+std::size_t
+get( Polyhedron_vertex_deformation_index_map, typename P::Vertex_handle vh)
+{
+ return vh->id();
+}
+
+template
+void
+put( Polyhedron_vertex_deformation_index_map&, typename P::Vertex_handle vh, std::size_t s)
+{
+ vh->id() = s;
+}
+
+
+
+template
+class Polyhedron_edge_deformation_index_map
+{
+private:
+
+ typedef P Polyhedron ;
+
+
+public:
+
+ typedef boost::read_write_property_map_tag category;
+ typedef std::size_t value_type;
+ typedef std::size_t reference;
+ typedef typename boost::graph_traits::edge_descriptor key_type;
+
+ Polyhedron_edge_deformation_index_map()
+ {}
+
+};
+
+namespace boost {
+
+ template
+ std::size_t
+ get( Polyhedron_edge_deformation_index_map pmap, typename P::Halfedge_handle eh)
+ {
+ return eh->id();
+ }
+
+ template
+ void
+ put( Polyhedron_edge_deformation_index_map& pmap, typename P::Halfedge_handle eh, std::size_t s)
+ {
+ eh->id() = s;
+ }
+}
+
+template
+class Polyhedron_edge_deformation_length_map
+{
+private:
+
+ typedef P Polyhedron ;
+
+
+public:
+ std::vector& m_lengths;
+
+ typedef boost::read_write_property_map_tag category;
+ typedef double value_type;
+ typedef double& reference;
+ typedef typename boost::graph_traits::edge_descriptor key_type;
+
+ Polyhedron_edge_deformation_length_map(const P&,std::vector& lengths)
+ : m_lengths(lengths) {}
+};
+
+namespace boost {
+
+ template
+ double
+ get( Polyhedron_edge_deformation_length_map pmap, typename P::Halfedge_handle eh)
+ {
+ CGAL_assertion( pmap.m_lengths.size() > eh->id() );
+ return pmap.m_lengths[eh->id()];
+ }
+
+ template
+ void
+ put( Polyhedron_edge_deformation_length_map& pmap, typename P::Halfedge_handle eh, double s)
+ {
+ CGAL_assertion( pmap.m_lengths.size() > eh->id() );
+ pmap.m_lengths[eh->id()] = s;
+ }
+}
+
+#endif //PROPERTY_MAPS_FOR_EDIT_PLUGIN
diff --git a/Polyhedron/demo/Polyhedron/Scene_edit_polyhedron_item.cpp b/Polyhedron/demo/Polyhedron/Scene_edit_polyhedron_item.cpp
index 4fb6ec0deb5..7fd8394d798 100644
--- a/Polyhedron/demo/Polyhedron/Scene_edit_polyhedron_item.cpp
+++ b/Polyhedron/demo/Polyhedron/Scene_edit_polyhedron_item.cpp
@@ -3,6 +3,11 @@
#include "Polyhedron_type.h"
#include
+#include
+#include
+#include
+#include "Property_maps_for_edit_plugin.h"
+#include
#include
#include
@@ -14,35 +19,86 @@
#include
+
+
+
+
typedef Polyhedron::Vertex_handle Vertex_handle;
+typedef Polyhedron::Halfedge_handle Halfedge_handle;
typedef std::set Selected_vertices;
+typedef std::vector > Transform_vectors;
typedef Selected_vertices::iterator Selected_vertices_it;
+typedef Polyhedron_vertex_deformation_index_map Vertex_index_map;
+typedef Polyhedron_edge_deformation_length_map Edge_length_map;
+typedef boost::iterator_property_map::iterator, Vertex_index_map> Dist_pmap;
+
+#define PI 3.14159265359
struct Scene_edit_polyhedron_item_priv {
Scene_polyhedron_item* poly_item;
- int zone_size;
+ int handlesRegionSize;
+ int interestRegionSize;
+ bool geodesicCircle;
+ bool sharpFeature;
+ int usageScenario;
+ bool selected_vertex_changed;
+ bool selected_handles_moved;
qglviewer::ManipulatedFrame* frame;
- Selected_vertices selected_vertices;
+ Selected_vertices selected_handles;
+ Selected_vertices non_selected_handles;
+ Selected_vertices selected_roi;
+ Selected_vertices non_selected_roi;
Vertex_handle selected_vertex;
+ Transform_vectors selected_vectors;
+ Transform_vectors non_selected_vectors;
Kernel::Point_3 orig_pos;
+ Kernel::Point_3 last_pos;
+ Vertex_index_map* vertex_index_map;
+ std::vector geodesic_distance;
+ Dist_pmap* dist_pmap;
+ std::vector is_sharp_vertices;
}; // end struct Scene_edit_polyhedron_item_priv
Scene_edit_polyhedron_item::Scene_edit_polyhedron_item(Scene_polyhedron_item* poly_item)
: d(new Scene_edit_polyhedron_item_priv)
{
d->poly_item = poly_item;
- d->zone_size = 0;
+ d->handlesRegionSize = 0;
d->frame = new ManipulatedFrame();
d->frame->setProperty("item", QVariant::fromValue(this));
if(!connect(poly_item, SIGNAL(selected_vertex(void*)),
this, SLOT(vertex_has_been_selected(void*))))
std::cerr << __FILE__ << ": connection failed!\n";
poly_item->enable_facets_picking(true);
+
+ d->vertex_index_map = new Vertex_index_map();
+ int idx = 0;
+ for ( Vertex_handle vh = poly_item->polyhedron()->vertices_begin(); vh != poly_item->polyhedron()->vertices_end(); vh++ )
+ {
+ put(*d->vertex_index_map, vh, idx++);
+ }
+ std::vector lengths(poly_item->polyhedron()->size_of_halfedges(),0);
+ Edge_length_map edge_length_map(*poly_item->polyhedron(),lengths);
+ for ( Halfedge_handle eh = poly_item->polyhedron()->edges_begin(); eh != poly_item->polyhedron()->edges_end(); eh++ )
+ {
+ Kernel::Vector_3 edge = eh->vertex()->point() - eh->opposite()->vertex()->point();
+ double edge_length = std::sqrt(edge.squared_length());
+ boost::put(edge_length_map, eh, edge_length);
+ }
+ d->geodesic_distance.resize(boost::num_vertices(*poly_item->polyhedron()), 0);
+ d->dist_pmap = new Dist_pmap(d->geodesic_distance.begin(), *d->vertex_index_map);
+ find_sharp_vertices_1();
+
+ connect(d->frame, SIGNAL(modified()),
+ this, SIGNAL(modified()));
+
}
Scene_edit_polyhedron_item::~Scene_edit_polyhedron_item()
{
delete d->frame;
+ delete d->vertex_index_map;
+ delete d->dist_pmap;
delete d;
}
@@ -73,19 +129,78 @@ Scene_edit_polyhedron_item::toolTip() const
void Scene_edit_polyhedron_item::draw() const {
d->poly_item->direct_draw();
- if(!d->selected_vertices.empty()) {
+ if(!d->non_selected_handles.empty() || !d->non_selected_roi.empty()
+ || !d->selected_handles.empty() || !d->selected_roi.empty() ) {
CGAL::GL::Point_size point_size; point_size.set_point_size(5);
- CGAL::GL::Color color; color.set_rgb_color(0, 0, 0);
+ CGAL::GL::Color color;
+ color.set_rgb_color(1.f, 0, 0);
::glBegin(GL_POINTS);
for(Selected_vertices_it
- it = d->selected_vertices.begin(),
- end = d->selected_vertices.end();
+ it = d->selected_handles.begin(),
+ end = d->selected_handles.end();
+ it != end; ++it)
+ {
+ const Kernel::Point_3& p = (*it)->point();
+ ::glVertex3d(p.x(), p.y(), p.z());
+ }
+ ::glEnd();
+ color.set_rgb_color(1.f, 0.5f, 0);
+ ::glBegin(GL_POINTS);
+ for(Selected_vertices_it
+ it = d->non_selected_handles.begin(),
+ end = d->non_selected_handles.end();
it != end; ++it)
{
const Kernel::Point_3& p = (*it)->point();
::glVertex3d(p.x(), p.y(), p.z());
}
::glEnd();
+
+ color.set_rgb_color(0, 1.f, 0);
+ ::glBegin(GL_POINTS);
+ for(Selected_vertices_it
+ it = d->selected_roi.begin(),
+ end = d->selected_roi.end();
+ it != end; ++it)
+ {
+ const Kernel::Point_3& p = (*it)->point();
+ ::glVertex3d(p.x(), p.y(), p.z());
+ }
+ ::glEnd();
+ color.set_rgb_color(0, 1.f, 0);
+ ::glBegin(GL_POINTS);
+ for(Selected_vertices_it
+ it = d->non_selected_roi.begin(),
+ end = d->non_selected_roi.end();
+ it != end; ++it)
+ {
+ const Kernel::Point_3& p = (*it)->point();
+ ::glVertex3d(p.x(), p.y(), p.z());
+ }
+ ::glEnd();
+
+ color.set_rgb_color(1.f, 0, 0);
+ ::glBegin(GL_LINES);
+ for (std::size_t i = 0; i < d->selected_vectors.size(); i++)
+ {
+ const Kernel::Point_3& p0 = d->selected_vectors[i].first;
+ const Kernel::Point_3& p1 = d->selected_vectors[i].second;
+
+ ::glVertex3d(p0.x(), p0.y(), p0.z());
+ ::glVertex3d(p1.x(), p1.y(), p1.z());
+ }
+ ::glEnd();
+ color.set_rgb_color(1.f, 0.5f, 0);
+ ::glBegin(GL_LINES);
+ for (std::size_t i = 0; i < d->non_selected_vectors.size(); i++)
+ {
+ const Kernel::Point_3& p0 = d->non_selected_vectors[i].first;
+ const Kernel::Point_3& p1 = d->non_selected_vectors[i].second;
+
+ ::glVertex3d(p0.x(), p0.y(), p0.z());
+ ::glVertex3d(p1.x(), p1.y(), p1.z());
+ }
+ ::glEnd();
}
}
@@ -111,7 +226,7 @@ changed()
{
d->poly_item->changed();
Scene_item::changed();
- d->orig_pos = current_position();
+ d->last_pos = current_position();
}
void
@@ -141,19 +256,72 @@ Scene_polyhedron_item* Scene_edit_polyhedron_item::to_polyhedron_item() const {
}
void
-Scene_edit_polyhedron_item::setZoneSize(int i) {
+Scene_edit_polyhedron_item::setHandlesRegionSize(int i) {
if(i >= 0) {
- std::cerr << "item \"" << qPrintable(name())
- << "\".setZoneSize(" << i << ")\n";
- d->zone_size = i;
+ d->handlesRegionSize = i;
+ if(d->selected_vertex != Vertex_handle()) {
+ vertex_has_been_selected(&*d->selected_vertex);
+ }
}
}
+void
+Scene_edit_polyhedron_item::setInterestRegionSize(int i) {
+ if(i >= 0) {
+ d->interestRegionSize = i;
+ if(d->selected_vertex != Vertex_handle()) {
+ vertex_has_been_selected(&*d->selected_vertex);
+ }
+ }
+}
+
+void
+Scene_edit_polyhedron_item::setGeodesicCircle(bool status) {
+ d->geodesicCircle = status;
+ if(d->selected_vertex != Vertex_handle()) {
+ vertex_has_been_selected(&*d->selected_vertex);
+ }
+}
+
+void
+Scene_edit_polyhedron_item::setSharpFeature(bool status) {
+ d->sharpFeature = status;
+ if(d->selected_vertex != Vertex_handle()) {
+ vertex_has_been_selected(&*d->selected_vertex);
+ }
+}
+
+void
+Scene_edit_polyhedron_item::setUsageScenario(int i) {
+ d->usageScenario = i;
+}
+
+void
+Scene_edit_polyhedron_item::setSelectedVertexChanged(bool status) {
+ d->selected_vertex_changed = status;
+}
+
+void
+Scene_edit_polyhedron_item::setSelectedHandlesMoved(bool status) {
+ d->selected_handles_moved = status;
+}
+
qglviewer::ManipulatedFrame*
Scene_edit_polyhedron_item::manipulatedFrame() {
return d->frame;
}
+void
+Scene_edit_polyhedron_item::setSelectedVector(Kernel::Vector_3 translation_last)
+{
+ for (std::size_t i = 0; i < d->selected_vectors.size(); i++)
+ {
+ Kernel::Point_3 old_position = d->selected_vectors[i].second;
+ Kernel::Point_3 new_position = old_position + translation_last;
+ d->selected_vectors[i].second = new_position;
+ }
+}
+
struct Get_vertex_handle : public CGAL::Modifier_base
{
Polyhedron::Vertex* vertex_ptr;
@@ -163,6 +331,232 @@ struct Get_vertex_handle : public CGAL::Modifier_base
}
};
+double Scene_edit_polyhedron_item::dihedral_angle(edge_descriptor e)
+{
+ Polyhedron* poly = d->poly_item->polyhedron();
+ vertex_descriptor v0 = boost::target(e, *poly);
+ vertex_descriptor v1 = boost::source(e, *poly);
+ // Only one triangle for border edges
+ if (boost::get(CGAL::edge_is_border, *poly, e)||boost::get(CGAL::edge_is_border, *poly, CGAL::opposite_edge(e, *poly)))
+ {
+ return -1;
+ }
+ else
+ {
+ edge_descriptor e_cw = CGAL::next_edge_cw(e, *poly);
+ vertex_descriptor v2 = boost::source(e_cw, *poly);
+ edge_descriptor e_ccw = CGAL::next_edge_ccw(e, *poly);
+ vertex_descriptor v3 = boost::source(e_ccw, *poly);
+
+ Kernel::Vector_3 e01 = v1->point() - v0->point();
+ Kernel::Vector_3 e02 = v2->point() - v0->point();
+ Kernel::Vector_3 e03 = v3->point() - v0->point();
+ // compute dihedral angle between v0_v1_v2 and v0_v1_v3
+ // cross(e01, e02)
+ Kernel::Vector_3 n012( e01[1]*e02[2]-e01[2]*e02[1], e01[2]*e02[0]-e01[0]*e02[2], e01[0]*e02[1]-e01[1]*e02[0] );
+ // cross(e01, e03)
+ Kernel::Vector_3 n013( e01[1]*e03[2]-e01[2]*e03[1], e01[2]*e03[0]-e01[0]*e03[2], e01[0]*e03[1]-e01[1]*e03[0] );
+ // n012*n013 / (|n012|*|n013|)
+ double cos_angle = (n012[0]*n013[0]+n012[1]*n013[1]+n012[2]*n013[2]) / std::sqrt(n012.squared_length()*n013.squared_length());
+ return acos(cos_angle);
+ }
+}
+
+void
+Scene_edit_polyhedron_item::find_sharp_vertices()
+{
+ Polyhedron* poly = d->poly_item->polyhedron();
+ d->is_sharp_vertices.clear();
+ d->is_sharp_vertices.resize(poly->size_of_vertices(), false);
+ std::vector dihedral_angles;
+ vertex_iterator vb, ve;
+ for ( boost::tie(vb,ve) = boost::vertices(*poly); vb != ve; vb++ )
+ {
+ // compute dihedral angles
+ in_edge_iterator eb, ee;
+ dihedral_angles.clear();
+ double sum = 0;
+ for ( boost::tie(eb,ee) = boost::in_edges(*vb, *poly); eb != ee; eb++ )
+ {
+ double angle = dihedral_angle(*eb);
+ if (angle != -1)
+ {
+ dihedral_angles.push_back(angle);
+ sum += angle;
+ }
+ }
+ // compute variance of angles
+ double ave_angle = sum/dihedral_angles.size();
+ double var = 0;
+ for ( std::size_t i = 0; i < dihedral_angles.size(); i++ )
+ {
+ var += (dihedral_angles[i] - ave_angle)*(dihedral_angles[i] - ave_angle)/dihedral_angles.size();
+ }
+ if (var > 0.2)
+ {
+ d->is_sharp_vertices[ get(*d->vertex_index_map, *vb) ] = true ;
+ }
+
+ }
+}
+
+void
+Scene_edit_polyhedron_item::find_sharp_vertices_1()
+{
+ Polyhedron* poly = d->poly_item->polyhedron();
+ d->is_sharp_vertices.clear();
+ d->is_sharp_vertices.resize(poly->size_of_vertices(), false);
+ vertex_iterator vb, ve;
+ for ( boost::tie(vb,ve) = boost::vertices(*poly); vb != ve; vb++ )
+ {
+ // compute dihedral angles
+ in_edge_iterator eb, ee;
+ for ( boost::tie(eb,ee) = boost::in_edges(*vb, *poly); eb != ee; eb++ )
+ {
+ double angle = dihedral_angle(*eb);
+ if (angle < PI*3.0/4.0)
+ {
+ d->is_sharp_vertices[ get(*d->vertex_index_map, *vb) ] = true;
+ break;
+ }
+ }
+
+ }
+}
+
+Selected_vertices extend_once(Selected_vertices selected_vertices)
+{
+ std::set original_set = selected_vertices;
+ BOOST_FOREACH(Vertex_handle v, original_set) {
+ Polyhedron::Halfedge_around_vertex_circulator
+ he_it = v->vertex_begin(), he_it_end(he_it);
+ if(he_it != 0) {
+ do {
+ const Vertex_handle other_v = he_it->opposite()->vertex();
+ if( selected_vertices.find(other_v) == selected_vertices.end() )
+ {
+ selected_vertices.insert(other_v);
+ }
+ } while(++he_it != he_it_end);
+ }
+ }
+ return selected_vertices;
+}
+
+// extend k-neighboring vertices
+Selected_vertices extend_k_ring(Selected_vertices selected_vertices, int k)
+{
+ std::vector selected_vertices_vector;
+ selected_vertices_vector.insert(selected_vertices_vector.begin(), selected_vertices.begin(), selected_vertices.end());
+
+ int idx_lv = 0; // pointing the neighboring vertices on current level
+ int idx_lv_end;
+ for ( int lv = 0; lv < k; lv++ )
+ {
+ idx_lv_end = selected_vertices_vector.size();
+ for (; idx_lv < idx_lv_end; idx_lv++)
+ {
+ Vertex_handle v = selected_vertices_vector[idx_lv];
+ Polyhedron::Halfedge_around_vertex_circulator
+ he_it = v->vertex_begin(), he_it_end(he_it);
+ if(he_it != 0)
+ {
+ do {
+ const Vertex_handle other_v = he_it->opposite()->vertex();
+ std::vector::iterator
+ it = std::find(selected_vertices_vector.begin(), selected_vertices_vector.end(), other_v);
+ if (it == selected_vertices_vector.end())
+ {
+ selected_vertices_vector.push_back(other_v);
+ selected_vertices.insert(other_v);
+ }
+ } while(++he_it != he_it_end);
+ }
+ }
+ }
+
+ return selected_vertices;
+}
+
+
+// extend vertices inside specific radius, so that the selected region is close circle
+Selected_vertices extend_circle(Selected_vertices selected_vertices, double radius, Dist_pmap dist_pmap)
+{
+ std::vector selected_vertices_vector;
+ selected_vertices_vector.insert(selected_vertices_vector.begin(), selected_vertices.begin(), selected_vertices.end());
+ bool new_vertex_selected = true;
+ int idx_lv = 0; // pointing the neighboring vertices on current level
+ int idx_lv_end;
+ while (new_vertex_selected)
+ {
+ new_vertex_selected = false;
+ idx_lv_end = selected_vertices_vector.size();
+ for (; idx_lv < idx_lv_end; idx_lv++)
+ {
+ Vertex_handle v = selected_vertices_vector[idx_lv];
+ Polyhedron::Halfedge_around_vertex_circulator
+ he_it = v->vertex_begin(), he_it_end(he_it);
+ if(he_it != 0) {
+ do {
+ const Vertex_handle other_v = he_it->opposite()->vertex();
+ if( boost::get(dist_pmap, other_v) <= radius )
+ {
+ std::vector::iterator it = std::find(selected_vertices_vector.begin(), selected_vertices_vector.end(), other_v);
+ if (it == selected_vertices_vector.end())
+ {
+ selected_vertices_vector.push_back(other_v);
+ selected_vertices.insert(other_v);
+ new_vertex_selected = true;
+ }
+ }
+ } while(++he_it != he_it_end);
+ }
+ }
+ }
+
+ return selected_vertices;
+}
+
+
+// extend vertices until reaching the sharp edges
+Selected_vertices extend_sharp_edge(Selected_vertices selected_vertices, std::vector is_sharp_vertices, Vertex_index_map vertex_index_map)
+{
+ std::vector selected_vertices_vector;
+ selected_vertices_vector.insert(selected_vertices_vector.begin(), selected_vertices.begin(), selected_vertices.end());
+ bool new_vertex_selected = true;
+ int idx_lv = 0; // pointing the neighboring vertices on current level
+ int idx_lv_end;
+ while (new_vertex_selected)
+ {
+ new_vertex_selected = false;
+ idx_lv_end = selected_vertices_vector.size();
+ for (; idx_lv < idx_lv_end; idx_lv++)
+ {
+ Vertex_handle v = selected_vertices_vector[idx_lv];
+ Polyhedron::Halfedge_around_vertex_circulator
+ he_it = v->vertex_begin(), he_it_end(he_it);
+ if(he_it != 0) {
+ do {
+ const Vertex_handle other_v = he_it->opposite()->vertex();
+ int idx = get(vertex_index_map, other_v);
+ if( !is_sharp_vertices[idx] )
+ {
+ std::vector::iterator it = std::find(selected_vertices_vector.begin(), selected_vertices_vector.end(), other_v);
+ if (it == selected_vertices_vector.end())
+ {
+ selected_vertices_vector.push_back(other_v);
+ selected_vertices.insert(other_v);
+ new_vertex_selected = true;
+ }
+ }
+ } while(++he_it != he_it_end);
+ }
+ }
+ }
+
+ return selected_vertices;
+}
+
void Scene_edit_polyhedron_item::vertex_has_been_selected(void* void_ptr) {
Polyhedron* poly = d->poly_item->polyhedron();
@@ -174,66 +568,351 @@ void Scene_edit_polyhedron_item::vertex_has_been_selected(void* void_ptr) {
poly->delegate(get_vertex_handle);
Vertex_handle vh = get_vertex_handle.vh;
-
- std::cerr << "Selected vertex: " << void_ptr << " = " << vh->point()
- << std::endl;
- d->selected_vertices.clear();
-
- d->selected_vertices.insert(vh);
-
- std::cerr << "d->zone_size = " << d->zone_size << std::endl;
- // Naive way to compute the k-neighborhood of vh, with k==d->zone_size.
- for(int i = 0; i < d->zone_size; ++i) {
- std::set selected_vertices;
- for(Selected_vertices_it
- it = d->selected_vertices.begin(),
- end = d->selected_vertices.end();
- it != end; ++it) {
- selected_vertices.insert(*it);
+ if (d->selected_vertex != vh)
+ {
+ // re-compute geodesic distances relative to selected_vertex
+ std::vector lengths(poly->size_of_halfedges(),0);
+ Edge_length_map edge_length_map(*poly,lengths);
+
+ for ( Halfedge_handle eh = poly->edges_begin(); eh != poly->edges_end(); eh++ )
+ {
+ Kernel::Vector_3 edge = eh->vertex()->point() - eh->opposite()->vertex()->point();
+ double edge_length = std::sqrt(edge.squared_length());
+ boost::put(edge_length_map, eh, edge_length);
}
- BOOST_FOREACH(Vertex_handle v, selected_vertices) {
- Polyhedron::Halfedge_around_vertex_circulator
- he_it = v->vertex_begin(), he_it_end(he_it);
- if(he_it != 0) {
- do {
- const Vertex_handle other_v = he_it->opposite()->vertex();
- if( d->selected_vertices.find(other_v) == d->selected_vertices.end() )
- {
- d->selected_vertices.insert(other_v);
- }
- } while(++he_it != he_it_end);
+ boost::dijkstra_shortest_paths( *poly, vh,
+ boost::vertex_index_map (*d->vertex_index_map).
+ weight_map (edge_length_map).
+ distance_map (*d->dist_pmap));
+ }
+
+ // set new handles and ROI regions
+ Selected_vertices new_handles;
+ new_handles.insert(vh);
+ new_handles = extend_k_ring(new_handles, d->handlesRegionSize);
+ Selected_vertices new_roi;
+ if (d->sharpFeature)
+ {
+ new_roi.insert(vh);
+ new_roi = extend_sharp_edge(new_roi, d->is_sharp_vertices, *d->vertex_index_map);
+ }
+ else
+ {
+ new_roi = new_handles;
+ new_roi = extend_k_ring( new_roi, d->interestRegionSize - d->handlesRegionSize );
+ if (d->geodesicCircle)
+ {
+ double radius = 0;
+ BOOST_FOREACH(Vertex_handle v, new_handles)
+ {
+ double dist = boost::get(*d->dist_pmap, v);
+ if ( dist> radius ) radius = dist;
}
+ new_handles = extend_circle(new_handles, radius, *d->dist_pmap);
+
+ radius = 0;
+ BOOST_FOREACH(Vertex_handle v, new_roi)
+ {
+ double dist = boost::get(*d->dist_pmap, v);
+ if ( dist> radius ) radius = dist;
+ }
+ new_roi = extend_circle(new_roi, radius, *d->dist_pmap);
}
}
+
+ // multiple handles scenario
+ if (d->usageScenario == 1)
+ {
+ if (d->selected_vertex != vh) // selected_vertex changed
+ {
+ BOOST_FOREACH(Vertex_handle v, new_handles)
+ {
+ if ( d->non_selected_handles.find(v) != d->non_selected_handles.end() ||
+ d->selected_handles.find(v) != d->selected_handles.end() )
+ {
+ std::cerr << "New handles rejected: overlapped!\n";
+ return;
+ }
+ }
+ BOOST_FOREACH(Vertex_handle v, d->selected_handles)
+ {
+ // add the latest handles into non_selected_handles
+ if ( d->non_selected_handles.find(v) == d->non_selected_handles.end() )
+ {
+ d->non_selected_handles.insert(v);
+ }
+ }
+ BOOST_FOREACH(Vertex_handle v, d->selected_roi)
+ {
+ // add the latest ROI into non_selected_roi
+ if ( d->non_selected_roi.find(v) == d->non_selected_roi.end() )
+ {
+ d->non_selected_roi.insert(v);
+ }
+ }
+ for (std::size_t i = 0; i < d->selected_vectors.size(); i++)
+ {
+ std::pair v = d->selected_vectors[i];
+ Transform_vectors::iterator it = find(d->non_selected_vectors.begin(), d->non_selected_vectors.end(), v );
+ // add the latest transform vectors into non_selected_vectors
+ if ( it == d->non_selected_vectors.end() )
+ {
+ d->non_selected_vectors.push_back(v);
+ }
+ }
+
+ }
+ else
+ {
+ BOOST_FOREACH(Vertex_handle v, new_handles)
+ {
+ if ( d->non_selected_handles.find(v) != d->non_selected_handles.end() )
+ {
+ std::cerr << "New handles rejected: overlapped!\n";
+ return;
+ }
+ }
+ if (d->selected_handles_moved)
+ {
+ std::cerr << "Update of old handles rejected: already moved!\n";
+ return;
+ }
+ }
+ d->selected_vectors.clear();
+ std::pair v(vh->point(), vh->point());
+ d->selected_vectors.push_back(v);
+ }
+
+ d->selected_vertex = vh;
+ d->selected_handles = new_handles;
+ d->selected_handles_moved = false;
+
+ d->selected_roi = new_roi;
+ std::cerr << d->handlesRegionSize << " " << d->interestRegionSize << std::endl;
+
+
const Kernel::Point_3& p = vh->point();
d->orig_pos = p;
+ d->last_pos = p;
d->frame->setPosition(qglviewer::Vec(p.x(), p.y(), p.z()));
- connect(d->frame, SIGNAL(modified()),
- this, SIGNAL(modified()));
+
emit begin_edit();
}
+void Scene_edit_polyhedron_item::vertex_has_been_selected_2(void* void_ptr) {
+ Polyhedron* poly = d->poly_item->polyhedron();
+
+ // Need a modifier to get access to the HDS, to get the vertex handle
+ // from the vertex pointer.
+
+ Get_vertex_handle get_vertex_handle;
+ get_vertex_handle.vertex_ptr = static_cast(void_ptr);
+
+ poly->delegate(get_vertex_handle);
+ Vertex_handle vh = get_vertex_handle.vh;
+ if (d->selected_vertex != vh)
+ {
+ d->selected_vertex_changed = true;
+ d->selected_vertex = vh;
+ }
+ else
+ {
+ d->selected_vertex_changed = false;
+ }
+ if (d->selected_handles_moved) // re-compute variance of dihedral angles for each vertex
+ {
+ find_sharp_vertices_1();
+ }
+ if (d->selected_vertex_changed || d->selected_handles_moved) // selected_vertex is changed or moved
+ {
+ // compute geodesic distances relative to selected_vertex
+ std::vector lengths(poly->size_of_halfedges(),0);
+ Edge_length_map edge_length_map(*poly,lengths);
+
+ for ( Halfedge_handle eh = poly->edges_begin(); eh != poly->edges_end(); eh++ )
+ {
+ Kernel::Vector_3 edge = eh->vertex()->point() - eh->opposite()->vertex()->point();
+ double edge_length = std::sqrt(edge.squared_length());
+ boost::put(edge_length_map, eh, edge_length);
+ }
+ boost::dijkstra_shortest_paths( *poly, vh,
+ boost::vertex_index_map (*d->vertex_index_map).
+ weight_map (edge_length_map).
+ distance_map (*d->dist_pmap));
+
+ if (d->usageScenario == 1)
+ {
+ BOOST_FOREACH(Vertex_handle v, d->selected_handles)
+ {
+ // add the latest handles into non_selected_handles
+ if ( d->non_selected_handles.find(v) == d->non_selected_handles.end() )
+ {
+ d->non_selected_handles.insert(v);
+ }
+ }
+ BOOST_FOREACH(Vertex_handle v, d->selected_roi)
+ {
+ // add the latest ROI into non_selected_roi
+ if ( d->non_selected_roi.find(v) == d->non_selected_roi.end() )
+ {
+ d->non_selected_roi.insert(v);
+ }
+ }
+
+ }
+ }
+
+ d->selected_handles.clear();
+ d->selected_handles.insert(vh);
+ // compute the k-neighborhood of vh, with k==d->handlesRegionSize.
+ d->selected_handles = extend_k_ring(d->selected_handles, d->handlesRegionSize);
+ d->selected_handles_moved = false;
+
+ d->selected_roi = d->selected_handles;
+ std::cerr << d->handlesRegionSize << " " << d->interestRegionSize << std::endl;
+ d->selected_roi = extend_k_ring( d->selected_roi, d->interestRegionSize - d->handlesRegionSize );
+
+ //d->selected_roi = extend_sharp_edge(d->selected_roi, 0.2, d->dihedral_angle_variance, *d->vertex_index_map);
+ // add geodesic distance constraints into handles and ROI vertices
+ if (d->geodesicCircle)
+ {
+ double radius = 0;
+ BOOST_FOREACH(Vertex_handle v, d->selected_handles)
+ {
+ double dist = boost::get(*d->dist_pmap, v);
+ if ( dist> radius ) radius = dist;
+ }
+ d->selected_handles = extend_circle(d->selected_handles, radius, *d->dist_pmap);
+
+ radius = 0;
+ BOOST_FOREACH(Vertex_handle v, d->selected_roi)
+ {
+ double dist = boost::get(*d->dist_pmap, v);
+ if ( dist> radius ) radius = dist;
+ }
+ d->selected_roi = extend_circle(d->selected_roi, radius, *d->dist_pmap);
+ }
+
+
+ const Kernel::Point_3& p = vh->point();
+ d->orig_pos = p;
+ d->last_pos = p;
+ d->frame->setPosition(qglviewer::Vec(p.x(), p.y(), p.z()));
+ emit begin_edit();
+}
+
+
Vertex_handle
Scene_edit_polyhedron_item::selected_vertex() const {
return d->selected_vertex;
}
QList
-Scene_edit_polyhedron_item::selected_vertices() const {
+Scene_edit_polyhedron_item::selected_handles() const {
QList result;
- BOOST_FOREACH(Vertex_handle vh, d->selected_vertices) {
+ BOOST_FOREACH(Vertex_handle vh, d->selected_handles) {
result << vh;
}
return result;
}
+QList
+Scene_edit_polyhedron_item::non_selected_handles() const {
+ QList result;
+ BOOST_FOREACH(Vertex_handle vh, d->non_selected_handles) {
+ result << vh;
+ }
+ return result;
+}
+
+QList
+Scene_edit_polyhedron_item::selected_roi() const {
+ QList result;
+ BOOST_FOREACH(Vertex_handle vh, d->selected_roi) {
+ result << vh;
+ }
+ return result;
+}
+
+std::pair
+Scene_edit_polyhedron_item::selected_vector() const {
+ std::pair result;
+ if (!d->selected_vectors.empty())
+ {
+ result = d->selected_vectors[0];
+ }
+ return result;
+}
+
+QList
+Scene_edit_polyhedron_item::non_selected_roi() const {
+ QList result;
+ BOOST_FOREACH(Vertex_handle vh, d->non_selected_roi) {
+ result << vh;
+ }
+ return result;
+}
+
+void Scene_edit_polyhedron_item::clear_non_selected_roi() {
+ d->non_selected_roi.clear();
+}
+
+void Scene_edit_polyhedron_item::clear_selected_roi() {
+ d->selected_roi.clear();
+}
+
+
+void Scene_edit_polyhedron_item::clear_non_selected_handles() {
+ d->non_selected_handles.clear();
+}
+
+void Scene_edit_polyhedron_item::clear_selected_handles() {
+ d->selected_handles.clear();
+ d->selected_vertex = Vertex_handle();
+}
+
+void Scene_edit_polyhedron_item::clear_selected_vectors() {
+ d->selected_vectors.clear();
+}
+
+void Scene_edit_polyhedron_item::clear_non_selected_vectors() {
+ d->non_selected_vectors.clear();
+}
+
+int Scene_edit_polyhedron_item::usage_scenario() {
+ return d->usageScenario;
+}
+
+
Kernel::Point_3 Scene_edit_polyhedron_item::current_position() const {
const qglviewer::Vec vec = d->frame->position();
return Kernel::Point_3(vec.x, vec.y, vec.z);
}
+Kernel::Point_3 Scene_edit_polyhedron_item::last_position() const {
+ return d->last_pos;
+}
+
Kernel::Point_3 Scene_edit_polyhedron_item::original_position() const {
return d->orig_pos;
}
+void Scene_edit_polyhedron_item::setVisible(bool b) {
+ d->poly_item->setVisible(b);
+ Scene_item::setVisible(b);
+}
+void Scene_edit_polyhedron_item::setColor(QColor c) {
+ d->poly_item->setColor(c);
+ Scene_item::setColor(c);
+}
+void Scene_edit_polyhedron_item::setName(QString n) {
+ Scene_item::setName(n);
+ n.replace(" (edit)", "");
+ d->poly_item->setName(n);
+}
+void Scene_edit_polyhedron_item::setRenderingMode(RenderingMode m) {
+ d->poly_item->setRenderingMode(m);
+ Scene_item::setRenderingMode(m);
+}
+
#include "Scene_edit_polyhedron_item.moc"
diff --git a/Polyhedron/demo/Polyhedron/Scene_edit_polyhedron_item.h b/Polyhedron/demo/Polyhedron/Scene_edit_polyhedron_item.h
index 630de8eaf13..d5442c7f545 100644
--- a/Polyhedron/demo/Polyhedron/Scene_edit_polyhedron_item.h
+++ b/Polyhedron/demo/Polyhedron/Scene_edit_polyhedron_item.h
@@ -4,6 +4,8 @@
#include "Scene_edit_polyhedron_item_config.h"
#include "Scene_polyhedron_item.h"
#include "Polyhedron_type.h"
+#include
+#include
#include
#include
@@ -14,6 +16,12 @@
class QMenu;
struct Scene_edit_polyhedron_item_priv;
+typedef boost::graph_traits::vertex_descriptor vertex_descriptor;
+typedef boost::graph_traits::vertex_iterator vertex_iterator;
+typedef boost::graph_traits::edge_descriptor edge_descriptor;
+typedef boost::graph_traits::edge_iterator edge_iterator;
+typedef boost::graph_traits::in_edge_iterator in_edge_iterator;
+
// This class represents a polyhedron in the OpenGL scene
class SCENE_EDIT_POLYHEDRON_ITEM_EXPORT Scene_edit_polyhedron_item
: public Scene_item {
@@ -35,6 +43,11 @@ public:
// Function for displaying meta-data of the item
QString toolTip() const;
+ void setColor(QColor c);
+ void setName(QString n);
+ void setVisible(bool b);
+ void setRenderingMode(RenderingMode m);
+
// // Function to override the context menu
// QMenu* contextMenu();
@@ -53,8 +66,31 @@ public:
// Functions related to the edition
Kernel::Point_3 original_position() const;
Kernel::Point_3 current_position() const;
+ Kernel::Point_3 last_position() const;
Polyhedron::Vertex_handle selected_vertex() const;
- QList selected_vertices() const;
+
+ QList selected_handles() const;
+ QList non_selected_handles() const;
+ QList selected_roi() const;
+ QList non_selected_roi() const;
+ std::pair selected_vector() const;
+ void clear_selected_roi();
+ void clear_non_selected_roi();
+ void clear_selected_handles();
+ void clear_non_selected_handles();
+ void clear_selected_vectors();
+ void clear_non_selected_vectors();
+ int usage_scenario();
+ void setSelectedVertexChanged(bool status);
+ void setSelectedHandlesMoved(bool status);
+ void setSelectedVector(Kernel::Vector_3 translation_last);
+ double dihedral_angle(edge_descriptor e);
+ void find_sharp_vertices();
+ void find_sharp_vertices_1();
+
+ /// @deprecated
+ QList selected_vertices()
+ { return selected_handles(); }
/// Returns a Scene_polyhedron_item from the edit polyhedron item, and
/// transfer the ownership of the polyhedron to it.
@@ -74,8 +110,14 @@ public slots:
double dir_x,
double dir_y,
double dir_z);
- void setZoneSize(int i);
+ void setZoneSize(int i) { setHandlesRegionSize(i); } /// @deprecated
+ void setHandlesRegionSize(int i);
+ void setInterestRegionSize(int i);
+ void setGeodesicCircle(bool status);
+ void setSharpFeature(bool status);
+ void setUsageScenario(int i);
void vertex_has_been_selected(void* vertex_handle);
+ void vertex_has_been_selected_2(void* vertex_handle);
signals:
void begin_edit();
diff --git a/Polyhedron/demo/Polyhedron/data/negative.off b/Polyhedron/demo/Polyhedron/data/negative.off
new file mode 100644
index 00000000000..de7f3182f87
--- /dev/null
+++ b/Polyhedron/demo/Polyhedron/data/negative.off
@@ -0,0 +1,15 @@
+OFF
+7 6 0
+-215.983 70.3187 137.883
+-216.952 39.6826 144.676
+-207.932 -24.8993 148.723
+-247.708 69.538 123.733
+-246.196 45.203 131.288
+-246.937 14.9498 134.175
+-255.988 45.6255 130.774
+3 3 4 0
+3 1 0 4
+3 5 2 4
+3 1 4 2
+3 4 3 6
+3 4 6 5
diff --git a/Solver_interface/include/CGAL/Eigen_solver_traits.h b/Solver_interface/include/CGAL/Eigen_solver_traits.h
index fa8d782d9bc..c09aba99ac0 100644
--- a/Solver_interface/include/CGAL/Eigen_solver_traits.h
+++ b/Solver_interface/include/CGAL/Eigen_solver_traits.h
@@ -68,7 +68,7 @@ public:
// Public operations
public:
- Eigen_solver_traits(): m_solver_sptr(new EigenSolverT)
+ Eigen_solver_traits():m_mat(NULL), m_solver_sptr(new EigenSolverT)
{
}
@@ -93,8 +93,25 @@ public:
return m_solver_sptr->info() == Eigen::Success;
}
+
+ bool pre_factor (const Matrix& A, NT& D)
+ {
+ D = 1;
+
+ m_mat = &A.eigen_object();
+ solver().compute(*m_mat);
+ return solver().info() == Eigen::Success;
+ }
+
+ bool linear_solver(const Vector& B, Vector& X)
+ {
+ CGAL_precondition(m_mat!=NULL); //pre_factor should have been called first
+ X = solver().solve(B);
+ return solver().info() == Eigen::Success;
+ }
protected:
boost::shared_ptr m_solver_sptr;
+ const typename Matrix::EigenType* m_mat;
};
diff --git a/Surface_mesh_parameterization/include/CGAL/Taucs_solver_traits.h b/Surface_mesh_parameterization/include/CGAL/Taucs_solver_traits.h
index 4248b54e262..79867acdbc0 100644
--- a/Surface_mesh_parameterization/include/CGAL/Taucs_solver_traits.h
+++ b/Surface_mesh_parameterization/include/CGAL/Taucs_solver_traits.h
@@ -64,6 +64,10 @@ template // Tested with T = taucs_single or taucs_double
// May also work with T = taucs_dcomplex and taucs_scomplex
class Taucs_symmetric_solver_traits
{
+
+private:
+ boost::shared_ptr mtr;
+
// Public types
public:
@@ -174,6 +178,104 @@ public:
}
}
+
+ bool pre_factor (const Matrix& A, NT& D)
+ {
+ D = 1; // TAUCS does not support homogeneous coordinates
+
+#ifdef DEBUG_TRACE
+ // Turn on TAUCS trace to stderr or to a log file
+#if DEBUG_TRACE >= 2
+ std::cerr.flush();
+ taucs_logfile((char*)"stderr");
+#else
+ taucs_logfile((char*)"taucs.log");
+#endif
+
+#endif
+
+#ifdef WIN32
+ Win32_exception_handler eh; // catch Win32 structured exceptions
+#endif
+
+ try
+ {
+ int success;
+
+ // ordering
+ int* perm_raw = NULL;
+ int* invperm_raw = NULL;
+ taucs_ccs_order((taucs_ccs_matrix*) A.get_taucs_matrix(),
+ &perm_raw,
+ &invperm_raw,
+ (char*)"colamd");
+ boost::shared_ptr perm(perm_raw, free);
+ boost::shared_ptr invperm(invperm_raw, free);
+ if ( perm == NULL || invperm == NULL)
+ throw std::runtime_error("Ordering Failed");
+
+ // Create multi-file for out-of-core swapping.
+ // Note: g++ complains that tempnam() is deprecated. You may safely ignore the warning.
+#ifdef _MSC_VER
+ char template_name[13] = {'t', 'a', 'u', 'c', 's','.','X','X','X','X','X','X', '\0' };
+ char* matrixfile = _mktemp(template_name);
+ if (matrixfile == NULL)
+ throw std::runtime_error("Cannot Create Multifile");
+ boost::shared_ptr oocL(taucs_io_create_multifile(matrixfile), taucs_io_delete);
+ mtr = oocL;
+#else
+ boost::shared_ptr matrixfile(tempnam(NULL, "taucs.L"), free);
+ if (matrixfile == NULL)
+ throw std::runtime_error("Cannot Create Multifile");
+ boost::shared_ptr oocL(taucs_io_create_multifile(matrixfile.get()), taucs_io_delete);
+ mtr = oocL;
+#endif
+ if (mtr == NULL)
+ throw std::runtime_error("Cannot Create Multifile");
+
+ // factor
+ int memory_mb = int(taucs_available_memory_size()/1048576.0);
+ success = taucs_ooc_factor_llt((taucs_ccs_matrix*) A.get_taucs_matrix(),
+ mtr.get(),
+ memory_mb*1048576.0);
+ if (success != TAUCS_SUCCESS)
+ throw std::runtime_error("Factorization Failed");
+
+ return true;
+ }
+ catch (std::exception& e)
+ {
+ taucs_printf((char*)"\t");
+ taucs_printf((char*)(e.what() != NULL ? e.what() : "Incorrect Matrix"));
+ taucs_printf((char*)"\n");
+ return false;
+ }
+ catch (...)
+ {
+ taucs_printf((char*)"\tIncorrect Matrix\n");
+ return false;
+ }
+ }
+
+
+
+
+ bool solve (const Vector& B, Vector& X)
+ {
+ int success;
+ success = taucs_ooc_solve_llt(mtr.get(),
+ X.get_taucs_vector(),
+ (T*) B.get_taucs_vector());
+ if (success != TAUCS_SUCCESS)
+ throw std::runtime_error("Solving Failed");
+
+ return true;
+
+ }
+
+
+
+
private:
// Test if a floating point number is (close to) 0.0.
@@ -202,6 +304,11 @@ template // Tested with T = taucs_single or taucs_double
class Taucs_solver_traits
{
// Public types
+
+private:
+
+ boost::shared_ptr mtr;
+
public:
typedef Taucs_matrix Matrix;
@@ -336,6 +443,105 @@ public:
}
}
+
+
+ bool pre_factor (const Matrix& A, NT& D)
+ {
+ D = 1; // TAUCS does not support homogeneous coordinates
+
+#ifdef DEBUG_TRACE
+ // Turn on TAUCS trace to stderr or to a log file
+#if DEBUG_TRACE >= 2
+ std::cerr.flush();
+ taucs_logfile((char*)"stderr");
+#else
+ taucs_logfile((char*)"taucs.log");
+#endif
+
+#endif
+
+#ifdef WIN32
+ Win32_exception_handler eh; // catch Win32 structured exceptions
+#endif
+
+ try
+ {
+ int success;
+
+ // ordering
+ int* perm_raw = NULL;
+ int* invperm_raw = NULL;
+ taucs_ccs_order((taucs_ccs_matrix*) A.get_taucs_matrix(),
+ &perm_raw,
+ &invperm_raw,
+ (char*)"colamd");
+ boost::shared_ptr perm(perm_raw, free);
+ boost::shared_ptr invperm(invperm_raw, free);
+ if ( perm == NULL || invperm == NULL)
+ throw std::runtime_error("Ordering Failed");
+
+ // Create multi-file for out-of-core swapping.
+ // Note: g++ complains that tempnam() is deprecated. You may safely ignore the warning.
+#ifdef _MSC_VER
+ char template_name[13] = {'t', 'a', 'u', 'c', 's','.','X','X','X','X','X','X', '\0' };
+ char* matrixfile = _mktemp(template_name);
+ if (matrixfile == NULL)
+ throw std::runtime_error("Cannot Create Multifile");
+ boost::shared_ptr oocL(taucs_io_create_multifile(matrixfile), taucs_io_delete);
+ mtr = oocL;
+#else
+ boost::shared_ptr matrixfile(tempnam(NULL, "taucs.L"), free);
+ if (matrixfile == NULL)
+ throw std::runtime_error("Cannot Create Multifile");
+ boost::shared_ptr oocL(taucs_io_create_multifile(matrixfile.get()), taucs_io_delete);
+ mtr = oocL;
+#endif
+ if (mtr == NULL)
+ throw std::runtime_error("Cannot Create Multifile");
+
+ // factor
+ int memory_mb = int(taucs_available_memory_size()/1048576.0);
+ success = taucs_ooc_factor_lu((taucs_ccs_matrix*) A.get_taucs_matrix(),
+ perm.get(),
+ mtr.get(),
+ memory_mb*1048576.0);
+ if (success != TAUCS_SUCCESS)
+ throw std::runtime_error("Factorization Failed");
+
+ return true;
+ }
+ catch (std::exception& e)
+ {
+ taucs_printf((char*)"\t");
+ taucs_printf((char*)(e.what() != NULL ? e.what() : "Incorrect Matrix"));
+ taucs_printf((char*)"\n");
+ return false;
+ }
+ catch (...)
+ {
+ taucs_printf((char*)"\tIncorrect Matrix\n");
+ return false;
+ }
+ }
+
+
+
+
+ bool solve (const Vector& B, Vector& X)
+ {
+ int success;
+ success = taucs_ooc_solve_lu(mtr.get(),
+ X.get_taucs_vector(),
+ (T*) B.get_taucs_vector());
+ if (success != TAUCS_SUCCESS)
+ throw std::runtime_error("Solving Failed");
+
+ return true;
+
+ }
+
+
+
private:
// Test if a floating point number is (close to) 0.0.
diff --git a/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/CMakeLists.txt b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/CMakeLists.txt
new file mode 100644
index 00000000000..51961c6f8c2
--- /dev/null
+++ b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/CMakeLists.txt
@@ -0,0 +1,45 @@
+# Created by the script cgal_create_cmake_script
+# This is the CMake script for compiling a CGAL application.
+
+
+project( optimal_rotation_benchmark)
+
+cmake_minimum_required(VERSION 2.6.2)
+
+find_package(CGAL QUIET COMPONENTS Core )
+
+
+if ( CGAL_FOUND )
+
+ add_definitions(-DDEBUG_TRACE)
+
+ include( ${CGAL_USE_FILE} )
+
+ add_executable ( optimal_rotation_svd_eigen
+ optimal_rotation_svd_eigen.cpp)
+
+ add_executable ( optimal_rotation_svd_nr
+ optimal_rotation_svd_nr.cpp
+ nrutil.cpp)
+
+ add_executable ( optimal_rotation_polar
+ optimal_rotation_polar.cpp)
+
+ add_executable ( optimal_rotation_polar_eigen
+ optimal_rotation_polar_eigen.cpp)
+
+else()
+
+ message(STATUS "This program requires the CGAL library, and will not be compiled.")
+
+endif()
+
+
+find_package(Eigen3 3.0.0)
+
+if(EIGEN3_FOUND)
+ include( ${EIGEN3_USE_FILE} )
+ endif(EIGEN3_FOUND)
+
+
+
diff --git a/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/SVD_benchmark b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/SVD_benchmark
new file mode 100644
index 00000000000..d4bff398d2d
--- /dev/null
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+-7.53503e-005 0.000376362 -2.05164e-005
+-0.000100393 -3.20956e-005 0.000100646
+
+0.000442286 3.76353e-005 0.000188264
+3.09831e-005 0.00058302 -0.000111743
+0.000196195 -0.00013376 0.000195696
+
+0.00125269 -0.00403125 0.000850396
+-0.00422862 0.0217736 -0.00463688
+0.00106323 -0.00548689 0.00125069
+
+0.000161286 -2.56058e-006 -9.47024e-005
+-9.21817e-006 0.000174926 -3.96477e-005
+-9.05929e-005 -4.61185e-005 0.000105693
+
+0.000222644 9.46893e-006 -1.42421e-005
+7.56542e-006 0.000284501 4.70265e-005
+-1.29209e-005 4.49285e-005 0.000104926
+
+0.000782807 2.73277e-005 7.08453e-005
+2.75023e-005 0.000656859 9.87423e-005
+6.89242e-005 9.26241e-005 3.55912e-005
+
+0.00046243 0.000138946 -4.53474e-005
+0.000133445 0.000128492 -0.000171888
+-2.5364e-005 -0.000168273 0.000390645
+
+0.000609107 4.57559e-005 0.000732131
+4.30893e-005 0.00164787 7.78867e-006
+0.000738711 2.17145e-005 0.00102481
+
+0.000414156 0.000255694 0.000443281
+0.000255149 0.000983719 -0.000226118
+0.000448015 -0.000231804 0.000892182
+
+0.000219605 -8.2217e-005 0.000188451
+-7.37046e-005 0.000359252 1.41699e-005
+0.000224634 3.099e-005 0.000338636
+
+0.000416207 -1.22634e-005 0.000213529
+-1.03824e-005 0.000475966 2.61962e-005
+0.000178357 2.27749e-005 0.000155676
+
diff --git a/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/nrutil.cpp b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/nrutil.cpp
new file mode 100644
index 00000000000..46c6579302a
--- /dev/null
+++ b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/nrutil.cpp
@@ -0,0 +1,617 @@
+
+
+#if 1
+
+#include
+#include
+#include
+#define NR_END 1
+#define FREE_ARG char*
+
+
+void nrerror(char error_text[])
+/*Numerical Recipes standard error handler */
+{
+ fprintf(stderr,"Numerical Recipes run-time error...\n");
+ fprintf(stderr,"%s\n",error_text);
+ fprintf(stderr,"...now exiting to system...\n");
+ exit(1);
+}
+
+float *vec(long nl, long nh)
+/* allocate a float vector with subscript range v[nl..nh] */
+{
+ float *v;
+
+ v=(float *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(float)));
+ if (!v) nrerror("allocation failure in vector()");
+ return v-nl+NR_END;
+}
+
+int *ivector(long nl, long nh)
+/* allocate an int vector with subscript range v[nl..nh] */
+{
+ int *v;
+
+ v=(int *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(int)));
+ if (!v) nrerror("allocation failure in ivector()");
+ return v-nl+NR_END;
+}
+
+unsigned char *cvector(long nl, long nh)
+/* allocate an unsigned char vector with subscript range v[nl..nh] */
+{
+ unsigned char *v;
+
+ v=(unsigned char *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(unsigned char)));
+ if (!v) nrerror("allocation failure in cvector()");
+ return v-nl+NR_END;
+}
+
+unsigned long *lvector(long nl, long nh)
+/* allocate an unsigned long vector with subscript range v[nl..nh] */
+{
+ unsigned long *v;
+
+ v=(unsigned long *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(long)));
+ if (!v) nrerror("allocation failure in lvector()");
+ return v-nl+NR_END;
+}
+
+double *dvector(long nl, long nh)
+/* allocate a double vector with subscript range v[nl..nh] */
+{
+ double *v;
+
+ v=(double *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(double)));
+ if (!v) nrerror("allocation failure in dvector()");
+ return v-nl+NR_END;
+}
+
+float **matrix(long nrl, long nrh, long ncl, long nch)
+/* allocate a float matrix with subscript range m[nrl..nrh][ncl..nch] */
+{
+ long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
+ float **m;
+
+ /* allocate pointers to rows */
+ m=(float **) malloc((size_t)((nrow+NR_END)*sizeof(float*)));
+ if (!m) nrerror("allocation failure 1 in matrix()");
+ m += NR_END;
+ m -= nrl;
+
+ /* allocate rows and set pointers to them */
+ m[nrl]=(float *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(float)));
+ if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
+ m[nrl] += NR_END;
+ m[nrl] -= ncl;
+
+ for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
+
+ /* return pointer to array of pointers to rows */
+ return m;
+}
+
+double **dmatrix(long nrl, long nrh, long ncl, long nch)
+/* allocate a double matrix with subscript range m[nrl..nrh][ncl..nch] */
+{
+ long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
+ double **m;
+
+ /* allocate pointers to rows */
+ m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
+ if (!m) nrerror("allocation failure 1 in matrix()");
+ m += NR_END;
+ m -= nrl;
+
+ /* allocate rows and set pointers to them */
+ m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
+ if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
+ m[nrl] += NR_END;
+ m[nrl] -= ncl;
+
+ for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
+
+ /* return pointer to array of pointers to rows */
+ return m;
+}
+
+int **imatrix(long nrl, long nrh, long ncl, long nch)
+/* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */
+{
+ long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
+ int **m;
+
+ /* allocate pointers to rows */
+ m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));
+ if (!m) nrerror("allocation failure 1 in matrix()");
+ m += NR_END;
+ m -= nrl;
+
+
+ /* allocate rows and set pointers to them */
+ m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));
+ if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
+ m[nrl] += NR_END;
+ m[nrl] -= ncl;
+
+ for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
+
+ /* return pointer to array of pointers to rows */
+ return m;
+}
+
+float **submatrix(float **a, long oldrl, long oldrh, long oldcl, long oldch,
+ long newrl, long newcl)
+/* point a submatrix [newrl..][newcl..] to a[oldrl..oldrh][oldcl..oldch] */
+{
+ long i,j,nrow=oldrh-oldrl+1,ncol=oldcl-newcl;
+ float **m;
+
+ /* allocate array of pointers to rows */
+ m=(float **) malloc((size_t) ((nrow+NR_END)*sizeof(float*)));
+ if (!m) nrerror("allocation failure in submatrix()");
+ m += NR_END;
+ m -= newrl;
+
+ /* set pointers to rows */
+ for(i=oldrl,j=newrl;i<=oldrh;i++,j++) m[j]=a[i]+ncol;
+
+ /* return pointer to array of pointers to rows */
+ return m;
+}
+
+float **convert_matrix(float *a, long nrl, long nrh, long ncl, long nch)
+/* allocate a float matrix m[nrl..nrh][ncl..nch] that points to the matrix
+declared in the standard C manner as a[nrow][ncol], where nrow=nrh-nrl+1
+and ncol=nch-ncl+1. The routine should be called with the address
+&a[0][0] as the first argument. */
+{
+ long i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1;
+ float **m;
+
+ /* allocate pointers to rows */
+ m=(float **) malloc((size_t) ((nrow+NR_END)*sizeof(float*)));
+ if (!m) nrerror("allocation failure in convert_matrix()");
+ m += NR_END;
+ m -= nrl;
+
+ /* set pointers to rows */
+ m[nrl]=a-ncl;
+ for(i=1,j=nrl+1;i
+#define NR_END 1
+#define FREE_ARG char*
+
+void nrerror(error_text)
+char error_text[];
+/* Numerical Recipes standard error handler */
+{
+ void exit();
+
+ fprintf(stderr,"Numerical Recipes run-time error...\n");
+ fprintf(stderr,"%s\n",error_text);
+ fprintf(stderr,"...now exiting to system...\n");
+ exit(1);
+}
+
+float *vector(nl,nh)
+long nh,nl;
+/* allocate a float vector with subscript range v[nl..nh] */
+{
+ float *v;
+
+ v=(float *)malloc((unsigned int) ((nh-nl+1+NR_END)*sizeof(float)));
+ if (!v) nrerror("allocation failure in vector()");
+ return v-nl+NR_END;
+}
+
+int *ivector(nl,nh)
+long nh,nl;
+/* allocate an int vector with subscript range v[nl..nh] */
+{
+ int *v;
+
+ v=(int *)malloc((unsigned int) ((nh-nl+1+NR_END)*sizeof(int)));
+ if (!v) nrerror("allocation failure in ivector()");
+ return v-nl+NR_END;
+}
+
+unsigned char *cvector(nl,nh)
+long nh,nl;
+/* allocate an unsigned char vector with subscript range v[nl..nh] */
+{
+ unsigned char *v;
+
+ v=(unsigned char *)malloc((unsigned int) ((nh-nl+1+NR_END)*sizeof(unsigned char)));
+ if (!v) nrerror("allocation failure in cvector()");
+ return v-nl+NR_END;
+}
+
+unsigned long *lvector(nl,nh)
+long nh,nl;
+/* allocate an unsigned long vector with subscript range v[nl..nh] */
+{
+ unsigned long *v;
+
+ v=(unsigned long *)malloc((unsigned int) ((nh-nl+1+NR_END)*sizeof(long)));
+ if (!v) nrerror("allocation failure in lvector()");
+ return v-nl+NR_END;
+}
+
+double *dvector(nl,nh)
+long nh,nl;
+/* allocate a double vector with subscript range v[nl..nh] */
+{
+ double *v;
+
+ v=(double *)malloc((unsigned int) ((nh-nl+1+NR_END)*sizeof(double)));
+ if (!v) nrerror("allocation failure in dvector()");
+ return v-nl+NR_END;
+}
+
+float **matrix(nrl,nrh,ncl,nch)
+long nch,ncl,nrh,nrl;
+/* allocate a float matrix with subscript range m[nrl..nrh][ncl..nch] */
+{
+ long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
+ float **m;
+
+ /* allocate pointers to rows */
+ m=(float **) malloc((unsigned int)((nrow+NR_END)*sizeof(float*)));
+ if (!m) nrerror("allocation failure 1 in matrix()");
+ m += NR_END;
+ m -= nrl;
+
+ /* allocate rows and set pointers to them */
+ m[nrl]=(float *) malloc((unsigned int)((nrow*ncol+NR_END)*sizeof(float)));
+ if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
+ m[nrl] += NR_END;
+ m[nrl] -= ncl;
+
+ for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
+
+ /* return pointer to array of pointers to rows */
+ return m;
+}
+
+double **dmatrix(nrl,nrh,ncl,nch)
+long nch,ncl,nrh,nrl;
+/* allocate a double matrix with subscript range m[nrl..nrh][ncl..nch] */
+{
+ long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
+ double **m;
+
+ /* allocate pointers to rows */
+ m=(double **) malloc((unsigned int)((nrow+NR_END)*sizeof(double*)));
+ if (!m) nrerror("allocation failure 1 in matrix()");
+ m += NR_END;
+ m -= nrl;
+
+ /* allocate rows and set pointers to them */
+ m[nrl]=(double *) malloc((unsigned int)((nrow*ncol+NR_END)*sizeof(double)));
+ if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
+ m[nrl] += NR_END;
+ m[nrl] -= ncl;
+
+ for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
+
+ /* return pointer to array of pointers to rows */
+ return m;
+}
+
+int **imatrix(nrl,nrh,ncl,nch)
+long nch,ncl,nrh,nrl;
+/* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */
+{
+ long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
+ int **m;
+
+ /* allocate pointers to rows */
+ m=(int **) malloc((unsigned int)((nrow+NR_END)*sizeof(int*)));
+ if (!m) nrerror("allocation failure 1 in matrix()");
+ m += NR_END;
+ m -= nrl;
+
+
+ /* allocate rows and set pointers to them */
+ m[nrl]=(int *) malloc((unsigned int)((nrow*ncol+NR_END)*sizeof(int)));
+ if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
+ m[nrl] += NR_END;
+ m[nrl] -= ncl;
+
+ for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
+
+ /* return pointer to array of pointers to rows */
+ return m;
+}
+
+float **submatrix(a,oldrl,oldrh,oldcl,oldch,newrl,newcl)
+float **a;
+long newcl,newrl,oldch,oldcl,oldrh,oldrl;
+/* point a submatrix [newrl..][newcl..] to a[oldrl..oldrh][oldcl..oldch] */
+{
+ long i,j,nrow=oldrh-oldrl+1,ncol=oldcl-newcl;
+ float **m;
+
+ /* allocate array of pointers to rows */
+ m=(float **) malloc((unsigned int) ((nrow+NR_END)*sizeof(float*)));
+ if (!m) nrerror("allocation failure in submatrix()");
+ m += NR_END;
+ m -= newrl;
+
+ /* set pointers to rows */
+ for(i=oldrl,j=newrl;i<=oldrh;i++,j++) m[j]=a[i]+ncol;
+
+ /* return pointer to array of pointers to rows */
+ return m;
+}
+
+float **convert_matrix(a,nrl,nrh,ncl,nch)
+float *a;
+long nch,ncl,nrh,nrl;
+/* allocate a float matrix m[nrl..nrh][ncl..nch] that points to the matrix
+declared in the standard C manner as a[nrow][ncol], where nrow=nrh-nrl+1
+and ncol=nch-ncl+1. The routine should be called with the address
+&a[0][0] as the first argument. */
+{
+ long i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1;
+ float **m;
+
+ /* allocate pointers to rows */
+ m=(float **) malloc((unsigned int) ((nrow+NR_END)*sizeof(float*)));
+ if (!m) nrerror("allocation failure in convert_matrix()");
+ m += NR_END;
+ m -= nrl;
+
+ /* set pointers to rows */
+ m[nrl]=a-ncl;
+ for(i=1,j=nrl+1;i (dmaxarg2) ?\
+ (dmaxarg1) : (dmaxarg2))
+
+static double dminarg1,dminarg2;
+#define DMIN(a,b) (dminarg1=(a),dminarg2=(b),(dminarg1) < (dminarg2) ?\
+ (dminarg1) : (dminarg2))
+
+static float maxarg1,maxarg2;
+#define FMAX(a,b) (maxarg1=(a),maxarg2=(b),(maxarg1) > (maxarg2) ?\
+ (maxarg1) : (maxarg2))
+
+static float minarg1,minarg2;
+#define FMIN(a,b) (minarg1=(a),minarg2=(b),(minarg1) < (minarg2) ?\
+ (minarg1) : (minarg2))
+
+static long lmaxarg1,lmaxarg2;
+#define LMAX(a,b) (lmaxarg1=(a),lmaxarg2=(b),(lmaxarg1) > (lmaxarg2) ?\
+ (lmaxarg1) : (lmaxarg2))
+
+static long lminarg1,lminarg2;
+#define LMIN(a,b) (lminarg1=(a),lminarg2=(b),(lminarg1) < (lminarg2) ?\
+ (lminarg1) : (lminarg2))
+
+static int imaxarg1,imaxarg2;
+#define IMAX(a,b) (imaxarg1=(a),imaxarg2=(b),(imaxarg1) > (imaxarg2) ?\
+ (imaxarg1) : (imaxarg2))
+
+static int iminarg1,iminarg2;
+#define IMIN(a,b) (iminarg1=(a),iminarg2=(b),(iminarg1) < (iminarg2) ?\
+ (iminarg1) : (iminarg2))
+
+#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
+
+#if 1
+
+void nrerror(char error_text[]);
+float *vec(long nl, long nh);
+int *ivector(long nl, long nh);
+unsigned char *cvector(long nl, long nh);
+unsigned long *lvector(long nl, long nh);
+double *dvector(long nl, long nh);
+float **matrix(long nrl, long nrh, long ncl, long nch);
+double **dmatrix(long nrl, long nrh, long ncl, long nch);
+int **imatrix(long nrl, long nrh, long ncl, long nch);
+float **submatrix(float **a, long oldrl, long oldrh, long oldcl, long oldch,
+ long newrl, long newcl);
+float **convert_matrix(float *a, long nrl, long nrh, long ncl, long nch);
+float ***f3tensor(long nrl, long nrh, long ncl, long nch, long ndl, long ndh);
+void free_vector(float *v, long nl, long nh);
+void free_ivector(int *v, long nl, long nh);
+void free_cvector(unsigned char *v, long nl, long nh);
+void free_lvector(unsigned long *v, long nl, long nh);
+void free_dvector(double *v, long nl, long nh);
+void free_matrix(float **m, long nrl, long nrh, long ncl, long nch);
+void free_dmatrix(double **m, long nrl, long nrh, long ncl, long nch);
+void free_imatrix(int **m, long nrl, long nrh, long ncl, long nch);
+void free_submatrix(float **b, long nrl, long nrh, long ncl, long nch);
+void free_convert_matrix(float **b, long nrl, long nrh, long ncl, long nch);
+void free_f3tensor(float ***t, long nrl, long nrh, long ncl, long nch,
+ long ndl, long ndh);
+
+#else /* ANSI */
+/* traditional - K&R */
+
+void nrerror();
+float *vec();
+float **matrix();
+float **submatrix();
+float **convert_matrix();
+float ***f3tensor();
+double *dvector();
+double **dmatrix();
+int *ivector();
+int **imatrix();
+unsigned char *cvector();
+unsigned long *lvector();
+void free_vector();
+void free_dvector();
+void free_ivector();
+void free_cvector();
+void free_lvector();
+void free_matrix();
+void free_submatrix();
+void free_convert_matrix();
+void free_dmatrix();
+void free_imatrix();
+void free_f3tensor();
+
+#endif /* ANSI */
+
+#endif /* _NR_UTILS_H_ */
diff --git a/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_polar.cpp b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_polar.cpp
new file mode 100644
index 00000000000..0baa9990c1a
--- /dev/null
+++ b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_polar.cpp
@@ -0,0 +1,113 @@
+#include
+#include
+#include
+#include
+#include
+
+
+#include
+#include
+
+
+double norm_1(Eigen::Matrix3d X)
+{
+ double sum = 0;
+ for ( int i = 0; i < 3; i++ )
+ {
+ for ( int j = 0; j < 3; j++ )
+ {
+ sum += abs(X(i,j));
+ }
+ }
+ return sum;
+}
+
+double norm_inf(Eigen::Matrix3d X)
+{
+ double max_abs = abs(X(0,0));
+ for ( int i = 0; i < 3; i++ )
+ {
+ for ( int j = 0; j < 3; j++ )
+ {
+ double new_abs = abs(X(i,j));
+ if ( new_abs > max_abs )
+ {
+ max_abs = new_abs;
+ }
+ }
+ }
+ return max_abs;
+}
+
+
+void algorithm_polar(Eigen::Matrix3d A, Eigen::Matrix3d &U, double tolerance)
+{
+ Eigen::Matrix3d X = A;
+ int k = -1;
+ Eigen::Matrix3d Y;
+ double alpha, beta, gamma;
+ do
+ {
+ k++;
+ Y = X.inverse();
+ alpha = sqrt( norm_1(X) * norm_inf(X) );
+ beta = sqrt( norm_1(Y) * norm_inf(Y) );
+ gamma = sqrt(beta/alpha);
+ X = 0.5*( gamma*X + Y.transpose()/gamma );
+
+ } while ( abs(gamma-1) > tolerance );
+
+ U = X;
+}
+
+
+int main() {
+
+ std::ifstream file;
+ file.open("SVD_benchmark");
+ if (!file)
+ {
+ CGAL_TRACE_STREAM << "Error loading file!\n";
+ return 0;
+ }
+
+ int ite = 200000;
+ Eigen::Matrix3d A, U, H;
+
+ int matrix_idx = rand()%200;
+ for (int i = 0; i < matrix_idx; i++)
+ {
+ for (int j = 0; j < 3; j++)
+ {
+ for (int k = 0; k < 3; k++)
+ {
+ file >> A(j, k);
+ }
+ }
+ }
+ file.close();
+
+ A(0,0) = 0.0014667022958104185; A(0,1) = 0.0024644551180079627; A(0,2) = 0.0040659871060825092;
+ A(1,0) = 0.0028327558016991478; A(1,1) = 0.0054236820249146406; A(1,2) = 0.0079280090866983826;
+ A(2,0) = 0.0039090073251031232; A(2,1) = 0.0066744523074963374; A(2,2) = 0.010848552426718550;
+ A = A*10000;
+
+ CGAL::Timer task_timer;
+
+ CGAL_TRACE_STREAM << "Start SVD decomposition...";
+ task_timer.start();
+ for (int i = 0; i < ite; i++)
+ {
+ algorithm_polar(A, U, 1e-6);
+ U.transposeInPlace();
+ double det_2 = U.determinant();
+ int aaa = 0;
+ }
+ task_timer.stop();
+
+
+ CGAL_TRACE_STREAM << "done: " << task_timer.time() << "s\n";
+
+ return 0;
+}
+
diff --git a/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_polar_eigen.cpp b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_polar_eigen.cpp
new file mode 100644
index 00000000000..3183b6e6d52
--- /dev/null
+++ b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_polar_eigen.cpp
@@ -0,0 +1,162 @@
+#include
+#include
+#include
+#include
+#include
+#include
+
+
+#include
+#include
+
+
+double norm_1(Eigen::Matrix3d X)
+{
+ double sum = 0;
+ for ( int i = 0; i < 3; i++ )
+ {
+ for ( int j = 0; j < 3; j++ )
+ {
+ sum += abs(X(i,j));
+ }
+ }
+ return sum;
+}
+
+double norm_inf(Eigen::Matrix3d X)
+{
+ double max_abs = abs(X(0,0));
+ for ( int i = 0; i < 3; i++ )
+ {
+ for ( int j = 0; j < 3; j++ )
+ {
+ double new_abs = abs(X(i,j));
+ if ( new_abs > max_abs )
+ {
+ max_abs = new_abs;
+ }
+ }
+ }
+ return max_abs;
+}
+
+template
+void polar_eigen(const Mat& A, Mat& R, bool& SVD)
+{
+ typedef typename Mat::Scalar Scalar;
+ typedef Eigen::Matrix Vec;
+
+ const Scalar th = std::sqrt(Eigen::NumTraits::dummy_precision());
+
+ Eigen::SelfAdjointEigenSolver eig;
+ feclearexcept(FE_UNDERFLOW);
+ eig.computeDirect(A.transpose()*A);
+
+ if(fetestexcept(FE_UNDERFLOW) || eig.eigenvalues()(0)/eig.eigenvalues()(2)/100.0 svd;
+ svd.compute(A, Eigen::ComputeFullU | Eigen::ComputeFullV );
+ const Mat& u = svd.matrixU(); const Mat& v = svd.matrixV(); const Vec& w = svd.singularValues();
+ R = u*v.transpose();
+ SVD = true;
+ return;
+ }
+
+ Vec S = eig.eigenvalues().cwiseSqrt();
+ R = A * eig.eigenvectors() * S.asDiagonal().inverse()
+ * eig.eigenvectors().transpose();
+ SVD = false;
+}
+
+
+int main() {
+ std::ifstream file;
+ file.open("Polar_benchmark");
+ if (!file)
+ {
+ CGAL_TRACE_STREAM << "Error loading file!\n";
+ return 0;
+ }
+
+ Eigen::Matrix3d A, U, r;
+ bool SVD = false;
+ int num_svd = 0;
+ int num_mtr = 0;
+
+ CGAL_TRACE_STREAM << "start polar decomposition...\n";
+ while (!file.eof())
+ {
+ for (int j = 0; j < 3; j++)
+ {
+ for (int k = 0; k < 3; k++)
+ {
+ file >> A(j, k);
+ }
+ }
+ num_mtr++;
+ double det = A.determinant();
+ if (A.determinant() > 0)
+ {
+ polar_eigen (A, U, SVD);
+ if (SVD)
+ num_svd++;
+ U.transposeInPlace();
+ double det_2 = U.determinant();
+ if ( abs(det_2-1) > 1e-2 )
+ {
+ CGAL_TRACE_STREAM << "error matrix: det = " << det_2 << "\n";
+ }
+ }
+ }
+ file.close();
+
+ CGAL_TRACE_STREAM << "done. " << num_svd << " SVD decompositions in " << num_mtr << " matrices\n";
+ return 0;
+
+ /*int ite = 200000;
+ Eigen::JacobiSVD svd;
+ Eigen::Matrix3d A, U, H, r;
+
+ int matrix_idx = rand()%200;
+ for (int i = 0; i < matrix_idx; i++)
+ {
+ for (int j = 0; j < 3; j++)
+ {
+ for (int k = 0; k < 3; k++)
+ {
+ file >> A(j, k);
+ }
+ }
+ }
+ file.close();
+
+ A(0,0) = 0.0014667022958104185; A(0,1) = 0.0024644551180079627; A(0,2) = 0.0040659871060825092;
+ A(1,0) = 0.0028327558016991478; A(1,1) = 0.0054236820249146406; A(1,2) = 0.0079280090866983826;
+ A(2,0) = 0.0039090073251031232; A(2,1) = 0.0066744523074963374; A(2,2) = 0.010848552426718550;
+ A = A*10000;
+ double det = A.determinant();
+
+ CGAL::Timer task_timer;
+
+ CGAL_TRACE_STREAM << "Start SVD decomposition...";
+ task_timer.start();
+ for (int i = 0; i < ite; i++)
+ {
+ if (A.determinant() > 0)
+ {
+ polar_eigen (A, U);
+ U.transposeInPlace();
+ double det_2 = U.determinant();
+ r = U*U.transpose();
+ }
+ }
+ task_timer.stop();
+
+
+ CGAL_TRACE_STREAM << "done: " << task_timer.time() << "s\n";
+
+ return 0;*/
+}
+
diff --git a/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_svd_eigen.cpp b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_svd_eigen.cpp
new file mode 100644
index 00000000000..1b1d72c7350
--- /dev/null
+++ b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_svd_eigen.cpp
@@ -0,0 +1,57 @@
+
+#include
+#include
+#include
+#include
+#include
+
+
+#include
+#include
+
+int main() {
+
+ std::ifstream file;
+ file.open("SVD_benchmark");
+ if (!file)
+ {
+ CGAL_TRACE_STREAM << "Error loading file!\n";
+ return 0;
+ }
+
+ int ite = 200000;
+ Eigen::JacobiSVD svd;
+ Eigen::Matrix3d u, v, cov, r;
+ Eigen::Vector3d w;
+
+ int matrix_idx = rand()%200;
+ for (int i = 0; i < matrix_idx; i++)
+ {
+ for (int j = 0; j < 3; j++)
+ {
+ for (int k = 0; k < 3; k++)
+ {
+ file >> cov(j, k);
+ }
+ }
+ }
+
+
+ CGAL::Timer task_timer;
+
+ CGAL_TRACE_STREAM << "Start SVD decomposition...";
+ task_timer.start();
+ for (int i = 0; i < ite; i++)
+ {
+
+ svd.compute( cov, Eigen::ComputeFullU | Eigen::ComputeFullV );
+ u = svd.matrixU(); v = svd.matrixV(); w = svd.singularValues();
+ r = v*u.transpose();
+ }
+ task_timer.stop();
+ file.close();
+
+ CGAL_TRACE_STREAM << "done: " << task_timer.time() << "s\n";
+
+ return 0;
+}
\ No newline at end of file
diff --git a/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_svd_nr.cpp b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_svd_nr.cpp
new file mode 100644
index 00000000000..5389b198a51
--- /dev/null
+++ b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/optimal_rotation_svd_nr.cpp
@@ -0,0 +1,91 @@
+#include "svd.h"
+#include
+#include
+#include
+#include
+#include
+
+int main() {
+
+ std::ifstream file;
+ file.open("SVD_benchmark");
+ if (!file)
+ {
+ CGAL_TRACE_STREAM << "Error loading file!\n";
+ return 0;
+ }
+
+ // initialization of matrices
+ int ite = 200000;
+ double ***u;
+ u = new double** [ite];
+ for (int i = 0; i < ite; i++)
+ {
+ u[i] = new double* [4];
+ for (int j = 0; j < 4; j++)
+ {
+ u[i][j] = new double [4];
+ }
+ }
+ int matrix_idx = rand()%200;
+ for (int i = 0; i < matrix_idx; i++)
+ {
+ for (int j = 0; j < 3; j++)
+ {
+ for (int k = 0; k < 3; k++)
+ {
+ file >> u[0][j+1][k+1];
+ }
+ }
+ }
+ for (int i = 1; i < ite; i++)
+ {
+ for (int j = 0; j < 3; j++)
+ {
+ for (int k = 0; k < 3; k++)
+ {
+ u[i][j+1][k+1] = u[0][j+1][k+1];
+ }
+ }
+ }
+ double **v;
+ v = new double* [4];
+ for (int i = 0; i < 4; i++)
+ {
+ v[i] = new double[4];
+ }
+ double *w;
+ w = new double[4];
+
+ CGAL::Timer task_timer;
+
+ CGAL_TRACE_STREAM << "Start SVD decomposition...";
+ task_timer.start();
+ for (int i = 0; i < ite; i++)
+ {
+ svdcmp(u[i], 3, 3, w, v);
+ }
+ task_timer.stop();
+ file.close();
+
+ CGAL_TRACE_STREAM << "done: " << task_timer.time() << "s\n";
+
+ delete [] w;
+ for (int i = 0; i < 4; i++)
+ {
+ delete [] v[i];
+ }
+ delete [] v;
+ for (int i = 0; i < ite; i++)
+ {
+ for (int j = 0; j < 4; j++)
+ {
+ delete [] u[i][j];
+ }
+ delete [] u[i];
+ }
+ delete [] u;
+
+ return 0;
+}
+
diff --git a/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/svd.h b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/svd.h
new file mode 100644
index 00000000000..2c753984a32
--- /dev/null
+++ b/Surface_modeling/benchmark/Surface_modeling/optimal_rotation/svd.h
@@ -0,0 +1,209 @@
+#pragma once
+
+#include
+#include "nrutil.h"
+
+double pythag(double a, double b);
+
+inline void svdcmp(double **a, int m, int n, double w[], double **v)
+{
+ double pythag(double a, double b);
+ int flag,i,its,j,jj,k,l,nm;
+ double anorm,c,f,g,h,s,scale,x,y,z,*rv1;
+ rv1=dvector(1,n);
+ g=scale=anorm=0.0; //Householder reduction to bidiagonal form.
+ for (i=1;i<=n;i++) {
+ l=i+1;
+ rv1[i]=scale*g;
+ g=s=scale=0.0;
+ if (i <= m) {
+ for (k=i;k<=m;k++) scale += fabs(a[k][i]);
+ if (scale) {
+ for (k=i;k<=m;k++) {
+ a[k][i] /= scale;
+ s += a[k][i]*a[k][i];
+ }
+ f=a[i][i];
+ g = -SIGN(sqrt(s),f);
+ h=f*g-s;
+ a[i][i]=f-g;
+ for (j=l;j<=n;j++) {
+ for (s=0.0,k=i;k<=m;k++) s += a[k][i]*a[k][j];
+ f=s/h;
+ for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
+ }
+ for (k=i;k<=m;k++) a[k][i] *= scale;
+ }
+ }
+ w[i]=scale *g;
+ g=s=scale=0.0;
+ if (i <= m && i != n) {
+ for (k=l;k<=n;k++) scale += fabs(a[i][k]);
+ if (scale) {
+ for (k=l;k<=n;k++) {
+ a[i][k] /= scale;
+ s += a[i][k]*a[i][k];
+ }
+ f=a[i][l];
+ g = -SIGN(sqrt(s),f);
+ h=f*g-s;
+ a[i][l]=f-g;
+ for (k=l;k<=n;k++) rv1[k]=a[i][k]/h;
+ for (j=l;j<=m;j++) {
+ for (s=0.0,k=l;k<=n;k++) s += a[j][k]*a[i][k];
+ for (k=l;k<=n;k++) a[j][k] += s*rv1[k];
+ }
+ for (k=l;k<=n;k++) a[i][k] *= scale;
+ }
+ }
+ anorm=DMAX(anorm,(fabs(w[i])+fabs(rv1[i])));
+ }
+ for (i=n;i>=1;i--) { //Accumulation of right-hand transformations.
+ if (i < n) {
+ if (g) {
+ for (j=l;j<=n;j++) //Double division to avoid possible underflow.
+ v[j][i]=(a[i][j]/a[i][l])/g;
+ for (j=l;j<=n;j++) {
+ for (s=0.0,k=l;k<=n;k++) s += a[i][k]*v[k][j];
+ for (k=l;k<=n;k++) v[k][j] += s*v[k][i];
+ }
+ }
+ for (j=l;j<=n;j++) v[i][j]=v[j][i]=0.0;
+ }
+ v[i][i]=1.0;
+ g=rv1[i];
+ l=i;
+ }
+ for (i=IMIN(m,n);i>=1;i--) { //Accumulation of left-hand transformations.
+ l=i+1;
+ g=w[i];
+ for (j=l;j<=n;j++) a[i][j]=0.0;
+ if (g) {
+ g=1.0/g;
+ for (j=l;j<=n;j++) {
+ for (s=0.0,k=l;k<=m;k++) s += a[k][i]*a[k][j];
+ f=(s/a[i][i])*g;
+ for (k=i;k<=m;k++) a[k][j] += f*a[k][i];
+ }
+ for (j=i;j<=m;j++) a[j][i] *= g;
+ } else for (j=i;j<=m;j++) a[j][i]=0.0;
+ ++a[i][i];
+ }
+ for (k=n;k>=1;k--)
+ { //Diagonalization of the bidiagonal form: Loop over
+ for (its=1;its<=30;its++)
+ {
+ flag=1;
+ for (l=k;l>=1;l--)
+ { //Test for splitting.
+ nm=l-1; //Note that rv1[1] is always zero.
+ if ((double)(fabs(rv1[l])+anorm) == anorm)
+ {
+ flag=0;
+ break;
+ }
+ if ((double)(fabs(w[nm])+anorm) == anorm) break;
+ }
+ if (flag)
+ {
+ c=0.0; //Cancellation of rv1[l], if l > 1.
+ s=1.0;
+ for (i=l;i<=k;i++)
+ {
+ f=s*rv1[i];
+ rv1[i]=c*rv1[i];
+ if ((double)(fabs(f)+anorm) == anorm)
+ break;
+ g=w[i];
+ h=pythag(f,g);
+ w[i]=h;
+ h=1.0/h;
+ c=g*h;
+ s = -f*h;
+ for (j=1;j<=m;j++)
+ {
+ y=a[j][nm];
+ z=a[j][i];
+ a[j][nm]=y*c+z*s;
+ a[j][i]=z*c-y*s;
+ }
+ }
+ }
+ z=w[k];
+ if (l == k)
+ { //Convergence.
+ if (z < 0.0)
+ { //Singular value is made nonnegative.
+ w[k] = -z;
+ for (j=1;j<=n;j++)
+ v[j][k] = -v[j][k];
+ }
+ break;
+ }
+ /* if (its == 30)
+ nrerror("no convergence in 30 svdcmp iterations");*/
+ x=w[l]; //Shift from bottom 2-by-2 minor.
+ nm=k-1;
+ y=w[nm];
+ g=rv1[nm];
+ h=rv1[k];
+ f=((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y);
+ g=pythag(f,1.0);
+ f=((x-z)*(x+z)+h*((y/(f+SIGN(g,f)))-h))/x;
+ c=s=1.0; //Next QR transformation:
+ for (j=l;j<=nm;j++)
+ {
+ i=j+1;
+ g=rv1[i];
+ y=w[i];
+ h=s*g;
+ g=c*g;
+ z=pythag(f,h);
+ rv1[j]=z;
+ c=f/z;
+ s=h/z;
+ f=x*c+g*s;
+ g = g*c-x*s;
+ h=y*s;
+ y *= c;
+ for (jj=1;jj<=n;jj++)
+ {
+ x=v[jj][j];
+ z=v[jj][i];
+ v[jj][j]=x*c+z*s;
+ v[jj][i]=z*c-x*s;
+ }
+ z=pythag(f,h);
+ w[j]=z; //Rotation can be arbitrary if z = 0.
+ if (z)
+ {
+ z=1.0/z;
+ c=f*z;
+ s=h*z;
+ }
+ f=c*g+s*y;
+ x=c*y-s*g;
+ for (jj=1;jj<=m;jj++)
+ {
+ y=a[jj][j];
+ z=a[jj][i];
+ a[jj][j]=y*c+z*s;
+ a[jj][i]=z*c-y*s;
+ }
+ }
+ rv1[l]=0.0;
+ rv1[k]=f;
+ w[k]=x;
+ }
+ }
+ free_dvector(rv1,1,n);
+}
+
+inline double pythag(double a, double b)
+{
+ double absa,absb;
+ absa=fabs(a);
+ absb=fabs(b);
+ if (absa > absb) return absa*sqrt(1.0+DSQR(absb/absa));
+ else return (absb == 0.0 ? 0.0 : absb*sqrt(1.0+DSQR(absa/absb)));
+}
\ No newline at end of file
diff --git a/Surface_modeling/examples/Surface_modeling/CMakeLists.txt b/Surface_modeling/examples/Surface_modeling/CMakeLists.txt
new file mode 100644
index 00000000000..2317567bdef
--- /dev/null
+++ b/Surface_modeling/examples/Surface_modeling/CMakeLists.txt
@@ -0,0 +1,29 @@
+# Created by the script cgal_create_cmake_script
+# This is the CMake script for compiling a CGAL application.
+
+
+project( Surface_modeling_example )
+
+cmake_minimum_required(VERSION 2.6.2)
+
+find_package(CGAL QUIET COMPONENTS Core )
+
+if ( CGAL_FOUND )
+
+ include( ${CGAL_USE_FILE} )
+
+ include( CGAL_CreateSingleSourceCGALProgram )
+
+ include_directories (BEFORE ../../include)
+
+ create_single_source_cgal_program( "hello.cpp" )
+ create_single_source_cgal_program( "k-ring.cpp" )
+ create_single_source_cgal_program( "k-ring_BGL.cpp" )
+ create_single_source_cgal_program( "example.cpp" )
+
+else()
+
+ message(STATUS "This program requires the CGAL library, and will not be compiled.")
+
+endif()
+
diff --git a/Surface_modeling/examples/Surface_modeling/example.cpp b/Surface_modeling/examples/Surface_modeling/example.cpp
new file mode 100644
index 00000000000..2bda56a4638
--- /dev/null
+++ b/Surface_modeling/examples/Surface_modeling/example.cpp
@@ -0,0 +1,55 @@
+#include
+#include
+#include
+
+typedef CGAL::Cartesian Kernel;
+typedef Kernel::Vector_3 Vector;
+typedef CGAL::Polyhedron_3 Polyhedron;
+typedef CGAL::Deform_mesh_BGL > Deform_mesh;
+
+typedef boost::graph_traits::vertex_iterator vertex_iterator;
+
+typedef Polyhedron::Vertex_handle Vertex_handle;
+
+
+int main() {
+
+ // read an off file
+ Polyhedron P; //source mesh
+ std::cout << "Please input filename: ";
+ std::string filename;
+ std::cin >> filename;
+ std::string fullname = filename + ".off";
+ std::ifstream input(&fullname[0]);
+ input >> P;
+ std::cout << P.size_of_vertices() << " vertices; " << P.size_of_facets() << "facets" << std::endl;
+ input.close();
+
+ Deform_mesh deform(P);
+
+ vertex_iterator vb, ve;
+ boost::tie(vb,ve) = boost::vertices(P);
+ Vertex_handle vv = P.vertices_begin();
+ // takes arbitrary vertex as handle
+ deform.handles(vv, vv);
+
+ // determine the k-ring
+ deform.region_of_interest(vv, vv, 1);
+
+ // does the precomputation
+ deform.preprocess();
+
+ // displaces the handle by the Vector_3 v - origin
+ Vector translation = (vv)->point() - CGAL::ORIGIN;
+ deform(vv, translation);
+
+ // write the polyhedron to a file
+ std::string outname = filename + "_arap.off";
+ std::cout << "output to " << outname << "...";
+ std::ofstream output(&outname[0]);
+ output << deform.polyhedron;
+ output.close();
+ std::cout << "done." << std::endl;
+ output.close();
+ return 0;
+}
diff --git a/Surface_modeling/examples/Surface_modeling/hello.cpp b/Surface_modeling/examples/Surface_modeling/hello.cpp
new file mode 100644
index 00000000000..68f6649558a
--- /dev/null
+++ b/Surface_modeling/examples/Surface_modeling/hello.cpp
@@ -0,0 +1,128 @@
+#include
+#include
+#include
+#include
+#include
+#include
+#include
+
+typedef CGAL::Simple_cartesian Kernel;
+typedef CGAL::Polyhedron_3 Polyhedron;
+typedef Polyhedron::HalfedgeDS HalfedgeDS;
+
+typedef Polyhedron::Vertex_const_handle Vertex_handle;
+typedef Polyhedron::Halfedge_around_vertex_const_circulator HV_circulator;
+
+using namespace std;
+
+// A modifier creating a triangle with the incremental builder.
+template
+class Build_triangle : public CGAL::Modifier_base {
+public:
+ Build_triangle() {}
+ void operator()( HDS& hds) {
+
+ string filename;
+ cin >> filename;
+ ifstream file;
+ file.open(&filename[0]);
+ string title;
+ file >> title;
+ if (title != "OFF")
+ {
+ cout << "Wrong format!" << endl;
+ return;
+ }
+ int nV, nF, nE;
+ file >> nV >> nF >> nE;
+ // Postcondition: `hds' is a valid polyhedral surface.
+ CGAL::Polyhedron_incremental_builder_3 B( hds, true);
+ B.begin_surface( nV, nF);
+ typedef typename HDS::Vertex Vertex;
+ typedef typename Vertex::Point Point;
+ for (int idx = 0; idx < nV; idx ++)
+ {
+ double x, y, z;
+ file >> x >> y >> z;
+ B.add_vertex( Point( x, y, z));
+ }
+ for (int fidx = 0; fidx < nF; fidx ++)
+ {
+ int nP;
+ file >> nP;
+ B.begin_facet();
+ for (int i = 0; i < nP; i ++)
+ {
+ int idx;
+ file >> idx;
+ B.add_vertex_to_facet(idx);
+ }
+ B.end_facet();
+ }
+ B.end_surface();
+ file.close();
+
+ }
+};
+
+
+void LoadOFF(Polyhedron &P)
+{
+ Build_triangle triangle;
+ P.delegate( triangle);
+}
+
+
+void k_ring(Polyhedron &P, Vertex_handle v, size_t k, vector &neigh_vtx)
+{
+ neigh_vtx.clear();
+ neigh_vtx.push_back(v);
+ int idx_lv = 0; // pointing the neighboring vertices on current level
+ int idx_lv_end;
+
+
+ for (size_t lv = 0; lv < k; lv++)
+ {
+ idx_lv_end = neigh_vtx.size();
+ for ( ;idx_lv < idx_lv_end; idx_lv++ )
+ {
+ Vertex_handle vh = neigh_vtx[idx_lv];
+ HV_circulator wc = vh->vertex_begin(), done(wc);
+ do {
+ Vertex_handle wh = wc->opposite()->vertex();
+ vector ::iterator result = find(neigh_vtx.begin(), neigh_vtx.end(), wh);
+ if (result == neigh_vtx.end())
+ {
+ neigh_vtx.push_back(wh);
+ }
+ ++wc;
+ }while(wc != done);
+ }
+ }
+
+}
+
+int main() {
+ Polyhedron P;
+ string filename;
+ cin >> filename;
+ ifstream file;
+ file.open(&filename[0]);
+ file >> P;
+ cout << P.size_of_vertices() << " vertices; " << P.size_of_facets() << "facets" << endl;
+
+ vector neigh_vtx;
+ cout << "Determine level of k-ring: ";
+ size_t k;
+ cin >> k;
+ cout << "Determine vertex index: ";
+ k_ring(P, P.vertices_begin(), k, neigh_vtx);
+ cout << endl << neigh_vtx.size() << " neighboring vertices:" << endl;
+ /*for (int i = 0; i < neigh_vtx.size(); i++)
+ {
+ cout << neigh_vtx[i] << endl;
+ }*/
+
+ return 0;
+}
+
diff --git a/Surface_modeling/examples/Surface_modeling/k-ring.cpp b/Surface_modeling/examples/Surface_modeling/k-ring.cpp
new file mode 100644
index 00000000000..42283696d0c
--- /dev/null
+++ b/Surface_modeling/examples/Surface_modeling/k-ring.cpp
@@ -0,0 +1,71 @@
+#include
+#include
+#include
+#include
+#include
+#include
+#include