CS 284: CAGD
Lecture #1  Tu 8/29, 2006.
CS
284 HOME <     > CURRENT
<     > NEXT
Preparation:
read Rockwood: pp 130.
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

TSplines

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; handson 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
See Rockwood pp 919

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
See Rockwood pp 2030

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:
A Conceptual Task: (to make you conscious of what we are up against).
Think about how you would model
 with the tools that you have already at your disposal 
a completely
smooth Genus2 Object ( = Twohole torus).
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 writeup to class on Wednesday;
also be prepared to explain your approach in a few sentences.
Next Reading Assignment:
"RC" = Rockwood & Chambers
skim: RC pp 119;
review: RC pp 2030;
read in preparation for next time: RC pp 3148.
CS
284 HOME <     > CURRENT
<     > NEXT
Page Editor: Carlo H. Séquin