Alg_Metric_Base_2 Class Reference

2D Algebraic Metric Base Class More...

#include <Algebraic_Metrics_2.h>

Inheritance diagram for Alg_Metric_Base_2:

Collaboration diagram for Alg_Metric_Base_2:

Public Member Functions
	Alg_Metric_Base_2 ()
	Constructor. More...
virtual	~Alg_Metric_Base_2 ()
	Virtual Destructor. More...
virtual void	initialize (Vector_3< double > n[], int type)
	Initialize a 2D Algebraic Metric. More...
virtual void	initialize (Element_node_enumerator &ene)
virtual double	maxValue () const
	The maximum value for this metric. More...
virtual double	minValue () const
	The minimum value for this metric. More...
Public Member Functions inherited from Metric
	Metric ()
virtual	~Metric ()
virtual void	compute (double atts[]) const =0
	Compute the value of this metric. More...

Protected Member Functions
double	compute_size (double ref_area=1.) const
	Compute the size metric. More...
double	compute_shape () const
	Compute the shape metric. More...
double	compute_skew () const
	Compute the skew metric. More...

Protected Attributes
double	alpha [4]
J_Matrix	A [4]
Matrix	L [4]
int	type_

Friends
std::ostream &	operator<< (std::ostream &, const Alg_Metric_Base_2 &)

Detailed Description

2D Algebraic Metric Base Class

This class is the base class for the implementation of the specific 2D algebraic metrics defined by Patrick Knupp in "Aglebraic Mesh Quality Metrics for Unstructured Initial Meshes"

Definition at line 42 of file Algebraic_Metrics_2.h.

Constructor & Destructor Documentation

Alg_Metric_Base_2 ( )

inline

Constructor.

Definition at line 48 of file Algebraic_Metrics_2.h.

{}

virtual ~Alg_Metric_Base_2 ( )

inlinevirtual

Virtual Destructor.

Although the destructor does nothing, this member function must be declared since the class has other virtual functions.

Definition at line 55 of file Algebraic_Metrics_2.h.

{}  

Member Function Documentation

double compute_shape ( ) const

protected

Compute the shape metric.

Definition at line 117 of file Algebraic_Metrics_2.C.

References denom, i, and sqrt().

                                              {
  // Triangles
  if (type_ == COM::Connectivity::TRI3){
    return sqrt(3.0) * alpha[0] / 
      ( L[0](0,0) + L[0](1,1) - L[0](0,1));
  }

  // Quads
  else{
    assert (type_ == COM::Connectivity::QUAD4);
    double denom = 0;
    for (int i = 0; i < 4; i ++){
      denom += ( (L[i](0,0) + L[i](1,1))/alpha[i] );
    }
    return 8.0/denom;
  }
}

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double compute_size ( double  ref_area = 1. ) const

protected

Compute the size metric.

Parameters

ref_area

the ideal area for this element.

Definition at line 104 of file Algebraic_Metrics_2.C.

                                                             {
  double tau;
  if (type_ == COM::Connectivity::TRI3){
    tau = alpha[0]/(2.0*ref_area);
    return (tau < (1/tau))? tau : (1/tau);
  }
  else {
    assert (type_ == COM::Connectivity::QUAD4);
    tau = (alpha[0] + alpha[2])/(2*ref_area);
    return (tau < (1/tau))? tau : (1/tau);
  }
}

double compute_skew ( ) const

protected

Compute the skew metric.

Definition at line 135 of file Algebraic_Metrics_2.C.

References denom, i, and sqrt().

                                             {
  // only defined for quads, so return 1 if triangle
  if (type_ == COM::Connectivity::TRI3) {
    return 1;
  }
  // flag checks for divide by 0
  else {
    double denom = 0;
    int flag = 0;
    for (int i = 0; i < 4 ; i++) {
      if (alpha[i]==0) { flag = 1;}
      else {
        denom += ( sqrt ( L[i](0,0) * L[i](1,1)) / alpha[i] );
      }
    }
    if (flag){ return 0; }
    else     { return  4.0/denom; } 
  }
}

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void initialize ( Vector_3< double >  n[], int  type  )

virtual

Initialize a 2D Algebraic Metric.

Parameters

n[]	Ordered set of nodal coordinates.
type	Element type: TRI or QUAD

Implements Metric.

Definition at line 79 of file Algebraic_Metrics_2.C.

References A, i, j, and v.

Referenced by main().

                                                                {
  type_ = type;
  vector<Vector_3<double> > v(type_);
  if (type_ == COM::Connectivity::TRI3){
    for ( int i = 0; i < 3; i ++){
      v[0] = n[(i+1)%3] - n[i];
      v[1] = n[(i+2)%3] - n[i];
      A[i] = J_Matrix(&v[0],2);
      L[i] ^= A[i];
      alpha[i] = A[i].det();
    }
  }
  else if (type_ == COM::Connectivity::QUAD4){
    for ( int i = 0; i < 4; i ++){
      for (int j = 0; j < 3; j ++){
        v[0][j] = (n[(i+1)%4][j] - n[i][j]);
        v[1][j] = (n[(i+3)%4][j] - n[i][j]);
      }
        A[i] = J_Matrix(&v[0],2);
        L[i] ^= A[i];
        alpha[i] = A[i].det();
    }
  }
}

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MOP_BEGIN_NAMESPACE void initialize ( Element_node_enumerator &  ene )

virtual

Implements Metric.

Definition at line 40 of file Algebraic_Metrics_2.C.

References A, COM_assertion_msg, i, j, n, and v.

                                                              {
  type_ = ene.type();
  Element_node_vectors_k_const<double> n;
  n.set(ene.pane()->attribute("nc"),ene);
  vector<Vector_3<double> > v(2);
  if (type_ == COM::Connectivity::TRI3){
    for ( int i = 0; i < 3; i ++){
      int i1 = (i+1)%3, i2 = (i+2)%3;

      v[0][0] = n(i1,0)-n(i,0); 
      v[0][1] = n(i1,1)-n(i,1); 
      v[0][2] = n(i1,2)-n(i,2); 

      v[1][0] = n(i2,0)-n(i,0); 
      v[1][1] = n(i2,1)-n(i,1); 
      v[1][2] = n(i2,2)-n(i,2); 

      A[i] = J_Matrix(&v[0],2);
      L[i] ^= A[i];
      alpha[i] = A[i].det();
    }
  }
  else if (type_ == COM::Connectivity::QUAD4){
    for ( int i = 0; i < 4; i ++){
      for (int j = 0; j < 3; j ++){
        int i1 = (i+1)%4, i3 = (i+3)%4;

        v[0][j] = n(i1,j)-n(i,j);       
        v[1][j] = n(i3,0)-n(i,j); 
      }
        A[i] = J_Matrix(&v[0],2);
        L[i] ^= A[i];
        alpha[i] = A[i].det();
    }
  }
  else COM_assertion_msg(0,"Element type not supported for 2D Algebraic Metrics");
}

virtual double maxValue ( ) const

inlinevirtual

The maximum value for this metric.

Implements Metric.

Definition at line 67 of file Algebraic_Metrics_2.h.

Referenced by main().

{ return 1.0; }

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virtual double minValue ( ) const

inlinevirtual

The minimum value for this metric.

Implements Metric.

Definition at line 70 of file Algebraic_Metrics_2.h.

Referenced by main().

{ return 0.0; }

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Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream &  output, const Alg_Metric_Base_2 &  m  )

friend

Definition at line 175 of file Algebraic_Metrics_2.C.

                                                                 {
  for(int i =0; i < m.type_; i ++){
    output << "A[" << i << "]:" << endl << m.A[i];
    output << "L[" << i << "]:" << endl << m.L[i];
    output << "alpha"<<i << ": " << m.alpha[i] << endl << endl;
  }
  return output;
}  

Member Data Documentation

J_Matrix A[4]

protected

Definition at line 88 of file Algebraic_Metrics_2.h.

Referenced by operator<<().

double alpha[4]

protected

Definition at line 87 of file Algebraic_Metrics_2.h.

Referenced by operator<<().

Matrix L[4]

protected

Definition at line 89 of file Algebraic_Metrics_2.h.

Referenced by operator<<().

int type_

protected

Definition at line 90 of file Algebraic_Metrics_2.h.

Referenced by operator<<().

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The documentation for this class was generated from the following files:

• Algebraic_Metrics_2.h
• Algebraic_Metrics_2.C