From a503ce19040564e68fcdc0ffc5db901b1b33a9e0 Mon Sep 17 00:00:00 2001
From: Pierre Alliez <Pierre.Alliez@sophia.inria.fr>
Date: Thu, 24 Jul 2003 15:59:10 +0000
Subject: [PATCH] updated doc

---
 .../Tutorial/tutorial/Polyhedron/doc/makefile |   4 +-
 .../tutorial/Polyhedron/doc/tutorial.pdf      | Bin 3326534 -> 3332687 bytes
 .../tutorial/Polyhedron/doc/tutorial.tex      | 428 ++++++++++++++++--
 3 files changed, 394 insertions(+), 38 deletions(-)

diff --git a/Packages/Tutorial/tutorial/Polyhedron/doc/makefile b/Packages/Tutorial/tutorial/Polyhedron/doc/makefile
index 65b0bca1c06..e3ba8c575dd 100644
--- a/Packages/Tutorial/tutorial/Polyhedron/doc/makefile
+++ b/Packages/Tutorial/tutorial/Polyhedron/doc/makefile
@@ -14,12 +14,12 @@ all:
 	make ps
 	make pdf
 	make clean
-	\rm *.ps
+	\rm *.ps *.tmp
 	clear
 	ls -l
 
 clean:
-	\rm *.aux *.dvi *.log
+	\rm *.aux *.dvi *.log *.out *.blg *.bbl
 
 superclean:
 	\rm *.ps *.pdf *~
diff --git a/Packages/Tutorial/tutorial/Polyhedron/doc/tutorial.pdf b/Packages/Tutorial/tutorial/Polyhedron/doc/tutorial.pdf
index 23f591b7d611f59439842735ec46fd95fe164c0c..4f266a92586eb80bcaf4b686efc047f20f1c77a1 100644
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diff --git a/Packages/Tutorial/tutorial/Polyhedron/doc/tutorial.tex b/Packages/Tutorial/tutorial/Polyhedron/doc/tutorial.tex
index 246a3beeb61..b8e907dc9ca 100644
--- a/Packages/Tutorial/tutorial/Polyhedron/doc/tutorial.tex
+++ b/Packages/Tutorial/tutorial/Polyhedron/doc/tutorial.tex
@@ -931,6 +931,398 @@ Polyhedron (see Section~\ref{sec:builder}).
 
 Subdivision engine
 
+{ \scriptsize
+\begin{verbatim}
+
+#include "enriched_polyhedron.h"
+#include "builder.h"
+
+template <class HDS,class Polyhedron,class kernel>
+class CModifierQuadTriangle : public CGAL::Modifier_base<HDS>
+{
+private:
+  typedef typename kernel::FT           FT;
+  typedef typename HDS::Vertex          Vertex;
+  typedef typename Vertex::Point        Point;
+  typedef typename HDS::Face_handle     Face_handle;
+  typedef typename HDS::Halfedge_handle Halfedge_handle;
+  typedef typename CGAL::Enriched_polyhedron_incremental_builder_3<HDS> builder;
+  typedef typename Polyhedron::Halfedge_around_vertex_circulator Halfedge_around_vertex_circulator;
+  typedef typename Polyhedron::Facet_handle Facet_handle;
+  typedef typename Polyhedron::Vertex_handle Vertex_handle;
+
+  Polyhedron *m_pMesh;
+
+public:
+
+  // life cycle
+  CModifierQuadTriangle(Polyhedron *pMesh)
+  {
+    CGAL_assertion(pMesh != NULL);
+    m_pMesh = pMesh;
+  }
+  ~CModifierQuadTriangle() {}
+
+  // subdivision
+  void operator()( HDS& hds)
+  {
+    builder B(hds,true);
+    B.begin_surface(3,1,6);
+      add_vertices(B);
+      add_facets(B);
+    B.end_surface();
+  }
+
+private:
+  
+  //***************************************************
+  // add vertices
+  //***************************************************
+  void add_vertices(builder &B)
+  {
+    // put original vertices
+    int index = 0;
+    typename Polyhedron::Vertex_iterator pVertex;
+    for(pVertex = m_pMesh->vertices_begin();
+        pVertex != m_pMesh->vertices_end();
+        pVertex++)
+    {
+      pVertex->tag(index);
+      B.add_vertex(pVertex->point());
+      index++;
+    }
+
+    // as many as #edges
+    m_pMesh->tag_halfedges(-1);
+    typename Polyhedron::Halfedge_iterator pHalfedge;
+    for(pHalfedge = m_pMesh->halfedges_begin();
+        pHalfedge != m_pMesh->halfedges_end();
+        pHalfedge++)
+    {
+      if(pHalfedge->tag() != -1)
+        continue;
+
+      // simple edge bissection
+      const Point& p1 = pHalfedge->vertex()->point();
+      const Point& p2 = pHalfedge->opposite()->vertex()->point();
+      Point point = Point(0.5f*(p1.x()+p2.x()),
+                          0.5f*(p1.y()+p2.y()),
+                          0.5f*(p1.z()+p2.z()));
+      B.add_vertex(point);
+
+      // put vertex indices on both halfedges
+      pHalfedge->tag(index);
+      pHalfedge->opposite()->tag(index);
+      index++;
+    }
+
+    // and as many as #facets with degree > 3
+    m_pMesh->tag_facets(-1);
+    typename Polyhedron::Facet_iterator pFacet;
+    for(pFacet = m_pMesh->facets_begin();
+        pFacet != m_pMesh->facets_end();
+        pFacet++)
+    {
+      unsigned int degree = Polyhedron::degree(pFacet);
+      CGAL_assertion(degree >= 3);
+      // forget about triangles, they are
+      // simply 1-to-4 subdivided by edge bisection
+      if(degree == 3)
+        continue; 
+
+      // barycentric subdivision
+      Point barycenter;
+	    m_pMesh->compute_facet_center(pFacet,barycenter);
+      B.add_vertex(barycenter);
+      pFacet->tag(index);
+      index++;
+    }
+  }
+
+  //***************************************************
+  // add facets
+  //***************************************************
+  void add_facets(builder &B)
+  {
+    typename Polyhedron::Facet_iterator pFacet;
+    for(pFacet = m_pMesh->facets_begin();
+        pFacet != m_pMesh->facets_end();
+        pFacet++)
+    {
+      unsigned int degree = Polyhedron::degree(pFacet);
+      CGAL_assertion(degree >= 3);
+
+      if(degree == 3)
+      {
+        typename Polyhedron::Halfedge_handle pHalfedge = pFacet->halfedge();
+        int i0 = pHalfedge->tag();
+        int i1 = pHalfedge->vertex()->tag();
+        int i2 = pHalfedge->next()->tag();
+        int i3 = pHalfedge->next()->vertex()->tag();
+        int i4 = pHalfedge->next()->next()->tag();
+        int i5 = pHalfedge->next()->next()->vertex()->tag();
+        CGAL_assertion(i0 >= 0);
+        CGAL_assertion(i1 >= 0);
+        CGAL_assertion(i2 >= 0);
+        CGAL_assertion(i3 >= 0);
+        CGAL_assertion(i4 >= 0);
+        CGAL_assertion(i5 >= 0);
+
+        // create 4 triangles
+        B.begin_facet();
+          B.add_vertex_to_facet(i1);
+          B.add_vertex_to_facet(i2);
+          B.add_vertex_to_facet(i0);
+        const Halfedge_handle& h1 = B.end_facet();
+        B.begin_facet();
+          B.add_vertex_to_facet(i3);
+          B.add_vertex_to_facet(i4);
+          B.add_vertex_to_facet(i2);
+        const Halfedge_handle& h2 = B.end_facet();
+        B.begin_facet();
+          B.add_vertex_to_facet(i5);
+          B.add_vertex_to_facet(i0);
+          B.add_vertex_to_facet(i4);
+        const Halfedge_handle& h3 = B.end_facet();
+
+        // center face
+        B.begin_facet();
+          B.add_vertex_to_facet(i0);
+          B.add_vertex_to_facet(i2);
+          B.add_vertex_to_facet(i4);
+        Halfedge_handle h4 = B.end_facet();
+
+        h1->control_edge(false);
+        h1->next()->control_edge(false);
+        h1->next()->next()->control_edge(false);
+
+        h2->control_edge(false);
+        h2->next()->control_edge(false);
+        h2->next()->next()->control_edge(false);
+
+        h3->control_edge(false);
+        h3->next()->control_edge(false);
+        h3->next()->next()->control_edge(false);
+
+        h4->control_edge(false);
+        h4->next()->control_edge(false);
+        h4->next()->next()->control_edge(false);
+        
+        if(pHalfedge->control_edge())
+        {
+          h1->control_edge(true);
+          h3->next()->control_edge(true);
+        }
+        if(pHalfedge->next()->control_edge())
+        {
+          h1->next()->control_edge(true);
+          h2->control_edge(true);
+        }
+        if(pHalfedge->next()->next()->control_edge())
+        {
+          h2->next()->control_edge(true);
+          h3->control_edge(true);
+        }
+      }
+      else
+      {
+        // i1: index of barycenter vertex
+        int i1 = pFacet->tag();
+        CGAL_assertion(i1 >= 0);
+
+        // for each halfedge
+        typename Polyhedron::Halfedge_around_facet_circulator h;
+        h = pFacet->facet_begin();
+        do
+        {
+          // i2,3,4: indices of three consecutive
+          // vertices on halfedges
+          int i2 = h->tag();
+          int i3 = h->vertex()->tag();
+          int i4 = h->next()->tag();
+          CGAL_assertion(i2 >= 0);
+          CGAL_assertion(i3 >= 0);
+          CGAL_assertion(i4 >= 0);
+
+          // create a quad
+          B.begin_facet();
+            B.add_vertex_to_facet(i3);
+            B.add_vertex_to_facet(i4);
+            B.add_vertex_to_facet(i1);
+            B.add_vertex_to_facet(i2);
+          const Halfedge_handle& pNewHalfedge = B.end_facet();
+
+          pNewHalfedge->control_edge(false);
+          pNewHalfedge->next()->control_edge(false);
+          pNewHalfedge->next()->next()->control_edge(false);
+          pNewHalfedge->next()->next()->next()->control_edge(false);
+
+          if(h->control_edge())
+            pNewHalfedge->control_edge(true);
+          if(h->next()->control_edge())
+            pNewHalfedge->next()->control_edge(true);
+        }
+        while(++h != pFacet->facet_begin());
+      }
+    }
+  }
+
+  //***************************************************
+  // correcting factor
+  //***************************************************
+	static float correcting_factor(unsigned int ne,
+		                             unsigned int nq)
+  {
+    if(ne == 2 && nq == 1)
+      return -0.20505f;
+    if(ne == 3 && nq == 1)
+      return 0.80597f;
+    if(ne == 3 && nq == 2)
+      return 0.61539f;
+    if(ne == 4 && nq == 1)
+      return 0.34792f;
+    if(ne == 4 && nq == 2)
+      return 0.21380f;
+    if(ne == 4 && nq == 3)
+      return 0.10550f;
+    return 0.0f;
+  }
+public:  
+  //***************************************************
+  // smooth vertex positions
+  //***************************************************
+  static void smooth(Polyhedron *pMesh,
+                     bool smooth_boundary = true)
+  {
+    CGAL_assertion(pMesh != NULL);
+
+    // alloc position vectors
+    unsigned int nb_vertices = pMesh->size_of_vertices();
+    FT *pPos = new FT[3*nb_vertices];
+    CGAL_assertion(pPos != NULL);
+
+    // compute new positions
+    unsigned int index = 0;
+    typename Polyhedron::Vertex_iterator pVertex;
+    for(pVertex = pMesh->vertices_begin();
+        pVertex != pMesh->vertices_end();
+        pVertex++)
+    {
+      // border vertices will not move
+      if(Polyhedron::is_border(pVertex))
+      {
+        // do not smooth it
+        const Point& curr = pVertex->point();
+        if(!smooth_boundary)
+        {
+          pPos[3*index]   = curr.x();
+          pPos[3*index+1] = curr.y();
+          pPos[3*index+2] = curr.z();
+        }
+        // smooth using [1/4 1/2 1/4] cubic B-spline averaging mask
+        else 
+        {
+          const typename Polyhedron::Halfedge_handle& pHalfedge =
+            pMesh->get_border_halfedge(pVertex);
+          CGAL_assertion(pHalfedge != NULL);
+          const Point& next = pHalfedge->vertex()->point();
+          const Point& prev = pHalfedge->prev()->prev()->vertex()->point();
+          pPos[3*index]   = 0.25f*prev.x() + 0.5f*curr.x() + 0.25f*next.x();
+          pPos[3*index+1] = 0.25f*prev.y() + 0.5f*curr.y() + 0.25f*next.y();
+          pPos[3*index+2] = 0.25f*prev.z() + 0.5f*curr.z() + 0.25f*next.z();
+        }
+      } // end is border
+      else
+      {
+
+        unsigned int nb_quads = 0;
+        unsigned int nb_edges = 0;
+
+        // rotate around vertex to count #edges and #quads
+        Halfedge_around_vertex_circulator
+          pHalfEdge = pVertex->vertex_begin();
+        Halfedge_around_vertex_circulator end = pHalfEdge;
+        CGAL_For_all(pHalfEdge,end)
+        {
+          const Facet_handle& pFacet = pHalfEdge->facet();
+          CGAL_assertion(pFacet != NULL);
+          unsigned int degree = Polyhedron::degree(pFacet);
+          CGAL_assertion(degree == 4 || degree == 3);
+          if(degree == 4)
+            nb_quads++;
+          nb_edges++;
+        }
+
+        // compute coefficients
+        FT ne = (FT)nb_edges;
+        FT nq = (FT)nb_quads;
+        FT alpha = 1.0f / (1.0f + ne/2.0f + nq/4.0f);
+        FT beta = alpha / 2.0f;  // edges
+        FT gamma = alpha / 4.0f; // corners of incident quads
+        FT eta = correcting_factor(nb_edges,nb_quads);
+
+        // new position
+        pPos[3*index]   = alpha * pVertex->point().x();
+        pPos[3*index+1] = alpha * pVertex->point().y();
+        pPos[3*index+2] = alpha * pVertex->point().z();
+
+        // rotate around vertex to compute new position
+        pHalfEdge = pVertex->vertex_begin();
+        end = pHalfEdge;
+        CGAL_For_all(pHalfEdge,end)
+        {
+          const Facet_handle& pFacet = pHalfEdge->facet();
+          CGAL_assertion(pFacet != NULL);
+          unsigned int degree = Polyhedron::degree(pFacet);
+          CGAL_assertion(degree == 4 || degree == 3);
+
+          // add edge-vertex contribution
+          const Point& point = pHalfEdge->prev()->vertex()->point();
+          pPos[3*index]   += beta * point.x();
+          pPos[3*index+1] += beta * point.y();
+          pPos[3*index+2] += beta * point.z();
+
+          // add corner vertex contribution
+          if(degree == 4)
+          {
+            const Point& corner = pHalfEdge->next()->next()->vertex()->point();
+            pPos[3*index]   += gamma * corner.x();
+            pPos[3*index+1] += gamma * corner.y();
+            pPos[3*index+2] += gamma * corner.z();
+          }
+        }
+
+        // apply correction
+        pPos[3*index] = pPos[3*index] +
+          eta*(pPos[3*index]-pVertex->point().x());
+        pPos[3*index+1] = pPos[3*index+1] +
+          eta*(pPos[3*index+1]-pVertex->point().y());
+        pPos[3*index+2] = pPos[3*index+2] +
+          eta*(pPos[3*index+2]-pVertex->point().z());
+
+      } // end !is border
+      index++;
+    }
+
+    // set new positions
+    index = 0;
+    for(pVertex = pMesh->vertices_begin();
+        pVertex != pMesh->vertices_end();
+        pVertex++)
+    {
+      Point& point = pVertex->point();
+      point = Point(pPos[3*index],
+                    pPos[3*index+1],
+                    pPos[3*index+2]);
+      index++;
+    }
+
+    // cleanup
+    delete [] pPos;
+  }
+};
+\end{verbatim}}
+
 { \scriptsize
 \begin{verbatim}
 template <class Polyhedron,class kernel>
@@ -961,42 +1353,6 @@ public:
 };
 \end{verbatim}}
 
-Subdivision using a modified incremental builder
-
-{ \scriptsize
-\begin{verbatim}
-template <class HDS,class Polyhedron,class kernel>
-class CModifierQuadTriangle : public CGAL::Modifier_base<HDS>
-{
-private:
-  Polyhedron *m_pMesh;
-  typedef typename CGAL::Enriched_builder<HDS> builder;
-
-public:
-
-  // life cycle
-  CModifierQuadTriangle(Polyhedron *pMesh)
-  {
-    m_pMesh = pMesh;
-  }
-  ~CModifierQuadTriangle() {}
-
-  // subdivision
-  void operator()( HDS& hds)
-  {
-    builder B(hds,true);
-    B.begin_surface(3,1,6);
-      add_vertices(B);
-      add_facets(B);
-    B.end_surface();
-  }
-...
-};
-\end{verbatim}}
-
-
-
-
 % SurfLab
 
 \subsection{Subdivision using a rule template}