mirror of https://github.com/CGAL/cgal
48 lines
2.4 KiB
TeX
48 lines
2.4 KiB
TeX
% Related work and background
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% C++ and generic programming
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\noindent \textbf{Design patterns and generic programming.}
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Before using CGAL, it is mandatory to be familiar with C++,
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\emph{design patterns} and the \emph{generic programming paradigm}.
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Design patterns \cite{Gamma:1995:DP} describe successful and
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\emph{reusable} solutions to standard software problems. The generic
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programming paradigm \cite{Alexandrescu:2001:MCD} features the notion
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of C++ class templates and function templates, which is at the corner
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stone of all features provided by CGAL. Details of the design of the
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CGAL polyhedron data structure are given in next section.
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An example illustrating design patterns and the generic programming is
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the Standard Template Library (STL)~\cite{ms-stl-96}. Generality and
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flexibility is achieved with a set of \italic{concepts}, where a
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concept is a well defined set of requirements. One of them is the
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\italic{iterator} concept, which allows both referring to an item and
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traversing a sequence of items. Those items are stored in a data
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structure called \italic{container} in STL. Another concept, so-called
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\italic{circulator}, allows traversing some circular sequences. They
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share most of the requirements with iterators, except the lack of
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past-the-end position in the sequence. Since CGAL is strongly inspired
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from the generality of STL, it is important to become familiar with
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its concepts before starting using it.
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\noindent \textbf{Halfedge data structure.}
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\input hds
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\noindent \textbf{Geometry data structure and algorithms}
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A subdivision surface is the limit surface resulted from the
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application of a subdivision algorithm to a control polyhedron.
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Subdivision algorithms recursively \emph{refine} (subdivide) the
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control polyhedron and \emph{modify} (smooth) the geometry according
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to the stencils of the source mesh.
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%Subdivisions consist of two
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%meta-steps that most geometry processing algorithms have: the
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%\emph{connectivity operation} and the
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%\emph{geometry operation}. In this paper, we use subdivision
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%as the template of the geometry processing algorithms because it
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%connectivity operations are more complex than most other
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%algorithms. Some other simple algorithms, e.g.\ displacement map, the
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%connectivity operation is a null operation. In other words, the source
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%and the target mesh have the same connectivity.
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Further details on
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subdivisions can be found at \cite{Sub:course:2000}.
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