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The conference will
feature three prominent researchers as keynote speakers:
Geometry Images: Sampling Surfaces on Regular Grids
Surfaces in graphics are commonly represented using irregular meshes,
since these approximate many shapes using fewer vertices. However, their
flexible connectivity comes at a price, since most mesh operations require
random memory accesses and filter kernels must handle arbitrary neighborhoods.
In contrast, media like audio and images are represented using regular
samplings - 1D and 2D grids. Such grids allow efficient traversal, random
access, convolution, composition, downsampling, compression, and synthesis.
Many surface signals have now migrated into texture images. As the cost
of 3D transformations becomes negligible, one should re-evaluate whether
geometry itself could not also be represented using ordinary grids.
This talk will present several recent projects involving geometry images.
These are constructed by parametrizing the surface over a planar domain,
and resampling the surface geometry on a regular domain grid. One exciting
possibility is to then exploit the highly parallel GPU rasterizer to directly
Hugues Hoppe is a senior researcher in the Computer Graphics Group
at Microsoft Research. His primary interests lie in the acquisition, representation,
and rendering of geometric models. For his PhD work on surface reconstruction
from 3D scans, he was selected as a finalist in the 1995 Discover Awards
for Technological Innovation. He subsequently developed multiresolution
representations for geometry, including wavelet-based multiresolution
analysis [Eck et al 1995] for semi-regular meshing, progressive meshes
[Hoppe 1996] for irregular meshing, and geometry images [Gu et al 2002]
for completely regular meshing. Recent efforts have focused on surface
parametrization to exploit the highly parallel GPU rasterizer. Contributions
include lapped textures, normal-shooting parametrization, geometric-stretch
metrics, hierarchical solvers, and signal-specialized parametrization.
His most recent passion is the regular sampling of surfaces using geometry
images, to exploit the forthcoming unification of vertex and image buffers.
His publications include 17 papers at ACM SIGGRAPH, and he is associate
editor for ACM Transactions on Graphics. He received a BS summa cum laude
in electrical engineering in 1989 and a PhD in computer science in 1994
from the University of Washington.
of Commutative Relations for Subdivision Surfaces
While spectral methods for determining
the smoothness of subdivision surfaces at extraordinary vertices are relatively
well-known, a pervasive view in the geometric modeling community is that
operations with subdivision surfaces are much more complex than similar
operations for polynomial surfaces. A powerful, but little-known tool
for manipulating subdivision schemes based on applying linear algebra
to associated subdivision matrices makes it possible to perform a variety
of operations involving complex subdivison schemes in an efficient way.
Given a subdivision matrix S, the crux of this technique is to form a
commutative relation of the form D S = T D where the matrix D annihilates
some subset of the eigenvectors of S. This talk will consider three applications
of commutative relations of this type to:
- analyze the smoothness of mixed element meshes such as triangle-quad
- compute exact inner products such as enclosed volume over subdivision
- build smooth subdivision surfaces that loft (interpolate) curve networks.
Warren, a Professor of Computer Science at Rice University, is one of
the world's leading experts on subdivision. He has published a book "Subdivision
Methods for Geometric Design" and numerous papers of this topic and
its applications to computer graphics. These publications have appeared
in such forums as SIGGRAPH, Transactions on Graphics, Computer-Aided Geometric
Design and The Visual Computer. He has also organized and participated
in a number of international workshops, short courses and minisymposia
on the theory and practice of subdivision. Professor Warren's related
areas of expertise include computer graphics, geometric modeling and visualization.
made from Circles
important notions of surface theory such as curvature lines, conformal
parametrization, and Willmore energy (the integral of the squared mean
curvature) are invariant with respect to conformal transformations of
space. This suggests to use conformally invariant building blocks such
as circles for the corresponding discretizations. We will report on several
recent projects dealing with the description of discrete surfaces in terms
- discrete Willmore energy and its applications for fairing and restoration
of surfaces and optimization of triangulations,
- discrete conformal surfaces (as well as their special classes) in relation
to the theory of circle patterns.
Alexander Bobenko is a professor of mathematics
at the Technical University Berlin. His interests lie in differential
geometry, dynamical systems and mathematical visualization. His publications
include books and numerous papers in geometry and mathematical physics.
During the last years his main interest has moved to discrete differential
geometry, a mathematical area which aims to develop and apply discrete
analogs of the notions and methods of differential geometry. He has organized
and participated in a number of conferences in geometry, mathematical
physics and visualization. He received his PhD in mathematical physics
in 1985 from the Steklov Mathematical Institut, St. Petersburg.