Technion
 
CGGC seminar (talk #186)
 
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Date:  Thursday 24/03/2011  (note special day)
 
Time:  10:30 am  (note special time)
 
Room:  Taub 337
 
Speaker:  Michael Floater (University of Oslo, Norway)
 
Title:   Barycentric interpolation and mappings on smooth convex domains
 
Abstract:
 
In a recent paper, Warren, Schaefer, Hirani, and Desbrun
proposed a simple method of interpolating a function defined on
the boundary of a smooth convex domain, using an integral kernel
with properties similar to those of barycentric coordinates on
simplexes.
 
When applied to vector-valued data, the interpolation can map
one convex region into another, with various potential
applications in computer graphics, such as curve and image
deformation.
 
In this paper we establish some basic mathematical properties of
barycentric kernels in general, including the interpolation
property and a formula for the Jacobian of the mappings they
generate. We then use this formula to prove the injectivity of
the mapping of Warren et al.
 
This is joint work with Jiri Kosinka.
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
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