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> Volume 6, Issue 2
Preprint: Preprints from Graphics Group at Caltech.

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Peter Schroeder (ps@cs.caltech.edu) Guest

Posted: Fri Feb 07, 1997 11:12 pm Subject: Preprint: Preprints from Graphics Group at Caltech.




#8 Preprint: Preprints from Graphics Group at Caltech.
Dear Editor,
The following preprints are available from the Department of Computer
Science, Caltech:

C^k Continuity of Subdivision Surfaces
CSTR9623 (ftp://ftp.cs.caltech.edu/tr/cstr9623.ps.Z)
Denis Zorin
Stationary subdivision is an important tool for generating smooth
freeform surfaces for CAGD and computer graphics. One of the
challenges in construction of subdivision schemes for arbitrary meshes
is to guarantee that the limit surface will have smooth regular
parameterization in a neighborhood of any point. First results in this
direction were obtained only recently. In this paper we derive
necessary and sufficient criteria for $C^k$continuity that generalize
and extend most known conditions. We create a general mathematical
framework that can be used for analysis of more general types of
schemes. Finally, we prove a degree estimate for $C^k$continuous
polynomial schemes generalizing an estimate of Reif and give a
practical sufficient condition for smoothness.

Interactive Multiresolution Mesh Editing
CSTR9706 (http://www.cs.caltech.edu/~ps/multiediting.ps.gz)
Denis Zorin, Peter Schr"oder, Wim Sweldens
We describe a multiresolution representation for meshes based on
subdivision. Subdivision is a natural extension of the existing
patchbased surface representations. At the same time subdivision
algorithms can be viewed as operating directly on polygonal meshes,
which makes them a useful tool for mesh manipulation. Combination of
subdivision and smoothing algorithms of Taubin allows us to construct
a set of algorithms for interactive multiresolution editing of complex
meshes of arbitrary topology. Simplicity of the essential algorithms
for refinement and coarsification allows to make them local and
adaptive, considerably improving their efficiency. We have built a
scalable interactive multiresolution editing system based on such
algorithms.
See also http://www.gg.caltech.edu/~dzorin/ for figures and MPEG
movies.

Constructing Variationally Optimal Curves through Subdivision
CSTR9705 (http://www.cs.caltech.edu/~ps/variation.ps.gz)
Leif Kobbelt and Peter Schr"oder
Subdivision is a powerful paradigm for the generation of curves and
surfaces. It is easy to implement, computationally efficient, and
useful in a variety of applications because of its intimate connection
with multiresolution analysis. An important task in computer graphics
and geometric modeling is the construction of curves which interpolate
a given set of points and minimize a fairness functional (variational
design). In the context of subdivision, fairing leads to special
schemes requiring the solution of a (banded) linear system at every
step. We present several examples of such schemes including one which
reproduces nonuniform interpolating cubic Bsplines. By implementing
variational schemes in a wiring diagram formalism we find associated
wavelets and efficient algorithms to perform the corresponding
decomposition and reconstruction transformations. The computational
costs are low enough for interactive applications. 





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