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

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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:

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:

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.

• 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 ?
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 9-19
• 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 20-30
• 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 Genus-2 Object ( = Two-hole 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 write-up to class on Wednesday;
also be prepared to explain your approach in a few sentences.

"RC" = Rockwood & Chambers
skim: RC pp 1-19;
review: RC pp 20-30;
read in preparation for next time: RC pp 31-48.

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