mirror of https://github.com/CGAL/cgal
90 lines
2.8 KiB
TeX
90 lines
2.8 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: RegularCellBase_3.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{\RCSRegularcellbaseRev}{$Id$}
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\RCSdefDate{\RCSRegularcellbaseDate}{$Date$}
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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}{RegularTriangulationCellBase_3}
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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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weighted 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 stores those hidden points
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in its cells.
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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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three dimensional cell where its point component is located
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(the cell which hides it)
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is removed. Therefore we decided to store
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in each cell of a regular triangulation
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the list of hidden points that 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 cell 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{TriangulationCellBase_3} by adding
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in the cell a container to store hidden points.
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\ccRefines
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\ccc{TriangulationCellBase_3}
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\ccTypes
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\ccNestedType{Point}
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{Must be the same as the point type \ccc{TriangulationTraits_3::Point_3}
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defined by the geometric traits class of the triangulation.}
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\ccTypes
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\ccNestedType{Point_iterator}
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{Iterator of value type Point}
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\ccCreationVariable{rcb} %% choose variable name
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\ccHeading{Access Functions}
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\ccMethod{Point_iterator hidden_points_begin();}
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{Returns an iterator pointing to the first hidden point.}
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\ccMethod{Point_iterator hidden_points_end();}
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{Returns a past-the-end iterator.}
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\ccHeading{Setting}
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\ccMethod{void hide_point(const Point & p);}
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{Adds \ccc{p} to the set of hidden points of the cell.}
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\ccHasModels
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\ccc{CGAL::Regular_triangulation_cell_base_3}
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\ccSeeAlso
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\ccc{TriangulationCellBase_3}
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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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