mirror of https://github.com/CGAL/cgal
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@ -1247,6 +1247,12 @@ Qt_widget/doc_tex/Qt_widget/triangulation.gif -text svneol=unset#unset
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Qt_widget/doc_tex/Qt_widget/triangulation.pdf -text svneol=unset#unset
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Qt_widget/src/CGALQt/CGALQt.sln -text
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Qt_widget/src/CGALQt/CGALQt.vcproj -text
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Ridges_3/doc_tex/Ridges_3/ellipsoid_ridges.eps -text
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Ridges_3/doc_tex/Ridges_3/ellipsoid_ridges.pdf -text
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Ridges_3/doc_tex/Ridges_3/ellipsoid_ridges_mesh.eps -text
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Ridges_3/doc_tex/Ridges_3/ellipsoid_ridges_mesh.jpg -text
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Ridges_3/doc_tex/Ridges_3/ellipsoid_ridges_mesh.pdf -text
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Ridges_3/include/CGAL/algo.C -text
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Robustness/demo/Robustness/robustness.vcproj -text
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This chapter describes the \cgal's package for the extraction of
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ridges on meshes. Given a smooth surface, a ridge is a curve along
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which one of the principal curvatures has an extremum along its
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curvature line. Ridges are curves of {\em extremal} curvature and
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therefore encode important informations used in segmentation,
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registration, matching and surface analysis. Based on the results of
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the article \cite{rr}, we propose several algorithms to identify and
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extract different parts of this singular ridge curve and some of its
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singularites on a surface given as a mesh.
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\subsection{Overview}
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%%%%%%%%%%%%%%%%%%%%%%
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2 main versions
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\begin{itemize}
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\item
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non-topologically oriented: we output several lists of ridges which
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are polylines, each list associated to a type: crest min/max,
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ellip/hyper, red/blue.
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each line has a weight enabling interactive filtering for the visu
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\item
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topologically oriented : we output a list of umbilics and some lists
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of ridges outside umbilic patches, turning points?
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\end{itemize}
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%%%%%%%%%%%%%%%%%%%%%%%
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\section{Introduction}
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\label{sec:intro}
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%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Ridges of a smooth surface}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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A comprehensive description of ridges can be found in
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\cite{ip-nss-71,hgyg-ttdpf-99,ip-gd-01}, and in the sequel, we just
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introduce the basic notions so as to explain our algorithms.
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Consider a smooth embedded surface, and denote $k_1$ and $k_2$ the
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principal curvatures, with $k_1\geq k_2$. Umbilics are the points
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where $k_1=k_2$. For any non umbilical point, the corresponding
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principal directions of curvature are well defined, and we denote them
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$d_1$ and $d_2$. In local coordinates, we denote $\langle , \rangle$
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the inner product induced by the ambient Euclidean space, and $dk_1$,
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$dk_2$ the gradients of the principal curvatures. Ridges, illustrated
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on Figs \ref{pict:ellipsoid_ridges} and \ref{fig:ridges_ellipsoid},
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are defined by:
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%%
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\begin{definition}
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\label{def:ridge-extrema}
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A non umbilical point is called
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\begin{itemize}
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\item
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%a blue ridge point if $\langle dk_1,d_1 \rangle=0$,
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a blue ridge point if the {\em extremality coefficient} $b_0=\langle
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dk_1,d_1 \rangle$ vanishes, i.e. $b_0=0$.
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\item
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%a red ridge point if $\langle dk_2,d_2 \rangle=0$.
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a red ridge point if the {\em extremality coefficient} $b_3=\langle
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dk_2,d_2 \rangle$ vanishes, i.e. $b_3=0$.
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\end{itemize}
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\end{definition}
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%We denote $b_0=\langle dk_1,d_1 \rangle$ and $b_3=\langle dk_2,d_2
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%\rangle$, and we call these functions the {\em extremality
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%coefficients}.
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%%
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Notice that, as the principal curvatures are not differentiable at
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umbilics, the extremality coefficients are not defined at such
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points. In addition, the sign of the extremality coefficients is not
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defined since the principal directions can be oriented by two opposite
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unit vectors. Apart from umbilics, special points on ridges are {\em
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purple} points, which correspond to intersections between red and a
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blue ridges. The previous characterization of ridges involves
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third-order differential properties. Using fourth-order differential
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quantities, a ridge point can further be qualified as {\em elliptic}
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if it corresponds to a maximum of $k_1$ or a minimum of $k_2$, or {\em
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hyperbolic} otherwise. Ridges of a given color change from elliptic to
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hyperbolic at special points called {\em turning} points.
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The calculation of ridges poses difficult problems, which are of three
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kinds.
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\paragraph{Topological difficulties.}
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Ridges of a smooth surface form a singular curve on the surface, with
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self-intersections at umbilics (more precisely at so-called 3-ridges
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umbilics), and purple points. Moreover, ridges have complex
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interactions with curvature lines at turning points. From the
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application standpoint, reporting ridges of a surface faithfully
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requires reporting umbilics, purple points and turning points.
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\paragraph{Numerical difficulties.}
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As pointed out above, ridges are characterized and qualified through
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third and fourth order derivatives of the surface. Estimating them
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depends on the particular type of surface processed ---implicitly
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defined, parameterized, discretized by a mesh--- and is numerically a
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difficult task.
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\paragraph{Orientation difficulties.}
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Since coefficients $b_0$ and $b_3$ depend on a given orientation of
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the principal directions, their sign is not well defined.
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Practically, tracking the sign change of functions whose sign depends
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on the particular orientation of the frame in which they are expressed
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poses a problem. In particular, tracking a zero-crossing of $b_0$ or
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$b_3$ from sign changes along a curve segment on the surface imposes
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to find a coherent orientation of the principal frame at the
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endpoints. Given two principal directions at these endpoints, one way
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to find a local orientation consists of choosing two vectors so that
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they make an acute angle, whence the name {\em Acute Rule}.
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%%
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\begin{minipage}[c]{.45\linewidth}
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\begin{figure}[H]
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\centerline{
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\includegraphics[height=5cm]{Ridges_3/ellipsoid_ridges_mesh}}
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\caption{Umbilics, ridges, and principal blue foliation on the
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ellipsoid (10k points)}
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\label{pict:ellipsoid_ridges}
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\end{figure}
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\end{minipage}
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%%
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\hfill
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%%
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\begin{minipage}[c]{.45\linewidth}
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\begin{figure}[H]
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\centerline{
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\includegraphics[height=5cm]{Ridges_3/ellipsoid_ridges}}
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\caption{Schematic view of the umbilics and the ridges. Max of $k_1$:
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blue; Min of $k_1$: green; Min of $k_2$: red; Max of $k_2$: yellow}
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\label{fig:ridges_ellipsoid}
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\end{figure}
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\end{minipage}
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%%%%%%%%%%%%%%%%%%%%%%%
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\section{Software Design}
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%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Options and interface specifications}
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%%%%%%%%%%%%%%%%%%%%%
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\subsection{Template parameters}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Output}
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%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Examples}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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p1 p0 midpoint /q0 defp
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p1 p0 midpoint /q0 defp
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p1 p2 midpoint /q3 defp
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p1 q0 thirdpoint /q1 defp
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p1 q3 thirdpoint /q2 defp q0 moveto q1 q2 q3 curveto
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p2 p1 midpoint /q0 defp
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p2 p0 midpoint /q3 defp
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p2 q0 thirdpoint /q1 defp
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p2 q3 thirdpoint /q2 defp q1 q2 q3 curveto
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p0 p2 midpoint /q0 defp
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gr
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62.7902 116.96 np arc
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1 0.647059 0 sc sk
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121.422 241.36 np arc
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-79.9992 38.976
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|
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|
||||
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|
||||
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|
||||
xspl
|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
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|
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||||
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|
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|
||||
1 0 1 sc sk
|
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|
||||
|
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|
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1.2 [ 4 ] ss
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np % # 4
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-85.8528 -117.902 mt
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-79.0236 -117.902 lt
|
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|
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|
||||
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|
||||
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|
||||
1 0 1 sc sfi
|
||||
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|
||||
1 0 1 sc sk
|
||||
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|
||||
|
||||
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|
||||
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|
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1.2 [ 4 ] ss
|
||||
np % # 4
|
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38.0484 -35.0784 mt
|
||||
44.8776 -35.0784 lt
|
||||
44.8776 -42.8736 lt
|
||||
38.0484 -42.8736 lt
|
||||
cl % cl
|
||||
% fic
|
||||
1 0 1 sc sfi
|
||||
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|
||||
1 0 1 sc sk
|
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|
||||
|
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|
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% ss 3855
|
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1.2 [ 4 ] ss
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|
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-210.73 -37.0272 mt
|
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-203.9 -37.0272 lt
|
||||
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|
||||
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|
||||
cl % cl
|
||||
% fic
|
||||
1 0 1 sc sfi
|
||||
% skc
|
||||
1 0 1 sc sk
|
||||
% End
|
||||
|
||||
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|
||||
% ss 3855
|
||||
1.2 [ 4 ] ss
|
||||
np % # 4
|
||||
-177.559 21.4368 mt
|
||||
-170.73 21.4368 lt
|
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|
||||
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|
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cl % cl
|
||||
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|
||||
0 sg sfi
|
||||
% sk
|
||||
0 sg sk
|
||||
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|
||||
|
||||
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|
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% ss 3855
|
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1.2 [ 4 ] ss
|
||||
np % # 4
|
||||
8.7804 21.4368 mt
|
||||
15.6096 21.4368 lt
|
||||
15.6096 13.6416 lt
|
||||
8.7804 13.6416 lt
|
||||
cl % cl
|
||||
% fi
|
||||
0 sg sfi
|
||||
% sk
|
||||
0 sg sk
|
||||
% End
|
||||
|
||||
% Line
|
||||
% ss 3855
|
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1.2 [ 4 ] ss
|
||||
np % # 4
|
||||
7.8048 -97.44 mt
|
||||
14.634 -97.44 lt
|
||||
14.634 -105.235 lt
|
||||
7.8048 -105.235 lt
|
||||
cl % cl
|
||||
% fi
|
||||
0 sg sfi
|
||||
% sk
|
||||
0 sg sk
|
||||
% End
|
||||
|
||||
% Line
|
||||
% ss 3855
|
||||
1.2 [ 4 ] ss
|
||||
np % # 4
|
||||
-174.632 -97.44 mt
|
||||
-167.803 -97.44 lt
|
||||
-167.803 -105.235 lt
|
||||
-174.632 -105.235 lt
|
||||
cl % cl
|
||||
% fi
|
||||
0 sg sfi
|
||||
% sk
|
||||
0 sg sk
|
||||
% End
|
||||
|
||||
% Line
|
||||
% ss 3855
|
||||
1.2 [ 4 ] ss
|
||||
np % # 4
|
||||
-119.999 -4.872 mt
|
||||
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|
||||
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|
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|
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cl % cl
|
||||
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|
||||
1 0 1 sc sfi
|
||||
% skc
|
||||
1 0 1 sc sk
|
||||
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|
||||
|
||||
% Line
|
||||
% ss 3855
|
||||
1.2 [ 4 ] ss
|
||||
np % # 4
|
||||
-44.8776 -63.336 mt
|
||||
-38.0484 -63.336 lt
|
||||
-38.0484 -71.1312 lt
|
||||
-44.8776 -71.1312 lt
|
||||
cl % cl
|
||||
% fic
|
||||
1 0 1 sc sfi
|
||||
% skc
|
||||
1 0 1 sc sk
|
||||
% End
|
||||
|
||||
% End
|
||||
|
||||
end %% of Ipe figure
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|
||||
%%EndDocument
|
||||
@endspecial White 2211 1474 V 0 1477 2215 4 v Black
|
||||
eop end
|
||||
%%Trailer
|
||||
|
||||
userdict /end-hook known{end-hook}if
|
||||
%%EOF
|
||||
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|
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|
|
@ -0,0 +1,8 @@
|
|||
\chapter{Ridge extraction on meshes}
|
||||
\label{chap:Ridges_3}
|
||||
\ccChapterAuthor{Marc Pouget and Frédéric Cazals}
|
||||
|
||||
\minitoc
|
||||
|
||||
\input{Ridges_3/Ridges_3_user.tex}
|
||||
|
||||
|
|
@ -0,0 +1,226 @@
|
|||
#ifndef _POLYHEDRALSURF_H_
|
||||
#define _POLYHEDRALSURF_H_
|
||||
|
||||
#include <CGAL/Cartesian.h>
|
||||
#include <CGAL/Polyhedron_3.h>
|
||||
#include <CGAL/IO/Polyhedron_iostream.h>
|
||||
|
||||
#include <algorithm>
|
||||
#include <vector>
|
||||
#include <list>
|
||||
|
||||
#include <stdlib.h>
|
||||
#include <stdio.h>
|
||||
|
||||
#include "PolyhedralSurf_operations.h"
|
||||
|
||||
//----------------------------------------------------------------
|
||||
// A redefined items class for the Polyhedron_3 with a refined vertex
|
||||
// class that contains a member for the mesh normal vector and a refined
|
||||
// facet with a normal vector instead of the plane equation (this is
|
||||
// an alternative solution instead of using Polyhedron_traits_with_normals_3).
|
||||
//----------------------------------------------------------------
|
||||
// in addition vertices contains monge info
|
||||
// some tags....
|
||||
template < class Refs, class Tag, class Pt, class FGeomTraits >
|
||||
class My_vertex:public CGAL::HalfedgeDS_vertex_base < Refs, Tag, Pt >
|
||||
{
|
||||
protected:
|
||||
typedef typename Refs::Vertex Vertex;
|
||||
typedef typename Refs::Halfedge Halfedge;
|
||||
typedef typename Refs::Face Facet;
|
||||
|
||||
typedef typename FGeomTraits::FT FT;
|
||||
typedef typename FGeomTraits::Point_3 Point_3;
|
||||
typedef typename FGeomTraits::Vector_3 Vector_3;
|
||||
|
||||
protected:
|
||||
//monge info
|
||||
Vector_3 d1; //max ppal dir
|
||||
Vector_3 d2; //min ppal dir; monge normal is then n_m=d1^d2, should be so that n_m.n_mesh>0
|
||||
FT k1, k2; //max/min ppal curv
|
||||
FT b0, b3; //blue/red extremalities
|
||||
FT P1, P2; //if fourth order quantities
|
||||
|
||||
//this is for collecting i-th ring neighbours
|
||||
char ring_tag;
|
||||
int ring_index;
|
||||
|
||||
public:
|
||||
//monge info
|
||||
const Vector _3 d1() const { return d1; }
|
||||
Vector_3& d1() { return d1; }
|
||||
const Vector _3 d2() const { return d2; }
|
||||
Vector_3& d2() { return d2; }
|
||||
const FT k1() const { return k1; }
|
||||
FT& k1() { return k1; }
|
||||
const FT k2() const { return k2; }
|
||||
FT& k2() { return k2; }
|
||||
const FT b0() const { return b0; }
|
||||
FT& b0() { return b0; }
|
||||
const FT b3() const { return b3; }
|
||||
FT& b3() { return b3; }
|
||||
const FT P1() const { return P1; }
|
||||
FT& P1() { return P1; }
|
||||
const FT P2() const { return P2; }
|
||||
FT& P2() { return P2; }
|
||||
|
||||
//this is for collecting i-th ring neighbours
|
||||
void setRingIndex(int i) { ring_index = i; }
|
||||
int getRingIndex() { return ring_index; }
|
||||
void resetRingIndex() { ring_index = -1; }
|
||||
void setRingTag() { ring_tag = 1; }
|
||||
char getRingTag() { return ring_tag; }
|
||||
|
||||
My_vertex(const Point_3 & pt):
|
||||
CGAL::HalfedgeDS_vertex_base < Refs, Tag, Point_3 > (pt),
|
||||
ring_tag(0), ring_index(-1) {}
|
||||
My_vertex() {}
|
||||
};
|
||||
|
||||
//----------------------------------------------------------------
|
||||
// Facet with normal and possibly more types. types are recovered
|
||||
//from the FGeomTraits template arg
|
||||
//----------------------------------------------------------------
|
||||
template < class Refs, class Tag, class FGeomTraits >
|
||||
class My_facet:public CGAL::HalfedgeDS_face_base < Refs, Tag >
|
||||
{
|
||||
//protected:
|
||||
public:
|
||||
typedef typename Refs::Vertex Vertex;
|
||||
typedef typename Refs::Vertex_handle Vertex_handle;
|
||||
typedef typename Refs::Halfedge Halfedge;
|
||||
typedef typename Refs::Halfedge_handle Halfedge_handle;
|
||||
|
||||
typedef typename FGeomTraits::Vector_3 Vector_3;
|
||||
typedef typename FGeomTraits::Point_3 Point_3;
|
||||
|
||||
public:
|
||||
Vector_3 normal;
|
||||
|
||||
public:
|
||||
My_facet(): ring_index(-1) {}
|
||||
Vector_3 & getUnitNormal() { return normal; }
|
||||
void setNormal(Vector_3 & n) { normal = n; }
|
||||
|
||||
//this is for collecting i-th ring neighbours
|
||||
protected:
|
||||
int ring_index;
|
||||
public:
|
||||
void setRingIndex(int i) { ring_index = i; }
|
||||
int getRingIndex() { return ring_index; }
|
||||
void resetRingIndex() { ring_index = -1; }
|
||||
};
|
||||
|
||||
//----------------------------------------------------------------
|
||||
// Halfedge
|
||||
//----------------------------------------------------------------
|
||||
template < class Refs, class Tprev, class Tvertex, class Tface, class FGeomTraits >
|
||||
class My_halfedge:public CGAL::HalfedgeDS_halfedge_base < Refs, Tprev, Tvertex, Tface >
|
||||
{
|
||||
protected:
|
||||
typedef typename FGeomTraits::Point_3 Point_3;
|
||||
typedef typename FGeomTraits::Vector_3 Vector_3;
|
||||
|
||||
protected:
|
||||
int ring_index;
|
||||
double len;
|
||||
public:
|
||||
void setRingIndex(int i) { ring_index = i; }
|
||||
int getRingIndex() {return ring_index; }
|
||||
void resetRingIndex() {ring_index = -1; }
|
||||
public:
|
||||
My_halfedge(): ring_index(-1) {}
|
||||
void setLength(double l) { len = l; }
|
||||
double getLength() { return len; }
|
||||
};
|
||||
|
||||
//------------------------------------------------
|
||||
// Wrappers [Vertex, Face, Halfedge]
|
||||
//------------------------------------------------
|
||||
struct Wrappers_VFH:public CGAL::Polyhedron_items_3 {
|
||||
// wrap vertex
|
||||
template < class Refs, class Traits > struct Vertex_wrapper {
|
||||
typedef struct {
|
||||
public:
|
||||
typedef typename Traits::Point_3 Point_3;
|
||||
typedef typename Traits::Vector_3 Vector_3;
|
||||
typedef typename Traits::Plane_3 Plane_3;
|
||||
} FGeomTraits;
|
||||
typedef typename Traits::Point_3 Point_3;
|
||||
typedef My_vertex < Refs, CGAL::Tag_true, Point_3, FGeomTraits > Vertex;
|
||||
};
|
||||
|
||||
// wrap face
|
||||
//NOTE: [HDS, Face] renamed [Polyhedron, Facet]
|
||||
template < class Refs, class Traits > struct Face_wrapper {
|
||||
//typedef typename Traits::Vector_3 Vector_3;
|
||||
//all types needed by the facet...
|
||||
typedef struct {
|
||||
public:
|
||||
typedef typename Traits::Point_3 Point_3;
|
||||
typedef typename Traits::Vector_3 Vector_3;
|
||||
typedef typename Traits::Plane_3 Plane_3;
|
||||
} FGeomTraits;
|
||||
//custom type instantiated...
|
||||
typedef My_facet < Refs, CGAL::Tag_true, FGeomTraits > Face;
|
||||
};
|
||||
|
||||
// wrap halfedge
|
||||
template < class Refs, class Traits > struct Halfedge_wrapper {
|
||||
typedef struct {
|
||||
public:
|
||||
typedef typename Traits::Point_3 Point_3;
|
||||
typedef typename Traits::Vector_3 Vector_3;
|
||||
typedef typename Traits::Plane_3 Plane_3;
|
||||
} FGeomTraits;
|
||||
typedef My_halfedge < Refs,
|
||||
CGAL::Tag_true,
|
||||
CGAL::Tag_true, CGAL::Tag_true, FGeomTraits > Halfedge;
|
||||
};
|
||||
};
|
||||
|
||||
//------------------------------------------------
|
||||
// Polyhedron
|
||||
//------------------------------------------------
|
||||
//using standard Cartesian kernel
|
||||
typedef double DFT;
|
||||
typedef CGAL::Cartesian<DFT> Data_Kernel;
|
||||
|
||||
typedef CGAL::Polyhedron_3 < Data_Kernel, Wrappers_VFH > Polyhedron;
|
||||
typedef Polyhedron::Vertex Vertex;
|
||||
typedef Polyhedron::Vertex_handle Vertex_handle;
|
||||
typedef Polyhedron::Halfedge Halfedge;
|
||||
typedef Polyhedron::Halfedge_handle Halfedge_handle;
|
||||
|
||||
typedef Polyhedron::Vertex_iterator Vertex_iterator;
|
||||
typedef Polyhedron::Halfedge_iterator Halfedge_iterator;
|
||||
typedef Polyhedron::
|
||||
Halfedge_around_vertex_circulator Halfedge_around_vertex_circulator;
|
||||
typedef Polyhedron::
|
||||
Halfedge_around_facet_circulator Halfedge_around_facet_circulator;
|
||||
typedef Polyhedron::Facet_iterator Facet_iterator;
|
||||
|
||||
typedef Data_Kernel::Point_3 DPoint;
|
||||
typedef Data_Kernel::Vector_3 Vector_3;
|
||||
typedef Data_Kernel::Plane_3 Plane_3;
|
||||
typedef Data_Kernel::Sphere_3 Sphere_3;
|
||||
|
||||
/////////////////////class PolyhedralSurf///////////////////////////
|
||||
class PolyhedralSurf:public Polyhedron {
|
||||
public:
|
||||
typedef Data_Kernel::Point_3 DPoint;
|
||||
typedef Data_Kernel::Vector_3 Vector_3;
|
||||
typedef Data_Kernel::Plane_3 Plane_3;
|
||||
|
||||
public:
|
||||
static Vector_3 getHalfedge_vector(Halfedge * h);
|
||||
|
||||
PolyhedralSurf() {}
|
||||
void compute_edges_length();
|
||||
double compute_mean_edges_length_around_vertex(Vertex * v);
|
||||
void compute_facets_normals();
|
||||
Vector_3 computeFacetsAverageUnitNormal(Vertex * v);
|
||||
};
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,379 @@
|
|||
#ifndef _RIDGE_3_H_
|
||||
#define _RIDGE_3_H_
|
||||
|
||||
#include <pair>
|
||||
|
||||
|
||||
//Orient monge normal according to mesh normals.
|
||||
|
||||
CGAL_BEGIN_NAMESPACE
|
||||
|
||||
|
||||
enum Ridge_type {NONE=0, BLUE, RED, CREST, BE, BH, BC, RE, RH, RC};
|
||||
|
||||
|
||||
//---------------------------------------
|
||||
//Ridge_line : a connected sequence of edges crossed by a ridge, with type and weigths
|
||||
//---------------------------------------
|
||||
template < class Poly > class Ridge_line
|
||||
{
|
||||
public:
|
||||
typedef typename Poly::Traits::FT FT;
|
||||
typedef typename Poly::Vertex_handle Vertex_handle;
|
||||
typedef typename Poly::Halfedge_handle Halfedge_handle;
|
||||
typedef typename Poly::Facet_handle Facet_handle;
|
||||
typedef std::pair<Halfedge_handle, FT> ridge_he;
|
||||
|
||||
protected:
|
||||
Ridge_type line_type
|
||||
std::list<ridge_he> line;
|
||||
FT strength;
|
||||
FT sharpness;
|
||||
|
||||
public:
|
||||
const FT weight() const {return weight;}
|
||||
const FT sharpness() const {return sharpness;}
|
||||
std::list<ridge_he>* line() { return &line;}
|
||||
|
||||
//constructor
|
||||
Ridge_line( Halfedge_handle h1, Halfedge_handle h2, Ridge_type r_type) :
|
||||
line_type(r_type), strength(0.)
|
||||
{};
|
||||
|
||||
//compute the barycentric coordinate of the xing point (blue or red)
|
||||
//for he: p->q coord is st xing_point = coord*p + (1-coord)*q
|
||||
FT bary_coord(Halfedge_handle he);
|
||||
void compute_weight(char color);
|
||||
void compute_sharpness(char color);
|
||||
//When the line is extended with a he, the bary coord of the
|
||||
//crossing point is computed, the pair (he,coord) is added and the
|
||||
//weigths are updated
|
||||
void addback( Halfedge_handle he);
|
||||
void addfront( Halfedge_handle he);
|
||||
|
||||
};
|
||||
|
||||
// IMPLEMENTATION OF Ridge_line members
|
||||
//////////////////////////////////////////////////////////////////////////////
|
||||
|
||||
//constructor
|
||||
template < class Poly >
|
||||
Ridge_line( Halfedge_handle h1, Halfedge_handle h2, Ridge_type r_type) :
|
||||
line_type(r_type), strength(0.)
|
||||
{
|
||||
line.push_back(h1);
|
||||
addback(h2);
|
||||
}
|
||||
|
||||
template < class Poly >
|
||||
void Ridge_line<Poly>::
|
||||
addback( Halfedge_handle he)
|
||||
{
|
||||
Halfedge_handle he_cur = ( --(line.end()) )->first;
|
||||
FT coord = bary_coord(he);
|
||||
FT coord_cur = bary_coord(he_cur);
|
||||
Vertex_handle v_p = he->opposite()->vertex(), v_q = he->vertex(),
|
||||
v_p_cur = he_cur->opposite()->vertex(), v_q_cur = he->vertex(); // he: p->q
|
||||
FT k;
|
||||
if ( (line_type == BE) || (line_type == BH) || (line_type == BC) ) {
|
||||
k =( std::fabs(v_p->k1) * coord + std::fabs(v_q->k1) * (1-coord) )/2;
|
||||
}
|
||||
if ( (line_type == RE) || (line_type == RH) || (line_type == RC) ) {
|
||||
k =( std::fabs(v_p->k2) * coord + std::fabs(v_q->k2) * (1-coord) )/2;
|
||||
}
|
||||
Vector_3 segment = (v_p->point()-ORIGIN)*coord + (v_q->point()-ORIGIN)*(1-coord) -
|
||||
((v_p_cur->point()-ORIGIN)*coord_cur + (v_q_cur->point()-ORIGIN)*(1-coord_cur));
|
||||
strength += k * CGAL::sqrt(segment * segment);
|
||||
|
||||
line.push_back( pair(he, coord));
|
||||
}
|
||||
|
||||
template < class Poly >
|
||||
void Ridge_line<Poly>::
|
||||
addfront( Halfedge_handle he)
|
||||
{
|
||||
Halfedge_handle he_cur = ( line.begin() )->first;
|
||||
FT coord = bary_coord(he);
|
||||
FT coord_cur = bary_coord(he_cur);
|
||||
Vertex_handle v_p = he->opposite()->vertex(), v_q = he->vertex(),
|
||||
v_p_cur = he_cur->opposite()->vertex(), v_q_cur = he->vertex(); // he: p->q
|
||||
FT k;
|
||||
if ( (line_type == BE) || (line_type == BH) || (line_type == BC) ) {
|
||||
k =( std::fabs(v_p->k1) * coord + std::fabs(v_q->k1) * (1-coord) )/2;
|
||||
}
|
||||
if ( (line_type == RE) || (line_type == RH) || (line_type == RC) ) {
|
||||
k =( std::fabs(v_p->k2) * coord + std::fabs(v_q->k2) * (1-coord) )/2;
|
||||
}
|
||||
Vector_3 segment = (v_p->point()-ORIGIN)*coord + (v_q->point()-ORIGIN)*(1-coord) -
|
||||
((v_p_cur->point()-ORIGIN)*coord_cur + (v_q_cur->point()-ORIGIN)*(1-coord_cur));
|
||||
strength += k * CGAL::sqrt(segment * segment);
|
||||
|
||||
line.push_front( pair(he, coord));
|
||||
}
|
||||
|
||||
|
||||
template < class Poly >
|
||||
FT Ridge_line<Poly>::
|
||||
bary_coord(Halfedge_handle he)
|
||||
{
|
||||
FT b_p, b_q; // extremalities at p and q for he: p->q
|
||||
if ( (line_type == BE) || (line_type == BH) || (line_type == BC) ) {
|
||||
b_p = he->opposite()->vertex()->b0();
|
||||
b_q = he->vertex()->b0();
|
||||
}
|
||||
if ( (line_type == RE) || (line_type == RH) || (line_type == RC) ) {
|
||||
b_p = he->opposite()->vertex()->b3();
|
||||
b_q = he->vertex()->b3();
|
||||
}
|
||||
return std::fabs(b_q) / ( std::fabs(b_q) + std::fabs(b_p) );
|
||||
}
|
||||
|
||||
|
||||
/////////Ridge_approximation//////////////////////////////////////////
|
||||
|
||||
//Find BLUE ridges (Elliptic or Hyperbolic)
|
||||
//do the same for RED and CREST
|
||||
//iterate on P facets, find a non-visited, regular, 2BXing triangle,
|
||||
//follow non-visited, regular, 2BXing triangles in both sens to create
|
||||
//a Ridge line.
|
||||
//Each time a edge is added the strength of the current line is updated
|
||||
// + length(edge)*|k|
|
||||
void
|
||||
compute_ridges(Ridge_type r_type)
|
||||
{
|
||||
//set all facets non visited
|
||||
|
||||
|
||||
Facet_iterator itb = P.facets_begin(), ite = P.facets_end();
|
||||
for(;itb!=ite;itb++)
|
||||
{
|
||||
Facet_handle f= &(*itb);
|
||||
if (f->is_visited()) continue;
|
||||
f->set_visited(true);
|
||||
Halfedge_handle h1, h2, curhe1, curhe2, curhe;
|
||||
|
||||
//h1 h2 are the hedges crossed if any, r_type should be BLUE,
|
||||
//RED or CREST ; cur_ridge_type should be BE, BH, BC, RE, RH, RC or NONE
|
||||
Ridge_type cur_ridge_type = facet_ridge_type(f,h1,h2,r_type)
|
||||
if ( cur_ridge_type == NONE ) continue;
|
||||
|
||||
//When a he is inserted in a Ridge_line, a pair <he,bary_coord>
|
||||
//is created and the weight(s) are updated
|
||||
Ridge_line *cur_ridge_line = new Ridge_line(h1,h2,cur_ridge_type);
|
||||
*ridge_lines_it++ = cur_ridge_line;
|
||||
|
||||
//next triangle adjacent to h1 (push_front)
|
||||
if ( !(h1->is_border_edge()) )
|
||||
{
|
||||
f = h1->opposite()->facet();
|
||||
curhe = h1;
|
||||
while (cur_ridge_type == facet_ridge_type(f,curhe1,curhe2,r_type))
|
||||
{
|
||||
//follow the ridge from curhe
|
||||
if (f->is_visited()) break;
|
||||
f->set_visited(true);
|
||||
if (curhe->opposite() == curhe1) curhe = curhe2;
|
||||
else curhe = curhe1;
|
||||
cur_ridge_line->addfront(curhe);
|
||||
if ( !(curhe->is_border_edge()) ) f =
|
||||
curhe->opposite()->facet();
|
||||
else break;
|
||||
}
|
||||
//exit from the while if
|
||||
//1. border
|
||||
//2. not same type, then do not set visisted cause a BE
|
||||
// follows a BH
|
||||
}
|
||||
|
||||
//next triangle adjacent to h2 (push_back)
|
||||
if ( !(h2->is_border_edge()) )
|
||||
{
|
||||
f = h2->opposite()->facet();
|
||||
curhe = h2;
|
||||
while (cur_ridge_type == facet_ridge_type(f,curhe1,curhe2,r_type))
|
||||
{
|
||||
//follow the ridge from curhe
|
||||
if (f->is_visitedB()) break;
|
||||
f->set_visitedB(true);
|
||||
if (curhe->opposite() == curhe1) curhe = curhe2;
|
||||
else curhe = curhe1;
|
||||
cur_ridge_line->addback(curhe);
|
||||
if ( !(curhe->is_border_edge()) ) f =
|
||||
curhe->opposite()->facet();
|
||||
else break;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
Ridge_type
|
||||
facet_ridge_type(Facet_handle f, Halfedge_handle& he1, Halfedge_handle&
|
||||
he2, Ridge_type r_type)
|
||||
{
|
||||
//polyhedral data
|
||||
//we have v1--h1-->v2--h2-->v3--h3-->v1
|
||||
Halfedge_handle h1 = f->halfedge(), h2, h3;
|
||||
Vertex_handle v1, v2, v3;
|
||||
v2 = h1->vertex();
|
||||
h2 = h1->next();
|
||||
v3 = h2->vertex();
|
||||
h3 = h2->next();
|
||||
v1 = h3->vertex();
|
||||
|
||||
//check for regular facet
|
||||
if ( v1->d1()*v2->d1() * v1->d1()*v3->d1() * v2->d1()*v3->d1() < 0 ) return NONE;
|
||||
|
||||
//determine potential crest color
|
||||
Ridge_type crest_color = NONE;
|
||||
if (r_type == CREST)
|
||||
{
|
||||
if ( std::fabs(v1->k1()+v2->k1()+v3->k1()) > std::fabs(v1->k2()+v2->k2()+v3->k2()) )
|
||||
crest_color = BC;
|
||||
if ( std::fabs(v1->k1()+v2->k1()+v3->k1()) < std::fabs(v1->k2()+v2->k2()+v3->k2()) )
|
||||
crest_color = RC;
|
||||
if ( std::fabs(v1->k1()+v2->k1()+v3->k1()) = std::fabs(v1->k2()+v2->k2()+v3->k2()) )
|
||||
return NONE;
|
||||
}
|
||||
|
||||
//compute Xing on the 3 edges
|
||||
bool h1_is_crossed, h2_is_crossed, h3_is_crossed;
|
||||
if ( r_type == BLUE || crest_color == BC )
|
||||
{
|
||||
xing_on_edge(h1, h1_is_crossed, BLUE);
|
||||
xing_on_edge(h2, h2_is_crossed, BLUE);
|
||||
xing_on_edge(h3, h3_is_crossed, BLUE);
|
||||
}
|
||||
if ( r_type == RED || crest_color == RC )
|
||||
{
|
||||
xing_on_edge(h1, h1_is_crossed, RED);
|
||||
xing_on_edge(h2, h2_is_crossed, RED);
|
||||
xing_on_edge(h3, h3_is_crossed, RED);
|
||||
}
|
||||
|
||||
//test of 2Xing
|
||||
if ( !(h1_is_crossed && h2_is_crossed && !h3_is_crossed) &&
|
||||
!(h1_is_crossed && !h2_is_crossed && h3_is_crossed) &&
|
||||
(!h1_is_crossed && h2_is_crossed && h3_is_crossed) )
|
||||
return NONE;
|
||||
if (h1_is_crossed && h2_is_crossed && !h3_is_crossed)
|
||||
{
|
||||
he1 = h1;
|
||||
he2 = h2;
|
||||
}
|
||||
if (h1_is_crossed && !h2_is_crossed && h3_is_crossed)
|
||||
{
|
||||
he1 = h1;
|
||||
he2 = h3;
|
||||
}
|
||||
if (!h1_is_crossed && h2_is_crossed && h3_is_crossed)
|
||||
{
|
||||
he1 = h2;
|
||||
he2 = h3;
|
||||
}
|
||||
|
||||
Vertex_handle v_p1 = he1->opposite()->vertex(), v_q1 = he1->vertex(),
|
||||
v_p2 = he2->opposite()->vertex(), v_q2 = he2->vertex(); // he1: p1->q1
|
||||
|
||||
if ( r_type == BLUE || crest_color == BC )
|
||||
{
|
||||
FT coord1 = std::fabs(v_q1->b0()) / ( std::fabs(v_p1->b0()) + std::fabs(v_q1->b0()) ),
|
||||
coord2 = std::fabs(v_q2->b0()) / ( std::fabs(v_p2->b0()) + std::fabs(v_q2->b0()) );
|
||||
Vector_3 r1 = (v_p1->point()-ORIGIN)*coord1 + (v_q1->point()-ORIGIN)*(1-coord1),
|
||||
r2 = (v_p2->point()-ORIGIN)*coord2 + (v_q2->point()-ORIGIN)*(1-coord2);
|
||||
int b_sign = b_sign_pointing_to_ridge(v1, v2, v3, r1, r2, BLUE);
|
||||
if (b_sign == 1) { if (r_type == BLUE) return BE; else return BC;}
|
||||
if (b_sign == -1) return BH;
|
||||
}
|
||||
if ( r_type == RED || crest_color == RC )
|
||||
{
|
||||
FT coord1 = std::fabs(v_q1->b3()) / ( std::fabs(v_p1->b3()) + std::fabs(v_q1->b3()) ),
|
||||
coord2 = std::fabs(v_q2->b3()) / ( std::fabs(v_p2->b3()) + std::fabs(v_q2->b3()) );
|
||||
Vector_3 r1 = (v_p1->point()-ORIGIN)*coord1 + (v_q1->point()-ORIGIN)*(1-coord1),
|
||||
r2 = (v_p2->point()-ORIGIN)*coord2 + (v_q2->point()-ORIGIN)*(1-coord2);
|
||||
int b_sign = b_sign_pointing_to_ridge(v1, v2, v3, r1, r2, RED);
|
||||
if (b_sign == -1) { if (r_type == RED) return RE; else return RC;}
|
||||
if (b_sign == 1) return BH;
|
||||
}
|
||||
assert(0);
|
||||
}
|
||||
|
||||
void
|
||||
xing_on_edge(Halfedge_handle he, bool& is_crossed, Ridge_type color)
|
||||
{
|
||||
is_crossed = false;
|
||||
FT sign;
|
||||
FT b_p, b_q; // extremalities at p and q for he: p->q
|
||||
Vector_3 d_p = he->opposite()->vertex()->d1(),
|
||||
d_q = he->vertex()->d1(); //ppal dir
|
||||
if ( color == BLUE ) {
|
||||
b_p = he->opposite()->vertex()->b0();
|
||||
b_q = he->vertex()->b0();
|
||||
}
|
||||
else {
|
||||
b_p = he->opposite()->vertex()->b3();
|
||||
b_q = he->vertex()->b3();
|
||||
}
|
||||
if ( b_p == 0 && b_q == 0 ) return;
|
||||
if ( b_p == 0 && b_q !=0 ) sign = d_p*d_q * b_q;
|
||||
if ( b_p != 0 && b_q ==0 ) sign = d_p*d_q * b_p;
|
||||
if ( b_p != 0 && b_q !=0 ) sign = d_p*d_q * b_p * b_q;
|
||||
if ( sign < 0 ) is_crossed = true;
|
||||
}
|
||||
|
||||
|
||||
|
||||
//for a ridge segment in a triangle [r1,r2], let r = r2 - r1 and normalize,
|
||||
//the projection of a point p on the line (r1,r2) is pp=r1+tr, with t=(p-r1)*r
|
||||
//then the vector v starting at p is pointing to the ridge line (r1,r2) if
|
||||
//(pp-p)*v >0
|
||||
int
|
||||
b_sign_pointing_to_ridge(Vertex_handle v1, Vertex_handle v2, Vertex_handle v3,
|
||||
Vector_3 r1, Vector_3 r2, Ridge_type color)
|
||||
{
|
||||
Vector_3 r = r2 - r1, dv1, dv2, dv3;
|
||||
FT bv1, bv2, bv3;
|
||||
if ( color == BLUE ) {
|
||||
bv1 = v1->b0();
|
||||
bv2 = v2->b0();
|
||||
bv3 = v3->b0();
|
||||
dv1 = v1->d1();
|
||||
dv2 = v2->d1();
|
||||
dv3 = v3->d1();
|
||||
}
|
||||
else {
|
||||
bv1 = v1->b3();
|
||||
bv2 = v2->b3();
|
||||
bv3 = v3->b3();
|
||||
dv1 = v1->d2();
|
||||
dv2 = v2->d2();
|
||||
dv3 = v3->d2();
|
||||
}
|
||||
if ( r !=0 ) r = r/CGAL::sqrt(r*r);
|
||||
FT sign1, sign2, sign3;
|
||||
sign1 = (r1 - (v1->point()-ORIGIN) + (((v1->point()-ORIGIN)-r1)*r)*r )*dv1;
|
||||
sign2 = (r1 - (v2->point()-ORIGIN) + (((v2->point()-ORIGIN)-r1)*r)*r )*dv2;
|
||||
sign3 = (r1 - (v3->point()-ORIGIN) + (((v3->point()-ORIGIN)-r1)*r)*r )*dv3;
|
||||
|
||||
int compt = 0;
|
||||
if ( sign1 > 0 ) compt++; else if (sign1 < 0) compt--;
|
||||
if ( sign2 > 0 ) compt++; else if (sign2 < 0) compt--;
|
||||
if ( sign3 > 0 ) compt++; else if (sign3 < 0) compt--;
|
||||
|
||||
if (compt > 0) return 1; else return -1;
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
CGAL_END_NAMESPACE
|
||||
|
||||
#endif
|
||||
|
|
@ -0,0 +1,2 @@
|
|||
Marc Pouget <Marc.Pouget@sophia.inria.fr>
|
||||
Frédéric Cazals <Frédéric.Cazals@sophia.inria.fr>
|
||||
Loading…
Reference in New Issue