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minor rephrases in the documentation

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Laurent Rineau 2025-06-03 16:59:11 +02:00
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Constrained_triangulation_3/doc/Constrained_triangulation_3/Constrained_triangulation_3.txt
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@ -118,29 +118,29 @@ Right: the same CCDT seen with cutplane.
There is no universal or canonical way to represent all possible PLCs in \cgal.
Since any polyhedron is a PLC, any model of `FaceListGraph`, such as `CGAL::Surface_mesh`, can be
Any polyhedral surface is a PLC, so any model of `FaceListGraph`, such as `CGAL::Surface_mesh`, can be
used to represent a PLC.
In this case, the polygons of the PLC correspond to the faces of the
surface _mesh_, a collection of vertices (points), edges, and facets covering the surface of a
a geometric object.
The edges of the PLC correspond to the edges of the surface mesh. However, PLCs
represented in this way are restricted to be manifold, and their facets cannot have holes.
In this representation, the faces of the PLC correspond to the faces of the
surface mesh—a collection of vertices (points), edges, and facets that cover the surface of a
geometric object.
The vertices of the PLC are the vertices of the surface mesh, the edges of the PLC are the edges
of the surface mesh, and the polygons of the PLC are the facets of the surface mesh.
However, PLCs represented in this way are restricted to be manifold, and their facets cannot have holes.
A PLC can also be represented as a polygon soup: a collection of vertices and a set of polygons, where
each polygon is defined by an ordered list of vertices, and the connectivity information is not
explictly provided.
For a polygon soup to represent a valid PLC,
its polygons must satisfy the properties outlined in the previous section. This approach allows for
the representation of non-manifold geometries, but note that polygons in a polygon soup cannot have
holes.
each polygon is defined by an ordered list of vertices, without explicit connectivity information between
polygons. For a polygon soup to represent a valid PLC, its polygons must satisfy the properties described
in the previous section. This approach allows for the representation of non-manifold geometries; however,
polygons in a polygon soup cannot have holes.
This package provides a way to group polygons into distinct surface patches using a property map.
Each polygon is assigned a _patch_ identifier, allowing multiple polygons to form a continuous surface patch,
which may include holes. When these patches are planar and meet the necessary geometric conditions,
This package also provides a way to group polygons into distinct surface patches using a property map.
Each polygon can be assigned a _patch_ identifier, allowing multiple polygons to form a continuous surface patch,
which may include holes. When these patches are planar and satisfy the necessary geometric conditions,
they can be used to construct a conforming constrained Delaunay triangulation.
When a property map is provided:
- The vertices of the PLC are the ones from the original surface mesh or polygon soup.
- The edges of the PLC are those that belong to the surface mesh or polygon soup and have only one adjacent facet, specifically those marking the boundary of patches.
- The vertices of the PLC are those from the original surface mesh or polygon soup.
- The edges of the PLC are those belonging to the surface mesh or polygon soup that have only one
adjacent facet, specifically those marking the boundaries of patches.
- The surface patches themselves serve as the polygons (facets) in the resulting representation.
\subsection CT_3_api_classes Classes
@ -175,8 +175,9 @@ Delaunay triangulation from a given PLC.
\subsection CT_3_example_ccdt_soup Build a Conforming Constrained Delaunay Triangulation from a Polygon Soup
You can also construct a conforming constrained Delaunay triangulation from a polygon soup. The
following example demonstrates how to build such a triangulation.
You can also construct a conforming constrained Delaunay triangulation from a polygon soup.
The following example demonstrates how to create such a triangulation from a collection of polygons
without explicit connectivity information.
\cgalExample{Constrained_triangulation_3/ccdt_3_from_soup.cpp }
@ -188,12 +189,11 @@ provided and preserved throughout the construction of the conforming constrained
triangulation.
The following example demonstrates how to detect planar surface patches, remesh them as coarsely
as possible, and use
this segmentation during the tetrahedralization process.
as possible, and use this segmentation during the tetrahedralization process.
When the named parameter `plc_facet_id` is specified, each constrained facet in the 3D triangulation
is assigned to the corresponding input PLC facet, identified in the provided property map.
If this parameter is not specified, each input polygon, or PLC facet, is given a unique facet index.
is assigned to the corresponding input PLC facet, as identified by the provided property map.
If this parameter is not specified, each input polygon (or PLC facet) is assigned a unique facet index.
\cgalExample{Constrained_triangulation_3/conforming_constrained_Delaunay_triangulation_3_fimap.cpp}
@ -215,24 +215,23 @@ From left to right: Input PLC;
\subsection CT_3_example_ccdt_region_growing_fimap Build a Conforming Constrained Delaunay Triangulation with Detected Polygon Identifiers
If the user does not know the set of polygon identifiers to associate with each PLC facet, this information can be
detected using the \link CGAL::Polygon_mesh_processing::region_growing_of_planes_on_faces(const PolygonMesh& mesh,RegionMap region_map,const NamedParameters& np = parameters::default_values()) CGAL::Polygon_mesh_processing::region_growing_of_planes_on_faces()`\endlink
automatically detected using the \link CGAL::Polygon_mesh_processing::region_growing_of_planes_on_faces(const PolygonMesh& mesh,RegionMap region_map,const NamedParameters& np = parameters::default_values()) `CGAL::Polygon_mesh_processing::region_growing_of_planes_on_faces()`\endlink
function from the \ref PkgPolygonMeshProcessing package.
The following example demonstrates how to detect planar surface patches, and build a conforming
constrained Delaunay triangulation using the detected segmentation, using the
the named parameter `plc_facet_id` to associate each facet of the triangulation with the
corresponding input PLC facet.
The following example demonstrates how to detect planar surface patches and build a conforming
constrained Delaunay triangulation using the detected segmentation. The named parameter `plc_facet_id`
is used to associate each facet of the triangulation with the corresponding input PLC facet.
\cgalExample{Constrained_triangulation_3/ccdt_3_fimap_region_growing.cpp}
\subsection CT_3_examples_preprocessing Preprocessing the Input for Conforming Constrained Delaunay Triangulations
Given a PLC, the algorithms in this package can construct a conforming constrained Delaunay, provided
the input surface can be represented as a valid surface mesh or set of surface meshes,
Given a PLC, the algorithms in this package can construct a conforming constrained Delaunay triangulation, provided
the input surface can be represented as a valid surface mesh or a collection of surface meshes,
and does not contain self-intersections.
Numerous preprocessing functions are available in the \ref PkgPolygonMeshProcessing package to enforce these
preconditions.
Several preprocessing functions are available in the \ref PkgPolygonMeshProcessing package to help ensure these
preconditions are met.
\subsubsection CT_3_example_ccdt_autorefinement Autorefinement of the Input Mesh