#include <ShapeQualityMetric.hpp>

Inheritance diagram for ShapeQualityMetric:

Collaboration diagram for ShapeQualityMetric:

Public Member Functions
virtual	~ShapeQualityMetric ()
	virtual destructor ensures use of polymorphism during destruction More...

virtual	~ShapeQualityMetric ()
	virtual destructor ensures use of polymorphism during destruction More...

Public Member Functions inherited from QualityMetric
virtual	~QualityMetric ()

MetricType	get_metric_type ()

void	set_element_evaluation_mode (ElementEvaluationMode mode, MsqError &err)
	Sets the evaluation mode for the ELEMENT_BASED metrics. More...

ElementEvaluationMode	get_element_evaluation_mode ()
	Returns the evaluation mode for the metric. More...

void	set_averaging_method (AveragingMethod method, MsqError &err)

void	set_feasible_constraint (int alpha)

int	get_feasible_constraint ()
	Returns the feasible flag for this metric. More...

void	set_name (msq_std::string st)
	Sets the name of this metric. More...

msq_std::string	get_name ()
	Returns the name of this metric (as a string). More...

double	vertex_barrier_function (double det, double delta)
	Escobar Barrier Function for Shape and Other Metrics. More...

virtual bool	evaluate_vertex (PatchData &, MsqVertex *, double &, MsqError &err)
	Evaluate the metric for a vertex. More...

virtual bool	evaluate_element (PatchData &, MsqMeshEntity *, double &, MsqError &err)
	Evaluate the metric for an element. More...

void	set_gradient_type (GRADIENT_TYPE grad)
	Sets gradType for this metric. More...

void	set_hessian_type (HESSIAN_TYPE ht)
	Sets hessianType for this metric. More...

bool	compute_vertex_gradient (PatchData &pd, MsqVertex &vertex, MsqVertex *vertices[], Vector3D grad_vec[], int num_vtx, double &metric_value, MsqError &err)
	Calls compute_vertex_numerical_gradient if gradType equals NUMERCIAL_GRADIENT. Calls compute_vertex_analytical_gradient if gradType equals ANALYTICAL_GRADIENT;. More...

bool	compute_element_gradient (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], int num_free_vtx, double &metric_value, MsqError &err)
	For MetricType == ELEMENT_BASED. Calls either compute_element_numerical_gradient() or compute_element_analytical_gradient() for gradType equal NUMERICAL_GRADIENT or ANALYTICAL_GRADIENT, respectively. More...

bool	compute_element_gradient_expanded (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], int num_free_vtx, double &metric_value, MsqError &err)

bool	compute_element_hessian (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], Matrix3D hessian[], int num_free_vtx, double &metric_value, MsqError &err)
	For MetricType == ELEMENT_BASED. Calls either compute_element_numerical_hessian() or compute_element_analytical_hessian() for hessianType equal NUMERICAL_HESSIAN or ANALYTICAL_HESSIAN, respectively. More...

void	set_negate_flag (int neg)

int	get_negate_flag ()
	Returns negateFlag. More...

virtual void	change_metric_type (MetricType t, MsqError &err)

virtual	~QualityMetric ()

MetricType	get_metric_type ()

void	set_element_evaluation_mode (ElementEvaluationMode mode, MsqError &err)
	Sets the evaluation mode for the ELEMENT_BASED metrics. More...

ElementEvaluationMode	get_element_evaluation_mode ()
	Returns the evaluation mode for the metric. More...

void	set_averaging_method (AveragingMethod method, MsqError &err)

void	set_feasible_constraint (int alpha)

int	get_feasible_constraint ()
	Returns the feasible flag for this metric. More...

void	set_name (msq_std::string st)
	Sets the name of this metric. More...

msq_std::string	get_name ()
	Returns the name of this metric (as a string). More...

double	vertex_barrier_function (double det, double delta)
	Escobar Barrier Function for Shape and Other Metrics. More...

virtual bool	evaluate_vertex (PatchData &, MsqVertex *, double &, MsqError &err)
	Evaluate the metric for a vertex. More...

virtual bool	evaluate_element (PatchData &, MsqMeshEntity *, double &, MsqError &err)
	Evaluate the metric for an element. More...

void	set_gradient_type (GRADIENT_TYPE grad)
	Sets gradType for this metric. More...

void	set_hessian_type (HESSIAN_TYPE ht)
	Sets hessianType for this metric. More...

bool	compute_vertex_gradient (PatchData &pd, MsqVertex &vertex, MsqVertex *vertices[], Vector3D grad_vec[], int num_vtx, double &metric_value, MsqError &err)

bool	compute_element_gradient (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], int num_free_vtx, double &metric_value, MsqError &err)
	For MetricType == ELEMENT_BASED. Calls either compute_element_numerical_gradient() or compute_element_analytical_gradient() for gradType equal NUMERICAL_GRADIENT or ANALYTICAL_GRADIENT, respectively. More...

bool	compute_element_gradient_expanded (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], int num_free_vtx, double &metric_value, MsqError &err)

bool	compute_element_hessian (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], Matrix3D hessian[], int num_free_vtx, double &metric_value, MsqError &err)
	For MetricType == ELEMENT_BASED. Calls either compute_element_numerical_hessian() or compute_element_analytical_hessian() for hessianType equal NUMERICAL_HESSIAN or ANALYTICAL_HESSIAN, respectively. More...

void	set_negate_flag (int neg)

int	get_negate_flag ()
	Returns negateFlag. More...

virtual void	change_metric_type (MetricType t, MsqError &err)

Protected Member Functions
bool	condition_number_2d (Vector3D temp_vec[], size_t v_ind, PatchData &pd, double &fval, MsqError &err)
	Given the 2-d jacobian matrix, compute the condition number, fval. More...

bool	condition_number_3d (Vector3D temp_vec[], PatchData &pd, double &fval, MsqError &err)
	Given the 3-d jacobian matrix, compute the condition number, fval. More...

bool	condition_number_2d (Vector3D temp_vec[], size_t v_ind, PatchData &pd, double &fval, MsqError &err)
	Given the 2-d jacobian matrix, compute the condition number, fval. More...

bool	condition_number_3d (Vector3D temp_vec[], PatchData &pd, double &fval, MsqError &err)
	Given the 3-d jacobian matrix, compute the condition number, fval. More...

Protected Member Functions inherited from QualityMetric
	QualityMetric ()

void	set_metric_type (MetricType t)
	This function should be used in the constructor of every concrete quality metric. More...

double	average_metrics (const double metric_values[], const int &num_values, MsqError &err)
	average_metrics takes an array of length num_values and averages the contents using averaging method data member avgMethod . More...

double	average_metric_and_weights (double metric_values[], int num_metric_values, MsqError &err)
	Given a list of metric values, calculate the average metric valude according to the current avgMethod and write into the passed metric_values array the the value weight/count to use when averaging gradient vectors for the metric. More...

double	weighted_average_metrics (const double coef[], const double metric_values[], const int &num_values, MsqError &err)
	takes an array of coefficients and an array of metrics (both of length num_value) and averages the contents using averaging method 'method'. More...

bool	compute_vertex_numerical_gradient (PatchData &pd, MsqVertex &vertex, MsqVertex *vertices[], Vector3D grad_vec[], int num_vtx, double &metric_value, MsqError &err)

bool	compute_element_numerical_gradient (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], int num_free_vtx, double &metric_value, MsqError &err)
	Non-virtual function which numerically computes the gradient of a QualityMetric of a given element for a given set of free vertices on that element. This is used by metric which mType is ELEMENT_BASED. For parameters, see compute_element_gradient() . More...

virtual bool	compute_vertex_analytical_gradient (PatchData &pd, MsqVertex &vertex, MsqVertex *vertices[], Vector3D grad_vec[], int num_vtx, double &metric_value, MsqError &err)
	Virtual function that computes the gradient of the QualityMetric analytically. The base class implementation of this function simply prints a warning and calls compute_numerical_gradient to calculate the gradient. This is used by metric which mType is VERTEX_BASED. More...

virtual bool	compute_element_analytical_gradient (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], int num_free_vtx, double &metric_value, MsqError &err)
	Virtual function that computes the gradient of the QualityMetric analytically. The base class implementation of this function simply prints a warning and calls compute_numerical_gradient to calculate the gradient. This is used by metric which mType is ELEMENT_BASED. For parameters, see compute_element_gradient() . More...

bool	compute_element_numerical_hessian (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], Matrix3D hessian[], int num_free_vtx, double &metric_value, MsqError &err)

virtual bool	compute_element_analytical_hessian (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], Matrix3D hessian[], int num_free_vtx, double &metric_value, MsqError &err)

	QualityMetric ()

void	set_metric_type (MetricType t)
	This function should be used in the constructor of every concrete quality metric. More...

double	average_metrics (const double metric_values[], const int &num_values, MsqError &err)
	average_metrics takes an array of length num_values and averages the contents using averaging method data member avgMethod . More...

double	average_metric_and_weights (double metric_values[], int num_metric_values, MsqError &err)
	Given a list of metric values, calculate the average metric valude according to the current avgMethod and write into the passed metric_values array the the value weight/count to use when averaging gradient vectors for the metric. More...

double	weighted_average_metrics (const double coef[], const double metric_values[], const int &num_values, MsqError &err)
	takes an array of coefficients and an array of metrics (both of length num_value) and averages the contents using averaging method 'method'. More...

bool	compute_vertex_numerical_gradient (PatchData &pd, MsqVertex &vertex, MsqVertex *vertices[], Vector3D grad_vec[], int num_vtx, double &metric_value, MsqError &err)

bool	compute_element_numerical_gradient (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], int num_free_vtx, double &metric_value, MsqError &err)
	Non-virtual function which numerically computes the gradient of a QualityMetric of a given element for a given set of free vertices on that element. This is used by metric which mType is ELEMENT_BASED. For parameters, see compute_element_gradient() . More...

virtual bool	compute_vertex_analytical_gradient (PatchData &pd, MsqVertex &vertex, MsqVertex *vertices[], Vector3D grad_vec[], int num_vtx, double &metric_value, MsqError &err)
	Virtual function that computes the gradient of the QualityMetric analytically. The base class implementation of this function simply prints a warning and calls compute_numerical_gradient to calculate the gradient. This is used by metric which mType is VERTEX_BASED. More...

virtual bool	compute_element_analytical_gradient (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], int num_free_vtx, double &metric_value, MsqError &err)
	Virtual function that computes the gradient of the QualityMetric analytically. The base class implementation of this function simply prints a warning and calls compute_numerical_gradient to calculate the gradient. This is used by metric which mType is ELEMENT_BASED. For parameters, see compute_element_gradient() . More...

bool	compute_element_numerical_hessian (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], Matrix3D hessian[], int num_free_vtx, double &metric_value, MsqError &err)

virtual bool	compute_element_analytical_hessian (PatchData &pd, MsqMeshEntity element, MsqVertex free_vtces[], Vector3D grad_vec[], Matrix3D hessian[], int num_free_vtx, double &metric_value, MsqError &err)

Additional Inherited Members
Public Types inherited from QualityMetric
enum	MetricType { MT_UNDEFINED, VERTEX_BASED, ELEMENT_BASED, VERTEX_BASED_FREE_ONLY, MT_UNDEFINED, VERTEX_BASED, ELEMENT_BASED, VERTEX_BASED_FREE_ONLY }

enum	ElementEvaluationMode { EEM_UNDEFINED, ELEMENT_VERTICES, LINEAR_GAUSS_POINTS, QUADRATIC_GAUSS_POINTS, CUBIC_GAUSS_POINTS, EEM_UNDEFINED, ELEMENT_VERTICES, LINEAR_GAUSS_POINTS, QUADRATIC_GAUSS_POINTS, CUBIC_GAUSS_POINTS }

enum	AveragingMethod { NONE, LINEAR, RMS, HMS, MINIMUM, MAXIMUM, HARMONIC, GEOMETRIC, SUM, SUM_SQUARED, GENERALIZED_MEAN, STANDARD_DEVIATION, MAX_OVER_MIN, MAX_MINUS_MIN, SUM_OF_RATIOS_SQUARED, NONE, LINEAR, RMS, HMS, MINIMUM, MAXIMUM, HARMONIC, GEOMETRIC, SUM, SUM_SQUARED, GENERALIZED_MEAN, STANDARD_DEVIATION, MAX_OVER_MIN, MAX_MINUS_MIN, SUM_OF_RATIOS_SQUARED }

enum	GRADIENT_TYPE { NUMERICAL_GRADIENT, ANALYTICAL_GRADIENT, NUMERICAL_GRADIENT, ANALYTICAL_GRADIENT }

enum	HESSIAN_TYPE { NUMERICAL_HESSIAN, ANALYTICAL_HESSIAN, NUMERICAL_HESSIAN, ANALYTICAL_HESSIAN }

enum	MetricType { MT_UNDEFINED, VERTEX_BASED, ELEMENT_BASED, VERTEX_BASED_FREE_ONLY, MT_UNDEFINED, VERTEX_BASED, ELEMENT_BASED, VERTEX_BASED_FREE_ONLY }

enum	ElementEvaluationMode { EEM_UNDEFINED, ELEMENT_VERTICES, LINEAR_GAUSS_POINTS, QUADRATIC_GAUSS_POINTS, CUBIC_GAUSS_POINTS, EEM_UNDEFINED, ELEMENT_VERTICES, LINEAR_GAUSS_POINTS, QUADRATIC_GAUSS_POINTS, CUBIC_GAUSS_POINTS }

enum	AveragingMethod { NONE, LINEAR, RMS, HMS, MINIMUM, MAXIMUM, HARMONIC, GEOMETRIC, SUM, SUM_SQUARED, GENERALIZED_MEAN, STANDARD_DEVIATION, MAX_OVER_MIN, MAX_MINUS_MIN, SUM_OF_RATIOS_SQUARED, NONE, LINEAR, RMS, HMS, MINIMUM, MAXIMUM, HARMONIC, GEOMETRIC, SUM, SUM_SQUARED, GENERALIZED_MEAN, STANDARD_DEVIATION, MAX_OVER_MIN, MAX_MINUS_MIN, SUM_OF_RATIOS_SQUARED }

enum	GRADIENT_TYPE { NUMERICAL_GRADIENT, ANALYTICAL_GRADIENT, NUMERICAL_GRADIENT, ANALYTICAL_GRADIENT }

enum	HESSIAN_TYPE { NUMERICAL_HESSIAN, ANALYTICAL_HESSIAN, NUMERICAL_HESSIAN, ANALYTICAL_HESSIAN }

Protected Attributes inherited from QualityMetric
AveragingMethod	avgMethod

int	feasible

msq_std::string	metricName

Detailed Description

Definition at line 48 of file includeLinks/ShapeQualityMetric.hpp.

Constructor & Destructor Documentation

virtual ~ShapeQualityMetric ( )

inlinevirtual

virtual destructor ensures use of polymorphism during destruction

Definition at line 57 of file includeLinks/ShapeQualityMetric.hpp.

58 {};

virtual ~ShapeQualityMetric ( )

inlinevirtual

virtual destructor ensures use of polymorphism during destruction

Definition at line 57 of file src/QualityMetric/Shape/ShapeQualityMetric.hpp.

58 {};

Member Function Documentation

bool condition_number_2d	(	Vector3D	temp_vec[],
		size_t	v_ind,
		PatchData &	pd,
		double &	fval,
		MsqError &	err
	)

inlineprotected

Given the 2-d jacobian matrix, compute the condition number, fval.

Definition at line 109 of file includeLinks/ShapeQualityMetric.hpp.

References PatchData::domain_set(), PatchData::get_barrier_delta(), PatchData::get_domain_normal_at_vertex(), MsqError::INVALID_MESH, Mesquite::MSQ_DBL_MIN, MSQ_ERRZERO, Mesquite::MSQ_MAX_CAP, MSQ_SETERR, and QualityMetric::vertex_barrier_function().

Referenced by ConditionNumberQualityMetric::evaluate_element(), and VertexConditionNumberQualityMetric::evaluate_vertex().

    {   
        //norm squared of J
      double term1=temp_vec[0]%temp_vec[0]+temp_vec[1]%temp_vec[1];
 
      Vector3D unit_surf_norm;
      if ( pd.domain_set() ) {
        pd.get_domain_normal_at_vertex(v_ind,true,unit_surf_norm,err);MSQ_ERRZERO(err);
      }
      else {
         return false;
      }
 
      // det J
      double temp_var=unit_surf_norm%(temp_vec[0]*temp_vec[1]);
 
      double h;
      double delta=pd.get_barrier_delta(err); MSQ_ERRZERO(err);
 
      // Note: technically, we want delta=eta*tau-max
      //       whereas the function above gives delta=eta*alpha-max
      //      
      //       Because the only requirement on eta is eta << 1,
      //       and because tau-max = alpha-max/0.707 we can
      //       ignore the discrepancy
 
      if (delta==0) { 
         if (temp_var < MSQ_DBL_MIN ) {
            return false;
         }
         else {
            h=temp_var;
         }
 
      // Note: when delta=0, the vertex_barrier_function
      //       formally gives h=temp_var as well.
      //       We just do it this way to avoid any 
      //       roundoff issues.
      // Also: when delta=0, this metric is identical
      //       to the original condition number with
      //       the barrier at temp_var=0
      }
      else {
         h = vertex_barrier_function(temp_var,delta);
 
         if (h<MSQ_DBL_MIN && fabs(temp_var) > MSQ_DBL_MIN ) { 
           h = delta*delta/fabs(temp_var); }
         // Note: Analytically, h is strictly positive, but
         //       it can be zero numerically if temp_var
         //       is a large negative number 
         //       In the case h=0, we use a different analytic
         //       approximation to compute h.
      }
 
      if (h<MSQ_DBL_MIN) {
        MSQ_SETERR(err)( "Barrier function is zero due to excessively large "
                         "negative area compared to delta. /n Try to untangle "
                         "mesh another way. ", MsqError::INVALID_MESH);
        return false;
      }
 
      fval=term1/(2*h);
 
      if (fval>MSQ_MAX_CAP) {
         fval=MSQ_MAX_CAP;
      }
      return true;
 
    }

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bool condition_number_2d	(	Vector3D	temp_vec[],
		size_t	v_ind,
		PatchData &	pd,
		double &	fval,
		MsqError &	err
	)

protected

Given the 2-d jacobian matrix, compute the condition number, fval.

bool condition_number_3d	(	Vector3D	temp_vec[],
		PatchData &	pd,
		double &	fval,
		MsqError &	err
	)

protected

Given the 3-d jacobian matrix, compute the condition number, fval.

bool condition_number_3d	(	Vector3D	temp_vec[],
		PatchData &	pd,
		double &	fval,
		MsqError &	err
	)

inlineprotected

Given the 3-d jacobian matrix, compute the condition number, fval.

Definition at line 186 of file includeLinks/ShapeQualityMetric.hpp.

References PatchData::get_barrier_delta(), MsqError::INVALID_MESH, Mesquite::MSQ_DBL_MIN, MSQ_ERRZERO, Mesquite::MSQ_MAX_CAP, MSQ_SETERR, sqrt(), and QualityMetric::vertex_barrier_function().

Referenced by ConditionNumberQualityMetric::evaluate_element(), and VertexConditionNumberQualityMetric::evaluate_vertex().

    {   
        //norm squared of J
      double term1=temp_vec[0]%temp_vec[0]+
         temp_vec[1]%temp_vec[1]+
         temp_vec[2]%temp_vec[2];
        //norm squared of adjoint of J
      double term2=(temp_vec[0]*temp_vec[1])%
         (temp_vec[0]*temp_vec[1])+
         (temp_vec[1]*temp_vec[2])%
         (temp_vec[1]*temp_vec[2])+
         (temp_vec[2]*temp_vec[0])%
         (temp_vec[2]*temp_vec[0]);
        //det of J
      double temp_var=temp_vec[0]%(temp_vec[1]*temp_vec[2]);
 
      double h;
      double delta=pd.get_barrier_delta(err); MSQ_ERRZERO(err);
 
      // Note: technically, we want delta=eta*tau-max
      //       whereas the function above gives delta=eta*alpha-max
      //      
      //       Because the only requirement on eta is eta << 1,
      //       and because tau-max = alpha-max/0.707 we can
      //       ignore the discrepancy
 
      if (delta==0) { 
         if (temp_var < MSQ_DBL_MIN ) {
            return false;
         }
         else {
            h=temp_var;
         }
 
      // Note: when delta=0, the vertex_barrier_function
      //       formally gives h=temp_var as well.
      //       We just do it this way to avoid any 
      //       roundoff issues.
      // Also: when delta=0, this metric is identical
      //       to the original condition number with
      //       the barrier at temp_var=0
 
      }
      else {
         h = vertex_barrier_function(temp_var,delta);
  
         if (h<MSQ_DBL_MIN && fabs(temp_var) > MSQ_DBL_MIN ) { 
           h = delta*delta/fabs(temp_var); }
  
         // Note: Analytically, h is strictly positive, but
         //       it can be zero numerically if temp_var
         //       is a large negative number 
         //       In the h=0, we use a different analytic
         //       approximation to compute h.
      }
      if (h<MSQ_DBL_MIN) {
        MSQ_SETERR(err)("Barrier function is zero due to excessively large "
                        "negative area compared to delta. /n Try to untangle "
                        "mesh another way. ", MsqError::INVALID_MESH);
        return false;
      }
 
      fval=sqrt(term1*term2)/(3*h);
 
      if (fval>MSQ_MAX_CAP) {
         fval=MSQ_MAX_CAP;
      }
      return true;
 
    }

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

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation