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#ifndef VCG_SPACE_NORMAL_EXTRAPOLATION_H
#define VCG_SPACE_NORMAL_EXTRAPOLATION_H
#include <vcg/math/matrix33.h>
#include <vcg/math/linear.h>
#include <vcg/math/lin_algebra.h>
#include <vcg/math/disjoint_set.h>
#include <vcg/space/box3.h>
#include <vcg/space/point3.h>
#include <vcg/space/index/octree.h>
#include <wrap/callback.h>
#include <vector>
#include <queue>
#include <algorithm>
#include <limits>
#include <stdlib.h>
namespace vcg
{
/*!
*/
template < class VERTEX_CONTAINER >
class NormalExtrapolation
{
public:
typedef typename VERTEX_CONTAINER::value_type VertexType;
typedef VertexType * VertexPointer;
typedef typename VERTEX_CONTAINER::iterator VertexIterator;
typedef typename VertexType::CoordType CoordType;
typedef typename VertexType::NormalType NormalType;
typedef typename VertexType::ScalarType ScalarType;
typedef typename vcg::Box3< ScalarType > BoundingBoxType;
typedef typename vcg::Matrix33<ScalarType> MatrixType;
enum NormalOrientation {IsCorrect=0, MustBeFlipped=1};
private:
/*************************************************
* Inner class definitions
**************************************************/
// Dummy class: no object marker is needed
class DummyObjectMarker {};
// Object functor: compute the distance between a vertex and a point
struct VertPointDistanceFunctor
{
inline bool operator()(const VertexType &v, const CoordType &p, ScalarType &d, CoordType &q) const
{
ScalarType distance = vcg::Distance(p, v.P());
if (distance>d)
return false;
d = distance;
q = v.P();
return true;
}
};
// Plane structure: identify a plain as a <center, normal> pair
struct Plane
{
Plane() { center.SetZero(); normal.SetZero();};
// Object functor: return the bounding-box enclosing a given plane
inline void GetBBox(BoundingBoxType &bb) { bb.Set(center); };
CoordType center;
NormalType normal;
int index;
};
// Object functor: compute the distance between a point and the plane
struct PlanePointDistanceFunctor
{
inline bool operator()(const Plane &plane, const CoordType &p, ScalarType &d, CoordType &q) const
{
ScalarType distance = vcg::Distance(p, plane.center);
if (distance>d)
return false;
d = distance;
q = plane.center;
return true;
}
};
// Represent an edge in the Riemannian graph
struct RiemannianEdge
{
RiemannianEdge(Plane *p=NULL, ScalarType w=std::numeric_limits<ScalarType>::max()) {plane=p; weight=w; }
Plane *plane;
ScalarType weight;
};
// Represent an edge in the MST tree
struct MSTEdge
{
MSTEdge(Plane *p0=NULL, Plane *p1=NULL, ScalarType w=std::numeric_limits<ScalarType>::max()) {u=p0; v=p1; weight=w;};
inline bool operator<(const MSTEdge &e) const {return weight<e.weight;}
Plane *u;
Plane *v;
ScalarType weight;
};
// Represent a node in the MST tree
struct MSTNode
{
MSTNode(MSTNode* p=NULL) {parent=p;}
MSTNode *parent;
VertexPointer vertex;
std::vector< MSTNode* > sons;
};
typedef std::vector< Plane > PlaneContainer;
typedef typename PlaneContainer::iterator PlaneIterator;
public:
/*!
*/
static void ExtrapolateNormals(const VertexIterator &begin, const VertexIterator &end, const unsigned int k, const int root_index=-1, NormalOrientation orientation=IsCorrect, CallBackPos *callback=NULL)
{
BoundingBoxType dataset_bb;
for (VertexIterator iter=begin; iter!=end; iter++)
dataset_bb.Add(iter->P());
ScalarType max_distance = dataset_bb.Diag();
// Step 1: identify the tangent planes used to locally approximate the surface
int vertex_count = int( std::distance(begin, end) );
int step = int(vertex_count/100)-1;
int progress = 0;
int percentage;
char message[128];
sprintf(message, "Locating tangent planes...");
std::vector< Plane > tangent_planes(vertex_count);
vcg::Octree< VertexType, ScalarType > octree_for_planes;
octree_for_planes.Set( begin, end );
std::vector< VertexPointer > nearest_vertices;
std::vector< CoordType > nearest_points;
std::vector< ScalarType > distances;
for (VertexIterator iter=begin; iter!=end; iter++)
{
if (callback!=NULL && (++progress%step)==0 && (percentage=int((progress*100)/vertex_count))<100) (callback)(percentage, message);
VertPointDistanceFunctor vpdf;
DummyObjectMarker dom;
octree_for_planes.GetKClosest(vpdf, dom, k, iter->P(), max_distance, nearest_vertices, distances, nearest_points);
// for each vertex *iter, compute the centroid as avarege of the k-nearest vertices of *iter
Plane *plane = &tangent_planes[ std::distance(begin, iter) ];
for (unsigned int n=0; n<k; n++)
plane->center += nearest_points[n];
plane->center /= ScalarType(k);
// then, identity the normal associated to the centroid
MatrixType covariance_matrix;
CoordType diff;
covariance_matrix.SetZero();
for (unsigned int n=0; n<k; n++)
{
diff = nearest_points[n] - plane->center;
for (int i=0; i<3; i++)
for (int j=0; j<3; j++)
covariance_matrix[i][j]+=diff[i]*diff[j];
}
CoordType eigenvalues;
MatrixType eigenvectors;
int required_rotations;
vcg::Jacobi< MatrixType, CoordType >(covariance_matrix, eigenvalues, eigenvectors, required_rotations);
vcg::SortEigenvaluesAndEigenvectors< MatrixType, CoordType >(eigenvalues, eigenvectors);
for (int d=0; d<3; d++)
plane->normal[d] = eigenvectors[d][2];
plane->normal.Normalize();
iter->N() = plane->normal;
plane->index = int( std::distance(begin, iter) );
}
// Step 2: build the Riemannian graph, i.e. the graph where each point is connected to the k-nearest neigbours.
dataset_bb.SetNull();
PlaneIterator ePlane = tangent_planes.end();
for (PlaneIterator iPlane=tangent_planes.begin(); iPlane!=ePlane; iPlane++)
dataset_bb.Add(iPlane->center);
max_distance = dataset_bb.Diag();
vcg::Octree< Plane, ScalarType > octree_for_plane;
octree_for_plane.Set( tangent_planes.begin(), tangent_planes.end());
std::vector< Plane* > nearest_planes(distances.size());
std::vector< std::vector< RiemannianEdge > > riemannian_graph(vertex_count); //it's probably that we are wasting the last position...
progress = 0;
sprintf(message, "Building Riemannian graph...");
for (PlaneIterator iPlane=tangent_planes.begin(); iPlane!=ePlane; iPlane++)
{
if (callback!=NULL && (++progress%step)==0 && (percentage=int((progress*100)/vertex_count))<100) (callback)(percentage, message);
unsigned int kk = k;
PlanePointDistanceFunctor ppdf;
DummyObjectMarker dom;
octree_for_plane.GetKClosest
(ppdf, dom, kk, iPlane->center, max_distance, nearest_planes, distances, nearest_points, true, false);
for (unsigned int n=0; n<k; n++)
if (iPlane->index<nearest_planes[n]->index)
riemannian_graph[iPlane->index].push_back(RiemannianEdge(nearest_planes[n], 1.0f - fabs(iPlane->normal .dot(nearest_planes[n]->normal))));
}
// Step 3: compute the minimum spanning tree (MST) over the Riemannian graph (we use the Kruskal algorithm)
std::vector< MSTEdge > E;
typename std::vector< std::vector< RiemannianEdge > >::iterator iRiemannian = riemannian_graph.begin();
typename std::vector< RiemannianEdge >::iterator iRiemannianEdge, eRiemannianEdge;
for (int i=0; i<vertex_count; i++, iRiemannian++)
for (iRiemannianEdge=iRiemannian->begin(), eRiemannianEdge=iRiemannian->end(); iRiemannianEdge!=eRiemannianEdge; iRiemannianEdge++)
E.push_back(MSTEdge(&tangent_planes[i], iRiemannianEdge->plane, iRiemannianEdge->weight));
std::sort( E.begin(), E.end() );
vcg::DisjointSet<Plane> planeset;
for (typename std::vector< Plane >::iterator iPlane=tangent_planes.begin(); iPlane!=ePlane; iPlane++)
planeset.MakeSet( &*iPlane );
typename std::vector< MSTEdge >::iterator iMSTEdge = E.begin();
typename std::vector< MSTEdge >::iterator eMSTEdge = E.end();
std::vector< MSTEdge > unoriented_tree;
Plane *u, *v;
for ( ; iMSTEdge!=eMSTEdge; iMSTEdge++)
if ((u=planeset.FindSet(iMSTEdge->u))!=(v=planeset.FindSet(iMSTEdge->v)))
unoriented_tree.push_back( *iMSTEdge ), planeset.Union(u, v);
E.clear();
// compute for each plane the list of sorting edges
std::vector< std::vector< int > > incident_edges(vertex_count);
iMSTEdge = unoriented_tree.begin();
eMSTEdge = unoriented_tree.end();
progress = 0;
int mst_size = int(unoriented_tree.size());
sprintf(message, "Building orieted graph...");
for ( ; iMSTEdge!=eMSTEdge; iMSTEdge++)
{
if (callback!=NULL && (++progress%step)==0 && (percentage=int((progress*100)/mst_size))<100) (callback)(percentage, message);
int u_index = int(iMSTEdge->u->index);
int v_index = int(iMSTEdge->v->index);
incident_edges[ u_index ].push_back( v_index ),
incident_edges[ v_index ].push_back( u_index );
}
// Traverse the incident_edges vector and build the MST
VertexIterator iCurrentVertex, iSonVertex;
std::vector< MSTNode > MST(vertex_count);
typename std::vector< Plane >::iterator iFirstPlane = tangent_planes.begin();
typename std::vector< Plane >::iterator iCurrentPlane, iSonPlane;
MSTNode *mst_root;
int r_index = (root_index!=-1)? root_index : rand()*vertex_count/RAND_MAX;
mst_root = &MST[ r_index ];
mst_root->parent = mst_root; //the parent of the root is the root itself
if (orientation==MustBeFlipped)
{
iCurrentVertex = begin;
std::advance(iCurrentVertex, r_index);
iCurrentVertex->N() = iCurrentVertex->N()*ScalarType(-1.0f);
}
{ // just to limit the scope of the variable border
std::queue< int > border;
border.push(r_index);
int maxSize = 0;
int queueSize = 0;
progress = 0;
sprintf(message, "Extracting the tree...");
while ((queueSize=int(border.size()))>0)
{
if (callback!=NULL && ((++progress%step)==0) && (percentage=int((maxSize-queueSize)*100/maxSize))<100) (callback)(percentage, message);
int current_node_index = border.front(); border.pop();
MSTNode *current_node = &MST[current_node_index]; //retrieve the pointer to the current MST node
std::advance((iCurrentVertex=begin), current_node_index); //retrieve the pointer to the correspective vertex
current_node->vertex = &*iCurrentVertex; //and associate it to the MST node
std::vector< int >::iterator iSon = incident_edges[ current_node_index ].begin();
std::vector< int >::iterator eSon = incident_edges[ current_node_index ].end();
for ( ; iSon!=eSon; iSon++)
{
MSTNode *son = &MST[ *iSon ];
if (son->parent==NULL) // the node hasn't been visited
{
son->parent = current_node; // Update the MST nodes
current_node->sons.push_back(son);
//std::advance((iSonVertex=begin), *iSon);//retrieve the pointer to the Vertex associated to son
border.push( *iSon );
}
maxSize = vcg::math::Max<int>(maxSize, queueSize);
}
}
}
// and finally visit the MST tree in order to propagate the normals
{
std::queue< MSTNode* > border;
border.push(mst_root);
sprintf(message, "Orienting normals...");
progress = 0;
int maxSize = 0;
int queueSize = 0;
while ((queueSize=int(border.size()))>0)
{
MSTNode *current_node = border.front(); border.pop();
//std::vector< MSTNode* >::iterator iMSTSon = current_node->sons.begin();
//std::vector< MSTNode* >::iterator eMSTSon = current_node->sons.end();
for (int s=0; s<int(current_node->sons.size()); s++)
{
if (callback!=NULL && ((++progress%step)==0) && (percentage=int((maxSize-queueSize)*100/maxSize))<100) (callback)(percentage, message);
if (current_node->vertex->N().dot(current_node->sons[s]->vertex->N())<ScalarType(0.0f))
current_node->sons[s]->vertex->N() *= ScalarType(-1.0f);
border.push( current_node->sons[s] );
maxSize = vcg::math::Max<int>(maxSize, queueSize);
}
}
}
if (callback!=NULL) (callback)(100, message);
};
};
};//end of namespace vcg
#endif //end of VCG_SPACE_NORMAL_EXTRAPOLATION_H