From e22e256e69975a9e32bc1aebabf1d3413d5d9cc7 Mon Sep 17 00:00:00 2001 From: Nuno Miguel Nobre Date: Tue, 20 Jun 2023 12:51:12 +0100 Subject: [PATCH] Tweak wording in the manuals for the 3D Polyhedral Surface pkg --- Polyhedron/doc/Polyhedron/CGAL/Polyhedron_3.h | 10 +++++----- Polyhedron/doc/Polyhedron/Polyhedron.txt | 16 +++++++++------- 2 files changed, 14 insertions(+), 12 deletions(-) diff --git a/Polyhedron/doc/Polyhedron/CGAL/Polyhedron_3.h b/Polyhedron/doc/Polyhedron/CGAL/Polyhedron_3.h index 6b05551327e..c848e1a247f 100644 --- a/Polyhedron/doc/Polyhedron/CGAL/Polyhedron_3.h +++ b/Polyhedron/doc/Polyhedron/CGAL/Polyhedron_3.h @@ -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 border halfedges and have no incident facet. An edge is a border edge if one of its halfedges is a border halfedge. A surface is closed 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 diff --git a/Polyhedron/doc/Polyhedron/Polyhedron.txt b/Polyhedron/doc/Polyhedron/Polyhedron.txt index 0cef005c0ab..6f986bd9e1e 100644 --- a/Polyhedron/doc/Polyhedron/Polyhedron.txt +++ b/Polyhedron/doc/Polyhedron/Polyhedron.txt @@ -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 polyhedron, 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 border halfedges and have no incident facet. An edge is a border edge if one of its halfedges is a border halfedge. A +hole). The halfedges along the boundary of a hole are called +border halfedges and have no incident facet. An edge is a +border edge if one of its halfedges is a border halfedge. A surface is closed 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