping
  
• Implicit Surfaces (cleanup of bad designs)
• Distance Fields (adaptive schemes for encoding 3D shapes)
  
• Point Clouds (reverse engineering, scanner data)
  --- 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, -- but this is much more than you need).
  
• 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; -- I want everybody to participate actively!
  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.
  (First readings are from Rockwood and Chambers, later some SIGGRAPH papers).
  
• Conceptual Thinking  Assignments:
  Equally important; ==> to make sure you can apply the discussed material.
  (A first example is below: How to make a genus-2 object).
  
• Programming  Assignments:
  One two-stage assignment to build a half-edge mesh data structure, and then to add texturing onto it.
  (This is a very key data structure useful in many applications).
  
• Course Projects:
  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 (and possibly build it on our FDM machine).
  (Examples from previous courses)
  
• Quizzes/Exams:
  Probably just one quiz, somewhere in the middle of the semester, to check whether the key concepts have sunk in.
  NO  Final Exam!

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;
  -- surface normal = 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 number 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 ...
  

First Homework Assignment:

DUE: MON 8/31/06, 10:40am.
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 next class;
also be prepared to explain your approach in a few sentences.

Next Reading Assignment: