CS 284: CAGD 
Lecture #17 -- Tu 10/24, 2006.

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Preparation: -- FO'92:  "Functional Optimization for Fair Surface Design" by H. P. Moreton and C. H. Sequin.


Differential Geometry of Surfaces (cont.)

See: "Intrinsic Properties of a Surface" by M. E. Mortenson  (handout)
Differential Geometry of Surfaces -- Selected Formulas by Jordan Smith

Introduction and Motivation to Minimum Variation Surfaces

Discussion of the salient points of the papers: Data structures, algorithms, difficulties ...

Reading Assignment: BR'92: "The Surface Evolver" K. Brakke

- skip Sections  3.4, 3.5, 4.2, 4.8, 5.4, 5.5, 6.2, 6.7, 9, 10.

Definitive Project Description (Phase 2)

Before Thursday 10/26/2006, midnight: E-mail me:  a 0.5 to 1.0 page description of your chosen project. Specify:

Homework Assignment:  Make a genus-L Surface with DLh Symmetry (Phase 1)

Generate a rough polyhedral surface of genus-L, where L is the number of letters in your first name.
The surface should have DLh symmetry; i.e. L-fold rotational symmetry around the z-axis, as well as
mirror symmetry across the x-y-plane and across L planes that comprise the z-axis.
Build only the fundamental domain of this surface; i.e.  1 / 4L  of the total object. 
Keep it as simple as possible; i.e. use only 3-5 quadrilaterals or about twice as many triangles.
This piece of polyhedral surface then get's suitably mirrored and replicated to form the whole closed, watertight genus-L surface.
Start from the basic set-up in  GenusL_SymmDLh.slf 
All you have to do in this file is: replace the two place-holder quadrilaterals and adjust the replication number in the final surface assembly.
In the next phase of the assignment we will then convert this surface piece into the format of Brakke's Surface Evolver
and experiment with it.
The goal is to find the surface of lowest bending energy while maintaining the specified genus and symmetries.

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