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Tweak wording in the manuals for the 3D Polyhedral Surface pkg

This commit is contained in:
Nuno Miguel Nobre 2023-06-20 12:51:12 +01:00
parent 43d2188068
commit e22e256e69
2 changed files with 14 additions and 12 deletions
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10
Polyhedron/doc/Polyhedron/CGAL/Polyhedron_3.h
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@ -11,14 +11,14 @@ namespace CGAL {
\image latex halfedge.png
Vertices represent points in 3d-space. Edges are straight line segments
between two endpoints. Facets are planar polygons without holes
defined by the circular sequence of halfedges along their boundary.
The polyhedral surface itself can have holes. The halfedges
between two endpoints. Facets are planar, possibly non-convex, polygons
without holes defined by the circular sequence of halfedges along their
boundary. The polyhedral surface itself can have holes. The halfedges
along the boundary of a hole are called <I>border halfedges</I> and
have no incident facet. An edge is a <I>border edge</I> if one of
its halfedges is a border halfedge. A surface is <I>closed</I> if it
contains no border halfedges. A closed surface is a boundary
representation for polyhedra in three dimensions. The convention is
representation for a polyhedron in three dimensions. The convention is
that the halfedges are oriented counterclockwise around facets as seen
from the outside of the polyhedron. An implication is that the
halfedges are oriented clockwise around the vertices. The notion of
@ -32,7 +32,7 @@ namespace CGAL {
always an orientable and oriented 2-manifold with border edges, i.e.,
the neighborhood of each point on the polyhedral surface is either
homeomorphic to a disc or to a half disc, except for vertices where
many holes and surfaces with boundary can join. Another implication is
multiple holes join. Another implication is
that the smallest representable surface is a triangle (for polyhedral
surfaces with border edges) or a tetrahedron (for polyhedra). Boundary
representations of orientable 2-manifolds are closed under Euler

16
Polyhedron/doc/Polyhedron/Polyhedron.txt
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@ -15,7 +15,7 @@ edges, facets and an incidence relationship on them. The organization
beneath is a halfedge data structure, which restricts the class of
representable surfaces to orientable 2-manifolds - with and without
boundary. If the surface is closed we call it a <I>polyhedron</I>, for
example, see the following model of a hammerhead:
example, see the following model of a hammerhead:
\image html shark.png
\image latex shark.png
@ -26,8 +26,8 @@ the combinatorial integrity of them. It is based on the highly
flexible design of the halfedge data structure, see the introduction
in Chapter \ref chapterHalfedgeDS "Halfedge Data Structures" and \cgalCite{k-ugpdd-99}. However, the
polyhedral surface can be used and understood without knowing the
underlying design. Some of the examples in this chapter introduce also
gradually into first applications of this flexibility.
underlying design. Some of the examples in this chapter gradually
introduce applications of this flexibility.
\section PolyhedronDefinition Definition
@ -41,13 +41,15 @@ halfedge are illustrated in the following figure:
\image latex halfedge_small.png
Vertices represent points in space. Edges are straight line segments
between two endpoints. Facets are planar polygons without
between two endpoints. Facets are planar, possibly non-convex, polygons without
holes. Facets are defined by the circular sequence of halfedges along
their boundary. The polyhedral surface itself can have holes (with at
least two facets surrounding it since a single facet cannot have a
hole). The halfedges along the boundary of a hole are called <I>border halfedges</I> and have no incident facet. An edge is a <I>border edge</I> if one of its halfedges is a border halfedge. A
hole). The halfedges along the boundary of a hole are called
<I>border halfedges</I> and have no incident facet. An edge is a
<I>border edge</I> if one of its halfedges is a border halfedge. A
surface is <I>closed</I> if it contains no border halfedges. A closed
surface is a boundary representation for polyhedra in three
surface is a boundary representation for a polyhedron in three
dimensions. The convention is that the halfedges are oriented
counterclockwise around facets as seen from the outside of the
polyhedron. An implication is that the halfedges are oriented
@ -62,7 +64,7 @@ implication of this definition is that the polyhedral surface is
always an orientable and oriented 2-manifold with border edges, i.e.,
the neighborhood of each point on the polyhedral surface is either
homeomorphic to a disc or to a half disc, except for vertices where
many holes and surfaces with boundary can join. Another implication is
multiple holes join. Another implication is
that the smallest representable surface avoiding self intersections is
a triangle (for polyhedral surfaces with border edges) or a
tetrahedron (for polyhedra). Boundary representations of orientable