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Added periodic weighted alpha shapes to the doc

This commit is contained in:
Mael Rouxel-Labbé 2017-07-31 16:17:23 +02:00
parent 06bfbfec6f
commit fd1c9d5dfa
5 changed files with 32 additions and 23 deletions
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39
Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt
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@ -198,10 +198,13 @@ We currently do not specify concepts for the underlying triangulation
type. Models that work for a family of alpha-shapes are the instantiations
of the classes `Delaunay_triangulation_3` and
`Periodic_3_Delaunay_triangulation_3` (see
example \ref AlphaShape_3DExampleForPeriodicAlphaShapes). A model that works for a fixed alpha-shape are the instantiations
example \ref AlphaShape_3DExampleForPeriodicAlphaShapes).
A model that works for a fixed alpha-shape are the instantiations
of the class `Delaunay_triangulation_3`.
A model that works for a weighted alpha-shape is
the class `Regular_triangulation_3`. The triangulation needs a geometric traits class
Models that work for a weighted alpha-shape are the instantiations
of the classes `Regular_triangulation_3` and
`Periodic_3_regular_triangulation_3`.
The triangulation needs a geometric traits class
and a triangulation data structure as template parameters.
\subsection AlphaShape3D_ConceptAndModelsAlphaShapes Alpha Shapes
@ -234,19 +237,20 @@ and `Fixed_alpha_shape_cell_base_3<Gt>`, respectively.
\subsection AlphaShape3D_ConceptAndModelsTDS Triangulation data structure
Additionally requirements are put when using `Regular_triangulation_3` or
`Periodic_3_Delaunay_triangulation_3` as underlying triangulations:
Additionally requirements are put when using weighted or
periodic triangulations as underlying triangulation:
<ul>
<li> When using `Regular_triangulation_3` as underlying triangulation, the vertex
<li> When using a weighted triangulation (`Regular_triangulation_3` or
`Periodic_3_regular_triangulation_3`), the vertex
and cell classes must be models to both `AlphaShapeVertex_3` and
`RegularTriangulationVertexBase_3`, as well as
`AlphaShapeCell_3` and `RegularTriangulationCellBase_3` respectively
(see example \ref AlphaShape_3DExampleforWeightedAlphaShapes).
<li> When using `Periodic_3_Delaunay_triangulation_3` as underlying
triangulation the vertex and cell classes need to be models to both
`AlphaShapeVertex_3` and `Periodic_3TriangulationDSVertexBase_3`, as well as
`AlphaShapeCell_3` and `Periodic_3TriangulationDSCellBase_3`
(see example \ref AlphaShape_3DExampleForPeriodicAlphaShapes).
(see example: \ref AlphaShape_3DExampleforWeightedAlphaShapes).
<li> When using a periodic triangulation (`Periodic_3_Delaunay_triangulation_3`
or `Periodic_3_regular_triangulation_3`), the vertex and cell classes must
be models to both `AlphaShapeVertex_3` and `Periodic_3TriangulationDSVertexBase_3`,
as well as `AlphaShapeCell_3` and `Periodic_3TriangulationDSCellBase_3`
(see example: \ref AlphaShape_3DExampleForPeriodicAlphaShapes).
</ul>
\section Alpha_shapes_3AlphaShape3OrFixedAlphaShape3 Alpha_shape_3 vs. Fixed_alpha_shape_3
@ -320,14 +324,15 @@ them with a traits with inexact constructions, the tag
\subsection AlphaShape_3DExampleForPeriodicAlphaShapes Example for Periodic Alpha Shapes
The following example shows how to use the periodic Delaunay
The following example shows how to use a periodic Delaunay
triangulation (Chapter \ref Chapter_3D_Periodic_Triangulations "3D Periodic Triangulations") as underlying
triangulation for the alpha shape computation.
triangulation for the alpha shape computation. Usage of a weighted Delaunay periodic
triangulation is presented in the example: \ref Alpha_shapes_3/ex_weighted_periodic_alpha_shapes_3.cpp "ex_weighted_periodic_alpha_shapes_3.cpp".
In order to define the original domain and to benefit from the
built-in heuristic optimizations of the periodic Delaunay
triangulation computation, it is recommended to first construct the
triangulation and then construct the alpha shape from it. The alpha
built-in heuristic optimizations of the periodic triangulation computation,
it is recommended to first construct the triangulation and
then construct the alpha shape from it. The alpha
shape constructor that takes a point range can be used as well but in
this case the original domain cannot be specified and the default unit
cube will be chosen and no optimizations will be used.

5
Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Alpha_shape_3.h
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@ -17,8 +17,9 @@ The modifying functions `insert` and `remove` will overwrite
the one inherited from the underlying triangulation class `Dt`.
At the moment, only the static version is implemented.
\tparam Dt must be either `Delaunay_triangulation_3`, `Regular_triangulation_3`
or `Periodic_3_triangulation_3`. Note that `Dt::Geom_traits`, `Dt::Vertex`, and `Dt::Face`
\tparam Dt must be either `Delaunay_triangulation_3`, `Regular_triangulation_3`,
`Periodic_3_Delaunay_triangulation_3` or `Periodic_3_regular_triangulation_3`.
Note that `Dt::Geom_traits`, `Dt::Vertex`, and `Dt::Face`
must be model the concepts `AlphaShapeTraits_3`,
`AlphaShapeVertex_3` and `AlphaShapeCell_3`, respectively.

5
Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Fixed_alpha_shape_3.h
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@ -12,8 +12,9 @@ represents connectivity and order among its faces. Each
\f$ k\f$-dimensional face of the `Dt` is associated with
a classification that specifies its status in the alpha complex, alpha being fixed.
\tparam Dt must be either `Delaunay_triangulation_3`, `Regular_triangulation_3`
or `Periodic_3_triangulation_3`. Note that `Dt::Geom_traits`, `Dt::Vertex`, and `Dt::Face`
\tparam Dt must be either `Delaunay_triangulation_3`, `Regular_triangulation_3`,
`Periodic_3_Delaunay_triangulation_3` or `Periodic_3_regular_triangulation_3`.
Note that `Dt::Geom_traits`, `Dt::Vertex`, and `Dt::Face`
must be model the concepts `AlphaShapeTraits_3`,
`AlphaShapeVertex_3` and `AlphaShapeFace_3`, respectively.

1
Alpha_shapes_3/doc/Alpha_shapes_3/examples.txt
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@ -5,5 +5,6 @@
\example Alpha_shapes_3/ex_fixed_weighted_alpha_shapes_3.cpp
\example Alpha_shapes_3/ex_periodic_alpha_shapes_3.cpp
\example Alpha_shapes_3/ex_weighted_alpha_shapes_3.cpp
\example Alpha_shapes_3/ex_weighted_periodic_alpha_shapes_3.cpp
\example Alpha_shapes_2/ex_alpha_projection_traits.cpp
*/

5
Periodic_3_triangulation_3/doc/Periodic_3_triangulation_3/Periodic_3_triangulation_3.txt
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@ -455,8 +455,9 @@ of a 3D regular triangulation.
\subsection Periodic_3_triangulation_3PeriodicAlphaShapes Periodic Alpha Shapes
It is possible to use the class `Periodic_3_Delaunay_triangulation_3`
as underlying triangulation for computing alpha shapes. For an example see
It is possible to use the classes `Periodic_3_Delaunay_triangulation_3`
and `Periodic_3_regular_triangulation_3` as underlying triangulations
to compute alpha shapes. Examples of usage can be found in
Section \ref AlphaShape_3DExampleForPeriodicAlphaShapes of the chapter on
3D alpha shapes.