mirror of https://github.com/CGAL/cgal
80 lines
2.5 KiB
TeX
80 lines
2.5 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: Regular_face_base.tex
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% +------------------------------------------------------------------------+
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% | 12.04.2000 Author
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% | Package: Package
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% |
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\RCSdef{\RCSRegularfacebaseRev}{$Id$}
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\RCSdefDate{\RCSRegularfacebaseDate}{$Date$}
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% |
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%%RefPage: end of header, begin of main body
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% +------------------------------------------------------------------------+
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\begin{ccRefConcept}{RegularTriangulationFaceBase_2}
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%% \ccHtmlCrossLink{} %% add further rules for cross referencing links
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%% \ccHtmlIndexC[concept]{} %% add further index entries
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\ccDefinition
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The regular triangulation of a set of weighted points does not
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necessarily
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have one vertex for each of the input points. Some of the input
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weigthed points have no cell in the dual power diagrams
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and therefore do not correspond to a vertex of the regular
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triangulation.
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Those weighted points are said to be {\it hidden} points.
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A point which is hidden at a given time may appear later as a vertex of
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the regular triangulation upon removal on some other weighted point.
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Therefore, hidden points have to be stored somewhere.
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The regular triangulation store those hidden points
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in special vertices called {\it hidden} vertices.
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A hidden point can appear as vertex of the triangulation
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only when the
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two dimensional face where its point component is located
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(the face which hides it)
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is removed. Therefore we decided to store
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in each face of a regular triangulation
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the list of hidden vertices whose points are located in the face.
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Thus points hidden by a face are easily reinserted in the triangulation
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when the face is removed.
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The base face of a regular triangulation
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has to be a model
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of the concept \ccRefName\ , which refines
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the concept \ccc{TriangulationFaceBase_2} by adding
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in the face a list to store hidden vertices.
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\ccRefines
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\ccc{TriangulationFaceBase_2}
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\ccTypes
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\ccTypedef{typedef std::list<Vertex_handle> Vertex_list;}
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{An std list of hidden vertices.}
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\ccCreationVariable{rfb} %% choose variable name
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\ccHeading{Access Functions}
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\ccMethod{Vertex_list& vertex_list();}
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{Returns a reference to the list of vertices hidden by the face.}
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\ccHasModels
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\ccc{CGAL::Regular_triangulation_face_base_2}
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\ccSeeAlso
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\ccc{TriangulationFaceBase_2} \\
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\ccc{RegularTriangulationVertexBase_2}
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\end{ccRefConcept}
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% +------------------------------------------------------------------------+
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%%RefPage: end of main body, begin of footer
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% EOF
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% +------------------------------------------------------------------------+
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