Schröder is currently an assistant professor
of computer science at the
California Institute of Technology, Pasadena, where he directs the
Caltech Multi-Res Modeling Group. He received a Master's degree from
the MIT Media Lab and a PhD
University. During 1990/91 he worked for Thinking Machines. From 1992 to 1994
he held a visiting research fellow appointment at the German National Computer Science
Research Center, and did postdoctoral work at the University of South Carolina. His
research contributions range from massively parallel visualization, to
physically based modeling, global illumination, wavelets and
multiresolution geometry. For the past 5 years his work has
concentrated on exploiting wavelets and multiresolution techniques to
build efficient representations and algorithms for many fundamental
computer graphics problems. He has taught in a number of Siggraph
courses and most recently co-led the course on Wavelets in Computer
Graphics (1996). His current research focuses on subdivision as a
fundamental paradigm for geometric modeling and rapid manipulation of
large, complex geometric models. The results of his work have been
published in venues ranging from Siggraph to special journal issues on
wavelets and WIRED magazine, and he is a frequent consultant to
|Denis Zorin || Denis Zorin is a
research associate at the Computer Science Department of
Stanford University. Starting
in the fall of 1998, he will be an assistant professor at the Courant Institute of Mathematical
Sciences, New York University. He
received a BS degree from the Moscow Institute of Physics and Technology,
a MS degree in Mathematics from Ohio State University and a PhD in
Computer Science from the California
Institute of Technology. His research interests include
multiresolution modeling, the theory of subdivision, and applications
of subdivision surfaces in Computer Graphics. He is also interested in
perceptually-based computer graphics algorithms. He has published
several papers in Siggraph proceedings.
Tony DeRose is currently a member of the Tools Group at Pixar
Animation Studios. He received a BS in Physics in 1981 from the University
of California, Davis; in 1985 he received a Ph.D. in Computer
from the University of California,
Berkeley. He received a Presidential Young Investigator award from
the National Science Foundation in 1989. In 1995 he was selected as a
in the software category of the Discover
Awards for Technical Innovation.
From September 1986 to December 1995 Dr. DeRose was a Professor of
Computer Science and Engineering at the University
of Washington. From September 1991 to August 1992 he was on
leave at the Xerox Palo Alto
Center and at Apple Computer. He
has served on various technical program committees including SIGGRAPH,
and from 1988 through 1994 was an associate editor of ACM Transactions
His research has focused on mathematical methods for surface
data fitting, and more recently, in the use of multiresolution
Recent projects include object acquisition from laser range data and
methods for high-performance computer graphics.
David Forsey is an assistant professor of Computer Science at the University of British Columbia in
Vancouver, Canada, where he co-directs the Imager Computer
Graphics Laboratory. He is currently on leave at Radical Entertainment Ltd developing
products based on Hierarchical B-splines. He obtained a BSc. in
Zoology at the University of Guelph (1980) and a M.Math (1985) and
PhD. (1990) from the University of Waterloo. He has taught in several
SIGGRAPH courses, and has had two animations in the
SIGGRAPH electronic theatre. His research interests include multiresolution
animation as well as simulation
tools as they relate to the artistic side of modeling and
Kobbelt currently holds a position as a post-doctoral
research fellow at the
University of Erlangen , Germany. His major research interest is
sophisticated free-form modeling based on polygonal meshes. He
received his master's (1992) and Ph.D. (1994) degrees from the University of Karlsruhe
, Germany. He then spent one year at the
University of Wisconsin, Madison as a visiting researcher in Carl
de Boor's group. Since 1996 he has been working in the geometric modeling
unit of the Computer Graphics Group at Erlangen. During the last 5
years he made significant contributions to the construction and
analysis of subdivision schemes and pioneered the combination of the
subdivision paradigm with variational methods from CAGD.
is on the R&D staff for Alias
| Wavefront in Seattle. He has a B.S. in Computer Science (1984) from
the University of Maryland. In 1994, he completed a Ph.D. in Computer Science
from the University of Washington,
where he studied the development of wavelets over subdivision surfaces.
He has taught in previous SIGGRAPH courses on wavelets, and has also published
research in surface interpolation. His other graphics interests include
fairness and compression issues for 3D surface modeling.
Peters is an associate professor at the department of
Computer Sciences at Purdue University
He received his PhD in 1990 from the University of Wisconsin-Madison
advised by Carl de Boor.
In 1991 and 1992 he held positions at the IBM T.J.
Watson Research Center and Rensselaer Polytechnic Institute
before joining the computer sciences department at Purdue in 1992.
In 1994, Dr. Peters was honored with a five year National Young
Investigator Award for his work on
Foundations and Tools for Surface Modeling
Currently Dr. Peters heads the
at CS Purdue and is a member of the
Center for Visualization
and Image Processing.
Peters' research focusses on represention and analysis of geometry on the
Notably, he has developed new tools for free-form modeling and design
that combine the advantages of parametric spline representations
and subdivision algorithms (recent papers).
The morning section will focus on the foundations of subdivision,
starting with subdivision curves and moving on to
surfaces. We will review and compare a number of different schemes
and discuss the relation between subdivision and splines. The
emphasis will be on properties of subdivsion most relevant for
Introduction and overview (Schröder); 15 min.
Foundations I: Basic Ideas (Schröder
and Zorin) 60 min.
- Course outline and schedule
- High-level introduction to the basic ideas of subdivision
- Quick overview of application examples
Foundations II: Construction and Analysis
of Subdivision Schemes (Zorin and Peters), 140 min.
- Constructing smooth curves through subdivision; 10 min.
examples: b-spline knot insertion and interpolating subdivision
- Subdivision for surfaces; 10 min.
an example of a subdivision scheme: Loop
- Properties of subdivision schemes: smoothness, locality,
hierarchical structure; 10 min.
- How splines are related to subdivision; 10 min.
- Advantages of subdivision: arbitrary topology, efficiency,
controllable surface features such as creases and cusps; 10 min.
The afternoon session will focus on applications of subdivision and
the algorithmic issues practictioners need to address to build
efficient, well behaving systems for modeling and animation with
- Overview of the analysis of subdivision; geometric smoothness
and smooth parameterizations; 10 min.
- Analysis for curves; subdivision matrices; 15 min.
- Properties of the subdivision matrix and geometric smoothness;
- Classic schemes, their definition, and basic properties; 30 min.
- Subdivision rules for special surface features; boundaries
and creases; 10 min.
- Subdivision matrices for surface schemes; smoothness criteria;
- Methods for constructing subdivision schemes; improving
smoothness, curvature continuity, mesh quality; 15 min.
- Computation of normals and moments; 20 min.
- Basic algorithms and data structures for implementing
subdivision; adaptive evaluation, level-of-detail rendering; 10 min.
- Applications and Algorithms:
- Interactive Multiresolution Mesh Editing, 40 min.
Subdivision can model smooth surfaces, but in many
applications one is interested in surfaces which carry
details at many levels of resolution. Multiresolution mesh
editing extends subdivision by including detail offsets at
every level of subdivision, unifying patch based editing
with the flexibility of high resolution polyhedral
meshes. The result is a hierarchical editing system built
around highly adaptive algorithms and datastructures to
deliver interactive performance on low end workstations
for complex geometric models. This section will detail
the underlying ideas and the algorithms necessary to build
a scalable multiresolution editing system. (Zorin)
- Subdivision Surfaces and Wavelets, 40 min.
Wavelet techniques are well understood for regular
domains, such as curves or rectangular tensor-product
splines. Subdivision methods let us extend these
techniques to more complex domains of arbitrary
topological type. By developing multiresolution analysis over
subdivision surfaces, we can apply wavelets to a wide variety of
practical problems, including compression of polygonal data and
multiresolution editing of smooth surfaces of arbitrary
- A Variational Approach to Subdivision, 40 min.
Surfaces generated using subdivision have certain orders
of continuity. However, it is well known from geometric
modeling that high quality surfaces often require
additional optimization (fairing). In the variational
approach to subdivision, refined meshes are not prescribed
by static rules, but are chosen so as to minimize some
energy functional. The approach combines the advantages of
subdivision (arbitrary topology) with those of variational
design (high quality surfaces). This section will describe
the theory of variational subdivision and highly efficient
algorithms to construct fair surfaces. (Kobbelt)
- Subdivision Surfaces in the Making of Geri's Game, 40 min.
Geri's Game is a 3.5 minute computer animated film that
Pixar recently completed (and which will be submitted to
the 1998 SIGGRAPH film show). The film marks the first
time that Pixar has used subdivision surfaces in a
production. In fact, subdivision surfaces were used to
model virtually everything that moves. This section
will describe what led Pixar to use subdivision surfaces,
discuss the issues encountered along the way, and
present several of the solutions developed. (DeRose)
- Exploiting Subdivision in Modeling and Animation, 40 min.
Subdivision provides the mechanism for a multiresolution
representation of smooth surfaces. This section explains
how multiresolution surfaces can be used to greatly
improve the modeling and animation of complex organic
forms. Examples are taken from two commercial
applications, where subdivision surfaces are used to
seamlessly join together hierarchical tensor-product
spline surfaces. (Forsey)
- Summary and Wrapup: (all speakers)