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