[Colloquium] Reminder: Guest Speaker @ TTI-C Today (4/12/06)

[Katherine Cumming]

**********TTI-C Guest Speaker Today ***********
                                 April 12, 2006
        Presented by:  Toyota Technological Institute at Chicago
 
 
Speaker:  Ken Clarkson, Bell Laboratories
Speaker's home page: http://cm.bell-labs.com/who/clarkson/
 
Date: Wednesday, April 12, 2006 
Location: TTI-C Conference Room
Time:  10:00 am
Title:   Approximating Surfaces with Meshes
Abstract:
How hard is it to approximate a smooth surface M with a piecewise-linear
mesh?  When M is the boundary of a convex body, remarkably tight bounds are
known for the smallest Hausdorff distance possible for a mesh with n
simplices.  In the case of more general surfaces, much less is understood.
I'll show that the smallest distance, when M is a d-manifold, is
O(S/n)^{2/d}, where S is the integral over M of the square root of the
Gaussian curvature.  (The constant factor here depends only on the
dimension.) Also, under some reasonably general conditions on the surface
and the mesh, this expression is also a lower bound, up to a constant
factor. The upper bound construction distributes the vertices of the mesh in
an "epsilon-net", in a metric based on directional curvature. The lower
bound relates the volume of a simplex to its interpolation error.

It may be helpful that a version of the slides is at
http://cm.bell-labs.com/who/clarkson/enet_tris/t2/t.xml, viewable with the
Firefox browser. 
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If you have questions, or would like to meet the speaker, please contact
Katherine at 773-834-1994 or kcumming at tti-c.org   
For information on future TTI-C talks and events, please go to the TTI-C
Events page:  http://www.tti-c.org/events.html.  TTI-C (1427 East 60th
Street, Chicago, IL  60637)
 
 
 
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