mirror of https://github.com/CGAL/cgal
fixes to take into account Efi's comments
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@ -4,14 +4,23 @@
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\minitoc
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\begin{ccTexOnly}
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%\begin{ccTexOnly}
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%\begin{center}
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%\includegraphics[height=10cm]{Surface_mesher/skull-surface}
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%\end{center}
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%\end{ccTexOnly}
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%\begin{ccHtmlOnly}
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%<img border="0" src="./skull-surface.png" align="center" height="75%">
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%\end{ccHtmlOnly}
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\begin{center}
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\includegraphics[height=10cm]{Surface_mesher/skull-surface}
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\begin{ccTexOnly}
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\includegraphics[height=10cm]{Surface_mesher/skull-surface}
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\end{ccTexOnly}
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\begin{ccHtmlOnly}
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<img border="0" src="./skull-surface.png" height="75%">
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\end{ccHtmlOnly}
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\end{center}
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\end{ccTexOnly}
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\begin{ccHtmlOnly}
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<img border="0" src="./skull-surface.png" align="center" height="75%">
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\end{ccHtmlOnly}
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\section{Introduction}
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\label{SurfaceMesher_section_intro}
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@ -263,7 +272,7 @@ on the distance (Hausdorff and even Frechet distance)
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between the mesh and the surface
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if the radius bound is everywhere smaller than
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the $\epsilon$ times the local feature size.
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Here $\epsilon$ is a constant whish has to be
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Here $\epsilon$ is a constant which has to be
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less than 0.16, and the local feature size
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$lfs(x)$ is defined on each point $x$ of the surface
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as the distance from $x$ to the medial axis.
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@ -277,10 +286,10 @@ of local feature size on
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this surface).
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The value of the local feature size on any point of the surface
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or its minimum on the surface it usually not known
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or its minimum on the surface it usually unknown
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although it can sometimes be guessed. Also it happens frequently
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that setting the meshing criteria so as to fulfill the theoretical
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conditions yield an over refined mesh.
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conditions yields an over refined mesh.
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On the other hand, when the size criteria are relaxed,
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no homeomorphism with the input surface is guaranteed,
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and the output mesh is not even guaranteed to be manifold.
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@ -41,7 +41,7 @@ in the input 3D gray image.
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%$f(x,y,z)=0$, and \ccc{FT(1)} if $f(x,y,z)<0$. \ccRefName\ is a model of
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%\ccc{ImplicitFunction}.
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\ccRefName\ is a wrapper around an auxiliary library called
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\ccRefName\ provides an interface with an auxiliary library called
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\emph{ImageIO}. An executable that uses \ccRefName\ must be linked with the \emph{ImageIO}
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library. This library is shipped with \cgal\ in the
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\ccc{examples/Surface_mesher/} subdirectory.
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@ -16,12 +16,19 @@
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\ccDefinition
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The concept \ccRefName\ describes the requirements of the traits class to
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be plugged as \ccc{Traits} in \ccc{Implicit_surface_3<Traits, Function>}.
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The concept provides the types, predicates and constructors objects
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that are used in
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\ccc{Surface_mesh_traits_generator_3<Implicit_surface_3<Traits, Function>
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>::Type}, which is the model of \ccc{SurfaceMeshTraits_3} that is used
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when the first version of \ccc{make_surface_mesh} is called.
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be plugged as \ccc{Traits} in \ccc{Implicit_surface_3<Traits,
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Function>}.
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When \ccc{make_surface_mesh} is called
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with a surface of type \ccc{Implicit_surface_3<Traits,Function>},
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the surface mesher traits generator generates automatically
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a traits class that is a model of \ccc{SurfaceMeshTraits_3}.
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Actually,
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the concept \ccRefName\ provides the types, predicates and constructors
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that are passed
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to the generated model of \ccc{SurfaceMeshTraits_3}.
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\ccTypes
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@ -37,7 +37,7 @@ that has to be implemented with a model of
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\ccc{ImplicitSurfaceTraits_3}.
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Actually, this traits class implements the oracle needed by the
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surface mesher:
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the types, predicates and constructors objects provided
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the types, predicates and constructors provided
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in \ccc{Traits} are
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passed by the surface mesher traits generator
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to the generated the traits class
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@ -61,7 +61,7 @@ the type \ccc{Traits::FT}.
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\ccConstructor{
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Implicit_surface_3(Function f,
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Sphere_3 bounding_sphere,
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FT error_bound);}
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FT error_bound = FT(1e-3));}
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{\ccc{f} is the object of type \ccc{Function} that represents the implicit
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surface.\\
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\ccc{bounding_sphere} is a bounding sphere of the implicit surface. The
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