CS 284: CAGD 
Lecture #20 -- Mo 11/03, 2003.

Preparation:

Modeling with Implicit Surfaces and Conversion to B-Reps

Some self-test questions:

• What does the user input to this design system ?
• What determines the number of sampling points on the surface ?
• Is the field around two collinear segments, joined at their ends, the same

as that of a single line segment equal in lenght to their combined length ?
• How do they avoid unwanted blending between unrelated bodies (segments) ?
• What are the options for visualizing these surfaces ?

• What kind of continuity do these implicit surfaces achieve ?
• Can we put a C1-continuous texture onto these surfaces ?

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Comments on Edge-based Surface Energies

• In-circle model (gives too much curvature):
• Circum-circle model (gives too little curvature):
• Using the angle itself should be about right in the limit:

• Assume all the bending energy is associated with the edges (seems very reasonable),
• This energy is representing the area from the edge itself to the centroids of the faces on either side.

• The edge-based bending energy approximates the total bending energy of the sphere (W = 4p = 12.57)

the better, the more edges there are, and the more regular the tessellation is:
• Some sample results:

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Preparing for 5-Minute Project Proposal Presentations (11/5/03)
("Venture Capitalist Rally" -- How to get the "gold".)

Let's start at 9:00am sharp, so we have a little less time pressure:

• Should last 4-5 minutes (hard 5 minute cutoff).
• Need to switch from one speaker to next one in 1 minute -- be prepared for this !
• Start your talk with an attention-grabber.
• Be enthusiastic, leave a (positive) impression.
• Show relevance, potential impact of your work.
• Be on time ! (you may be first at 9:00am !)

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Next Reading Assignments: (see list)

Next Programming Assignment: Surface Optimization