update abstract (proposition)

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Pierre Alliez 2004-04-07 18:44:52 +00:00
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% TITLE
% ------------------------------------------------------------------------
\title{Generic Subdivision Algorithms on Meshes \\
\title{Algorithms on Meshes \\
based on the CGAL Polyhedron}
% pierre: other suggestion for the title?
% Generic Algorithms on Meshes
% based on the CGAL Polyhedron
% for anonymous conference submission please enter your SUBMISSION ID
% instead of the author's name (and leave the affiliation blank) !!
% we should submit with N.N.
\author[Le-Jeng Shiue, Pierre Alliez, Radu Ursu, and Lutz Kettner]
{Le-Jeng Shiue\thanks{CISE, University of Florida},
Pierre Alliez\thanks{GEOMETRICA, INRIA Sophia-Antipolis},
Radu Ursu\thanks{GEOMETRICA, INRIA Sophia-Antipolis}, and
Lutz Kettner\thanks{MPII, Saarbr\"ucken}
}
% ------------------------------------------------------------------------
\author[N.N.]{N.N.}
% \author[Le-Jeng Shiue, Pierre Alliez, Radu Ursu, and Lutz Kettner]
% {Le-Jeng Shiue\thanks{CISE, University of Florida},
% Pierre Alliez\thanks{GEOMETRICA, INRIA Sophia-Antipolis},
% Radu Ursu\thanks{GEOMETRICA, INRIA Sophia-Antipolis}, and
% Lutz Kettner\thanks{MPII, Saarbr\"ucken}
% }
% ------------------------------------------------------------------------
% if the Editors-in-Chief have given you the data, you may uncomment
% the following five lines and insert it here
@ -105,41 +103,31 @@
% pierre: I suggest to keep the abstract without any formatting
% nor macros (ascii only)
The Computational Geometry Algorithms Library CGAL is an efficient
modern C++ library following the generic programming paradigm. It
contains a flexible data structure for meshes in graphics, the
Polyhedron. In generic programming, data structures and algorithms are
decoupled, for example, iterators decouple container classes from
conventional search and sorting algorithms in the C++ Standard
Template Library (STL). We describe two different approaches one can
take with the Polyhedron when implementing subdivision algorithms: An
example implementation of the square-root-of-three subdivision scheme
based on Euler operations provided by the Polyhedron, and an example
implementation of the quad-triangle subdivision based on the modifier
callback mechanism that enables lower-level modifications. Then we
describe a generic framework for subdivision algorithms; its key
feature is the separation of the topological refinement operator from
the geometric smoothing operator. This work is the core part of a
tutorial for the Polyhedron. The tutorial also provides general
amenities for working with meshes in graphics; we offer an interactive
visualizer based on OpenGL, file I/O, and support for getting
illustrations for publications.
% The computational geometry algorithms library (CGAL) adapts
% design patterns and the generic programming paradigm in the design
% and the implementation. The template parameterization
% of the CGAL polyhedron meshes enhances the flexibility and
% the adaptability of supporting geometry algorithms.
% We introduce the modification operations supported
% in the CGAL polyhedron and demonstrate the applications
% of subdivision surfaces. Based on the CGAL polyhedron meshes,
% we also propose a generic framework of the generic polyhedron and
% the soft-coupled geometry algorithms. The soft-coupled algorithms
% are generic and to be specialized as combinations of the
% topology and geometry operators. The geometry operators
% are user-programmable based on the user-specialized CGAL polyhedron.
modern C++ library following the generic programming paradigm. CGAL
provides the notion of a geometric kernel (a complete set of simple
geometric entities as well as predications) and a set of data
structures and algorithms for geometric computing. In particular, it
contains a flexible data structure for meshes, the Polyhedron, which
design is presented in this paper. The flexibility of the CGAL
Polyhedron data structure is moreover evaluated through the
implementation of several algorithms. Following the C++ Standard
Template Library (STL) -- where data structures and algorithms are
decoupled -- we first implement a generic subdivision algorithm acting
on the CGAL Polyhedron. A high level of flexibility is obtained by the
possibility to specify as a template parameter the subdivision rules
themselves, which greatly facilitates the implementation of a new
subdivision scheme. Remeshing techniques implemented with a
combination of Polyhedron and Delaunay triangulation are then shown to
demonstrate the versatility of the unified framework provided by CGAL.
Last, several additional functionalities such as minimum enclosing
ball, convex hull, self intersection and boolean operations are
demonstrated on large meshes. Extensible algorithm models based on
the robust and efficient mesh data structure and components provided
by CGAL are aimed at speeding up the research, and therefore benefit
the geometry processing community.
\begin{classification} % according to http://www.acm.org/class/1998/
\CCScat{I.3.5}{Computer Graphics}{Computational Geometry