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replace face by facet wherever it makes sense

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Jane Tournois 2025-06-02 12:15:39 +02:00
parent 9efcb22083
commit 08e0d6b839
1 changed files with 12 additions and 12 deletions
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24
Constrained_triangulation_3/doc/Constrained_triangulation_3/Constrained_triangulation_3.txt
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@ -38,12 +38,12 @@ This section introduces the key concepts necessary to understand and use this pa
\subsection CT_3_PLC Piecewise Linear Complex
A _Piecewise Linear Complex_ (PLC) is the three-dimensional generalization of a
planar straight-line graph. It consists of a finite set of vertices, edges, and polygons (faces)
planar straight-line graph. It consists of a finite set of vertices, edges, and polygons (facets)
that satisfy the following properties:
- The vertices and edges of the PLC form a simplicial complex: two edges may intersect only at a
shared vertex.
- The boundary of each polygon (face) in the PLC is an ordered list of vertices from the PLC, forming
- The boundary of each polygon (facet) in the PLC is an ordered list of vertices from the PLC, forming
one or more closed loops (for holes).
- If two polygons in the PLC intersect, their intersection is a union of edges and vertices from the
PLC. In particular, the interiors of two polygons cannot overlap.
@ -55,7 +55,7 @@ Polygons in a PLC may be non-convex, may have holes, and may have arbitrarily ma
<img src="plc.png" style="max-width:60%;"/>
</center>
\cgalFigureCaptionBegin{CT_3_plc_fig}
A Piecewise Linear Complex composed of planar faces connected by edges and vertices.
A Piecewise Linear Complex composed of planar facets connected by edges and vertices.
\cgalFigureCaptionEnd
@ -121,10 +121,10 @@ 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
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 faces covering the surface of a
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 faces cannot have holes.
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
@ -138,10 +138,10 @@ This package provides a way to group polygons into distinct surface patches usin
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,
they can be used to construct a conforming constrained Delaunay triangulation.
When a face patch property map is provided:
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 face, specifically those marking the boundary of patches.
- The surface patches themselves serve as the polygons (faces) in the resulting representation.
- 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 surface patches themselves serve as the polygons (facets) in the resulting representation.
\subsection CT_3_api_classes Classes
@ -183,16 +183,16 @@ following example demonstrates how to build such a triangulation.
\subsection CT_3_example_ccdt_fpmap Build a Conforming Constrained Delaunay Triangulation with Known Polygon Identifiers
If the user already knows the set of polygon identifiers to associate with each face, this information can be
If the user already knows the set of polygon identifiers to associate with each facet, this information can be
provided and preserved throughout the construction of the conforming constrained Delaunay
triangulation.
The following example demonstrates how to detect surface patches separated by sharp edges and use
this segmentation during the tetrahedralization process.
When the named parameter `plc_face_id` is specified, each constrained face in the 3D triangulation
is assigned to the corresponding input PLC face, identified in the provided property map.
If this parameter is not specified, each input polygon, or PLC face, is given a unique face index.
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.
\cgalExample{Constrained_triangulation_3/conforming_constrained_Delaunay_triangulation_3_fpmap.cpp}