T DDT2D::globalCostFunction ( Container <HalfEdge <T> *> &half_edges )
{
// Compute cost of the triangulation using selected criterion
const unsigned int n = half_edges.size();
T cost = 0;
//Loop all edges
for ( unsigned int i = 0; i < n; i++ )
{
//Take half edge
HalfEdge <T> *e = half_edges [i];
//Use simplex indentificator to eliminate T processing of the edge
if ( !e->isSimplexEdge() )
{
//Get the first triangle
const HalfEdge <T> *e12 = e->getNextEdge();
const HalfEdge <T> *e13 = e12->getNextEdge();
//Does a twin edge exist?
if ( e->getTwinEdge() )
{
//Get coordinates of the first triangle
const Point3DCartesian <T> *p11 = e->getPoint();
const Point3DCartesian <T> *p12 = e12->getPoint() ;
const Point3DCartesian <T> *p13 = e13->getPoint() ;
//Get second triangle
HalfEdge <T> *e21 = e->getTwinEdge();
const HalfEdge <T> *e22 = e21->getNextEdge();
const HalfEdge <T> *e23 = e22->getNextEdge();
//Get coordinates
const Point3DCartesian <T> *p21 = p12;
const Point3DCartesian <T> *p22 = p11;
const Point3DCartesian <T> *p23 = e23->getPoint();
//Compute local criterion
T fi = ( *pcriterion ) ( p11, p12, p13, p21, p22, p23 );
//Global cost
cost += fi;
//Set both edges to be processed
e->setEdgeAsSimplex ( true );
e21->setEdgeAsSimplex ( true );
}
}
}
//Reset attribute
for ( unsigned int i = 0; i < n; i++ )
{
( *half_edges ) [i]->setEdgeAsSimplex ( false );
}
//Return global cost of the triangulation
return cost;
}
void Face <T>::removeAdjacency()
{
//Set twin edges of Faces adjacent to actual Face to NULL
if ( edge != NULL )
{
//Get actual edge in cell
HalfEdge <T> *e = edge;
//Proces all edges of the Face
do
{
//Get twin edge
HalfEdge <T> *e_twin = e->getTwinEdge();
//Adjacent cell exists
if ( e_twin != NULL )
{
//Set pointer to NULL
e_twin -> setTwinEdge ( NULL );
}
//Increment edge
e = e->getNextEdge();
}
while ( e != edge );
}
}
void DDT2D::DDTLOP ( Container <Node3DCartesian <T> *> &nl, Container <HalfEdge <T> *> &half_edges, unsigned short swap_criterion_selected, const bool print_message, const bool print_exception, std::ostream * output )
{
// Data Depending triangulation using selected local criterion
bool swap_exist = true;
//Set iterations
unsigned iterations = 0;
//Create Delaunay triangulation
DT2D::DT ( nl, half_edges, print_message );
//Get number of HalfEdges
const unsigned int n = half_edges->size();
//Set local swap criterion
setSwapCriterion ( swap_criterion_selected );
//Global cost before swapping
const T global_cost_old = globalCostFunction ( half_edges );
T global_cost = global_cost_old;
//Print info
if ( print_message )
{
*output << "> Starting DDTLOP... " ;
}
//Initialize counters
unsigned int counter = MAX_INT, counter_old = MAX_INT;
try
{
//Run until swap exists or decrease number of swaps between two loops
do
{
//We suppose ordered set of triangles, no swap will be required
swap_exist = false;
//Remember old counter
counter_old = counter;
//Assign new counter value
counter = 0;
//Loop all edges
for ( unsigned int i = 0; i < n; i++ )
{
//Take half edge
HalfEdge <T> *e = ( *half_edges ) [i];
//Use simplex flag to eliminate T processing of the edge
if ( !e->isSimplexEdge() )
{
//Does twin edge exist?
if ( e->getTwinEdge() )
{
// Test of convexity for quadrilateral
HalfEdge <T> *e12 = e->getNextEdge();
HalfEdge <T> *e13 = e12->getNextEdge();
HalfEdge <T> *e21 = e->getTwinEdge();
HalfEdge <T> *e22 = e21->getNextEdge();
HalfEdge <T> *e23 = e22->getNextEdge();
// Get nodes, counterclockwise set of nodes
const Node3DCartesian <T> *p1 = e->getPoint();
const Node3DCartesian <T> *p2 = e23->getPoint();
const Node3DCartesian <T> *p3 = e12->getPoint();
const Node3DCartesian <T> *p4 = e13->getPoint();
//Is convex (non convex can not be swapped)
if ( ConvexQuadrilateral::isStrictlyConvex ( p1, p2, p3, p4 ) == 1 )
{
//Set twin edge to be processed
e->getTwinEdge()->setEdgeAsSimplex ( true );
//Get first triangle
e12 = e->getNextEdge();
e13 = e12->getNextEdge();
//Get coordinates (cast to parent using static_cast)
const Point3DCartesian <T> *p11 = e->getPoint();
const Point3DCartesian <T> *p12 = e12->getPoint();
const Point3DCartesian <T> *p13 = e13->getPoint();
//Get second triangle
e21 = e->getTwinEdge();
e22 = e21->getNextEdge();
e23 = e22->getNextEdge();
//Get coordinates
const Point3DCartesian <T> *p21 = p12;
const Point3DCartesian <T> *p22 = p11;
const Point3DCartesian <T> *p23 = e23->getPoint();
//Compute local criterion
const T c1 = ( *pcriterion ) ( p11, p12, p13, p21, p22, p23 );
//Calculation local criterion from swapped diagonal
const T c2 = ( *pcriterion ) ( p13, p11, p23, p12, p13, p23 );
//Swap diagonal
if ( c2 < c1 )
{
//Swap exists
swap_exist = true;
//Swap diagonal
DT2D::swapDiagonal ( e, e12, e13, e21, e22, e23 );
counter++;
}
//Set both edges to be processed
e->setEdgeAsSimplex ( true );
e21->setEdgeAsSimplex ( true );
}
}
}
}
//Set all edges as unused
for ( unsigned int i = 0; i < n; i++ )
{
//Take half edge
HalfEdge <T> *e = ( *half_edges ) [i];
//Set edge not to be a simplex
e->setEdgeAsSimplex ( false );
}
//Number of iterations
iterations ++;
}
while ( swap_exist );
//Global cost after swapping
global_cost = globalCostFunction ( half_edges );
//Compute change ratio
T ddt_ratio = 0;
if ( global_cost != global_cost_old )
{
ddt_ratio = 100 * ( global_cost - global_cost_old ) / global_cost_old;
}
//Print info
if ( print_message )
{
*output << "Completed..." << std::endl;
*output << "> DT global cost old: " << global_cost_old << " DT global cost new: " << global_cost << ", ratio: " << ddt_ratio << "%" << std::endl;
}
}
//Throw exception
catch ( Error & error )
{
if ( print_exception )
{
error.printException ( output );
}
//Delete lists
half_edges->clear();
*output << "DDT construction cancelled..." << std::endl;
throw;
}
}
float DDT2D::getInitialTemperature ( Container <HalfEdge <T> *> &half_edges )
{
// Compute cost of the triangulation using selected criterion
const unsigned int n = half_edges.size();
T max_difference = 0; ;
//Loop all edges
for ( unsigned int i = 0; i < n; i++ )
{
//Take half edge
HalfEdge <T> *e = half_edges [i];
if ( !e->isSimplexEdge() )
{
//Get next edges
const HalfEdge <T> *e12 = e->getNextEdge();
const HalfEdge <T> *e13 = e12->getNextEdge();
//Does a twin edge exist?
if ( e->getTwinEdge() )
{
//Get coordinates of the first triangle (cast to parent using static_cast)
const Point3DCartesian <T> *p11 = e->getPoint();
const Point3DCartesian <T> *p12 = e12->getPoint();
const Point3DCartesian <T> *p13 = e13->getPoint();
//Get second triangle
HalfEdge <T> *e21 = e->getTwinEdge();
HalfEdge <T> *e22 = e21->getNextEdge();
HalfEdge <T> *e23 = e22->getNextEdge();
//Get coordinates
const Point3DCartesian <T> *p21 = p12;
const Point3DCartesian <T> *p22 = p11;
const Point3DCartesian <T> *p23 = e23->getPoint();
//Only strictly convex quadrilaterals
if ( ConvexQuadrilateral::isStrictlyConvex ( p11, p23, p12, p13 ) == 1 )
{
//Compute local criterion for adjacent triangles
const T fi1 = ( *pcriterion ) ( p11, p12, p13, p21, p22, p23 );
//Compute local criterion for swapped triangles
const T fi2 = ( *pcriterion ) ( p13, p23, p12, p23, p13, p11 );
//Find max difference
if ( fabs ( fi2 - fi1 ) > max_difference )
{
max_difference = fabs ( fi2 - fi1 );
}
}
//Set both edges to be processed
e->setEdgeAsSimplex ( true );
e21->setEdgeAsSimplex ( true );
}
}
}
//Reset attribute
for ( unsigned int i = 0; i < n; i++ )
{
( *half_edges ) [i]->setEdgeAsSimplex ( false );
}
//Return result
return ( float ) ( 2 * max_difference );
}
void DDT2D::setNewState ( float tk, unsigned int & good_swap, unsigned int n, T & global_cost, Container <HalfEdge <T> *> &half_edges )
{
//Set new state or recover old state
unsigned int i = int ( n * rand() / ( RAND_MAX + 1.0 ) );
//i can not be grater than n
if ( i >= n )
{
i = n - 1;
}
//Get random edge
HalfEdge <T> *e = ( *half_edges ) [i];
//Cost difference
T cost_difference = 0.0001 * MAX_FLOAT;
//Compute cost difference (convex quadrilateral), else set difference to MAX_FLOAT
getCostDifference ( e, cost_difference, 0, 1 );
//Set new state, perform swap of the edge
if ( cost_difference < 0 )
{
//First triangle
HalfEdge <T> *e12 = e->getNextEdge();
HalfEdge <T> *e13 = e12->getNextEdge();
//Get the second triangle T2
HalfEdge <T> *e21 = e->getTwinEdge();
HalfEdge <T> *e22 = e21->getNextEdge();
HalfEdge <T> *e23 = e22->getNextEdge();
//Swap diagonal
DT2D::swapDiagonal ( e, e12, e13, e21, e22, e23 );
//Increment good swap
good_swap ++;
//Assign old global cost
global_cost += cost_difference;
}
//Decide if set a new state or old state
else
{
//Generate random number (0, 1)
const float theta = ( T ) rand() / ( T ) RAND_MAX;
//Compare with Boltzmann function and decide about new state
if ( theta < exp ( - cost_difference / tk ) )
{
//Set new state (acceptable increasing of the cost), perform the swap
//First triangle
HalfEdge <T> *e12 = e->getNextEdge();
HalfEdge <T> *e13 = e12->getNextEdge();
//Get the second triangle T2
HalfEdge <T> *e21 = e->getTwinEdge();
HalfEdge <T> *e22 = e21->getNextEdge();
HalfEdge <T> *e23 = e22->getNextEdge();
//Swap diagonal
DT2D::swapDiagonal ( e, e12, e13, e21, e22, e23 );
//Assign old global cost
global_cost += cost_difference;
}
}
}