/*------------------------------------------------------------------------------*/
void GW_VoronoiMesh::CreateVoronoiVertex()
{
/* Create Vornoi vertex and make the inverse map GeodesicVertex->VoronoiVertex */
this->SetNbrVertex( (GW_U32) BaseVertexList_.size() );
GW_U32 nNum = 0;
for( IT_GeodesicVertexList it = BaseVertexList_.begin(); it!=BaseVertexList_.end(); ++it )
{
GW_GeodesicVertex* pVert = *it;
GW_ASSERT( pVert!=NULL );
/* create a new voronoi vertex */
GW_VoronoiVertex* pVornoiVert = new GW_VoronoiVertex;
pVornoiVert->SetBaseVertex( *pVert );
this->SetVertex( nNum, pVornoiVert );
nNum++;
/* build the inverse map */
GW_ASSERT( VoronoiVertexMap_.find( pVert->GetID() )==VoronoiVertexMap_.end() );
VoronoiVertexMap_[ pVert->GetID() ] = pVornoiVert;
}
}
GW_Bool InsersionCallback( GW_GeodesicVertex& Vert, GW_Float rNewDist )
{
// check if the distance of the new point is less than the given distance
GW_U32 i = Vert.GetID();
bool doinsersion = nbr_iter<=niter_max;
if( L!=NULL )
doinsersion = doinsersion && (rNewDist<L[i]);
nbr_iter++;
return doinsersion;
}
GW_Bool StopMarchingCallback( GW_GeodesicVertex& Vert )
{
// check if the end point has been reached
GW_U32 i = Vert.GetID();
// display_message("ind %d",i );
// display_message("dist %f",Vert.GetDistance() );
if( Vert.GetDistance()>dmax )
return true;
for( int k=0; k<nend; ++k )
if( end_points[k]==i )
return true;
return false;
}
/*------------------------------------------------------------------------------*/
GW_Bool GW_VoronoiMesh::FastMarchingCallbackFunction_VertexInsersionRD2( GW_GeodesicVertex& CurVert, GW_Float rNewDist )
{
GW_ASSERT( pCurWeights_!=NULL );
GW_U32 nId = CurVert.GetID();
if( pCurWeights_->find(nId)!=pCurWeights_->end() ) // this is one of our natural neighbor, yeah.
{
if( (*pCurWeights_)[nId]<0 )
{
/* first time we encounter this vertex, sounds good */
if( rNewDist>0 )
(*pCurWeights_)[nId] = 1.0/(rNewDist);
else
(*pCurWeights_)[nId] = GW_INFINITE;
nNbrBaseVertex_RD_++;
}
else
GW_ASSERT( GW_False );
}
return GW_True;
}
GW_Float WeightCallback(GW_GeodesicVertex& Vert)
{
GW_U32 i = Vert.GetID();
return Ww[i];
}
GW_Float HeuristicCallback( GW_GeodesicVertex& Vert )
{
// return the heuristic distance
GW_U32 i = Vert.GetID();
return H[i];
}
/*------------------------------------------------------------------------------*/
void GW_VoronoiMesh::FlattenBasePoints( GW_GeodesicMesh& Mesh, T_Vector2DMap& FlatteningMap )
{
char str[100];
/* create a voronoi vertex for each basis vertex */
this->CreateVoronoiVertex();
GW_U32 n = this->GetNbrVertex();
GW_MatrixNxP dist_matrix(n,n,-1);
/* compute the distance matrix */
for( GW_U32 i=0; i<n; ++i )
{
GW_VoronoiVertex* pVoronoiVerti = (GW_VoronoiVertex*) this->GetVertex(i); GW_ASSERT( pVoronoiVerti!=NULL );
GW_GeodesicVertex* pGeodesicVerti = (GW_GeodesicVertex*) pVoronoiVerti->GetBaseVertex(); GW_ASSERT( pGeodesicVerti!=NULL );
sprintf( str, "Computing distance information for vertex %d.", i );
GW_OutputComment( str );
/* compute the distance map */
Mesh.ResetGeodesicMesh();
Mesh.PerformFastMarching( pGeodesicVerti );
for( GW_U32 j=0; j<n; ++j )
{
GW_VoronoiVertex* pVoronoiVertj = (GW_VoronoiVertex*) this->GetVertex(j); GW_ASSERT( pVoronoiVerti!=NULL );
GW_GeodesicVertex* pGeodesicVertj = (GW_GeodesicVertex*) pVoronoiVertj->GetBaseVertex(); GW_ASSERT( pGeodesicVerti!=NULL );
GW_Float rDist = pGeodesicVertj->GetDistance();
if( dist_matrix[i][j]<0 )
dist_matrix[i][j] = rDist*rDist;
else
dist_matrix[i][j] = (dist_matrix[i][j]+rDist*rDist)*0.5;
if( dist_matrix[j][i]<0 )
dist_matrix[j][i] = rDist*rDist;
else
dist_matrix[j][i] = (dist_matrix[j][i]+rDist*rDist)*0.5;
}
}
/* center the matrix */
sprintf( str, "Performing the multidimensional scaling.", i );
GW_OutputComment( str );
GW_MatrixNxP J(n,n,-1.0/n);
for( GW_U32 i=0; i<n; ++i )
J[i][i] += 1;
/* center the matrix */
dist_matrix = J*dist_matrix*J*(-0.5);
/* perform eigen-decomposition */
GW_MatrixNxP v(n,n);
GW_VectorND RealEig(n);
dist_matrix.Eigenvalue( v, NULL, &RealEig, NULL );
GW_Float rScaleX = 0;
GW_Float rScaleY = 0;
GW_I32 nEigenvectorX = -1;
GW_I32 nEigenvectorY = -1;
/* find the two maximum eigenvalues */
for( GW_U32 i=0; i<n; ++i )
{
if( RealEig[i]>=rScaleX )
{
rScaleY = rScaleX;
nEigenvectorY = nEigenvectorX;
rScaleX = RealEig[i];
nEigenvectorX = i;
}
else if( RealEig[i]>=rScaleY )
{
rScaleY = RealEig[i];
nEigenvectorY = i;
}
}
rScaleX = sqrt(rScaleX);
rScaleY = sqrt(rScaleY);
GW_ASSERT( nEigenvectorX>=0 );
GW_ASSERT( nEigenvectorY>=0 );
/* compute the 2D position */
FlatteningMap.clear();
if( nEigenvectorX>=0 && nEigenvectorY>=0 )
for( GW_U32 i=0; i<n; ++i )
{
GW_VoronoiVertex* pVoronoiVerti = (GW_VoronoiVertex*) this->GetVertex(i); GW_ASSERT( pVoronoiVerti!=NULL );
GW_GeodesicVertex* pGeodesicVerti = (GW_GeodesicVertex*) pVoronoiVerti->GetBaseVertex(); GW_ASSERT( pGeodesicVerti!=NULL );
GW_Vector2D pos;
pos[0] = rScaleX*v[i][nEigenvectorX];
pos[1] = rScaleY*v[i][nEigenvectorY];
FlatteningMap[ pGeodesicVerti->GetID() ] = pos;
}
}
