PoissonRecon/Src/MAT.inl

/*
Copyright (c) 2007, Michael Kazhdan
All rights reserved.

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are permitted provided that the following conditions are met:

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Neither the name of the Johns Hopkins University nor the names of its contributors
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*/

//////////////////////////////
// MinimalAreaTriangulation //
//////////////////////////////
template< class Real , unsigned int Dim >
_MinimalAreaTriangulation< Real , Dim >::_MinimalAreaTriangulation( ConstPointer( Point< Real , Dim > ) vertices , size_t vCount ) : _vertices( vertices ) , _vCount( vCount )
{
	_bestTriangulation = NullPointer( Real );
	_midpoint = NullPointer( int );
}
template< class Real , unsigned int Dim >
_MinimalAreaTriangulation< Real , Dim >::~_MinimalAreaTriangulation( void )
{
	FreePointer( _bestTriangulation );
	FreePointer( _midpoint );
}
template< class Real , unsigned int Dim >
std::vector< TriangleIndex > _MinimalAreaTriangulation< Real , Dim >::getTriangulation( void )
{
	std::vector< TriangleIndex > triangles;
	if( _vCount==3 )
	{
		triangles.resize(1);
		triangles[0].idx[0] = 0;
		triangles[0].idx[1] = 1;
		triangles[0].idx[2] = 2;
		return triangles;
	}
	else if( _vCount==4 )
	{
		TriangleIndex tIndex[2][2];
		Real area[] = { 0 , 0 };

		triangles.resize(2);

		tIndex[0][0].idx[0]=0;
		tIndex[0][0].idx[1]=1;
		tIndex[0][0].idx[2]=2;
		tIndex[0][1].idx[0]=2;
		tIndex[0][1].idx[1]=3;
		tIndex[0][1].idx[2]=0;

		tIndex[1][0].idx[0]=0;
		tIndex[1][0].idx[1]=1;
		tIndex[1][0].idx[2]=3;
		tIndex[1][1].idx[0]=3;
		tIndex[1][1].idx[1]=1;
		tIndex[1][1].idx[2]=2;

		Point< Real , Dim > p1 , p2;
		for( int i=0 ; i<2 ; i++ ) for( int j=0 ; j<2 ; j++ ) area[i] = SquareArea( _vertices[ tIndex[i][j].idx[0] ] , _vertices[ tIndex[i][j].idx[1] ] , _vertices[ tIndex[i][j].idx[2] ] );
		if( area[0]>area[1] ) triangles[0] = tIndex[1][0] , triangles[1] = tIndex[1][1];
		else                  triangles[0] = tIndex[0][0] , triangles[1] = tIndex[0][1];
		return triangles;
	}
	_set();
	_addTriangles( 1 , 0 , triangles );
	return triangles;
}
template< class Real , unsigned int Dim >
void _MinimalAreaTriangulation< Real , Dim >::_set( void )
{
	FreePointer( _bestTriangulation );
	FreePointer( _midpoint );
	_bestTriangulation = AllocPointer< Real >( _vCount * _vCount );
	_midpoint = AllocPointer< int >( _vCount * _vCount );
	for( int i=0 ; i<_vCount*_vCount ; i++ ) _bestTriangulation[i] = -1 , _midpoint[i] = -1;
	_subPolygonArea( 1 , 0 );
}

template< class Real , unsigned int Dim > size_t _MinimalAreaTriangulation< Real , Dim >::_subPolygonIndex( size_t i , size_t j ) const { return i*_vCount+j; }

template< class Real , unsigned int Dim >
void _MinimalAreaTriangulation< Real , Dim >::_addTriangles( size_t i , size_t j , std::vector< TriangleIndex >& triangles ) const
{
	TriangleIndex tIndex;
	if( j<i ) j += _vCount;
	if( i==j || i+1==j ) return;
	int mid = _midpoint[ _subPolygonIndex( i , j%_vCount ) ];
	if( mid>=0 )
	{
		tIndex.idx[0] = int( i );
		tIndex.idx[1] = int( mid );
		tIndex.idx[2] = int( j%_vCount );
		triangles.push_back( tIndex );
		_addTriangles( i , mid , triangles );
		_addTriangles( mid , j , triangles );
	}
}

// Get the minimial area of the sub-polygon [ v_i , ... , v_j ]
template< class Real , unsigned int Dim >
Real _MinimalAreaTriangulation< Real , Dim >::_subPolygonArea( size_t i , size_t j )
{
	size_t idx = _subPolygonIndex( i , j );
	if( _midpoint[idx]!=-1 ) return _bestTriangulation[idx];
	Real a = FLT_MAX , temp;
	if( j<i ) j += _vCount;
	// If either i==j or i+1=j, the polygon has trivial area
	if( i==j || i+1==j )
	{
		_bestTriangulation[idx] = 0;
		return 0;
	}
	// If we have already computed the minimal area for this edge
	if( _midpoint[idx]!=-1 ) return _bestTriangulation[idx];
	int mid=-1;

	// For each vertex r \in( i , j ):
	// -- Construct the triangle ( j , r , i )
	// -- Compute the Area(j,r,i) + Area( j , ... , r ) + Area( r , ... , i )
	for( size_t r=i+1 ; r<j ; r++ )
	{
		size_t idx1 = _subPolygonIndex( i , r%_vCount ); // SubPolygon( r , ... , i )
		size_t idx2 = _subPolygonIndex( r%_vCount , j%_vCount ); // SubPolygon( j , ... , r );

		temp = SquareArea( _vertices[i] , _vertices[r%_vCount] , _vertices[j%_vCount] );
		temp = temp<0 ? 0 : (Real)sqrt(temp);
		// If we have already computed Area( r , ... , i ), use that.
		if( _bestTriangulation[idx1]>=0 )
		{
			temp += _bestTriangulation[idx1];
			// If the partial area is already too large, terminate
			if( temp>a ) continue; // Terminate early
			// Otherwise, compute the total area
			temp += _subPolygonArea( r%_vCount , j%_vCount );
		}
		else
		{
			// Otherwise, compute it now
			temp += _subPolygonArea( r%_vCount , j%_vCount );
			// If the partial area is already too large, terminate
			if( temp>a ) continue;
			// Otherwise, compute the total area
			temp += _subPolygonArea( i , r%_vCount );
		}

		if( temp<a ) a=temp , mid=(int)(r%_vCount);
	}
	_bestTriangulation[idx] = a;
	_midpoint[idx] = mid;
	return a;
}