verdict_defines.hpp File Reference

#include <cmath>
#include "v_vector.h"
#include "VerdictVector.hpp"

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Macros
#define	VERDICT_MIN(a, b)   ( ( a ) < ( b ) ? ( a ) : ( b ) )
#define	VERDICT_MAX(a, b)   ( ( a ) > ( b ) ? ( a ) : ( b ) )
#define	jacobian_matrix(a, b, c, d, e, f, g)
#define	form_t(m11, m21, m12, m22, mw11, mw21, mw12, mw22, detmw, xm11, xm21, xm12, xm22)
#define	metric_matrix(m11, m21, m12, m22, gm11, gm12, gm22)

Enumerations
enum	VerdictBoolean { VERDICT_FALSE = 0 , VERDICT_TRUE = 1 }

Functions
double	determinant (double a, double b, double c, double d)
double	determinant (const VerdictVector &v1, const VerdictVector &v2, const VerdictVector &v3)
double	normalize_jacobian (double jacobi, VerdictVector &v1, VerdictVector &v2, VerdictVector &v3, int tet_flag=0)
double	norm_squared (double m11, double m21, double m12, double m22)
int	skew_matrix (double gm11, double gm12, double gm22, double det, double &qm11, double &qm21, double &qm12, double &qm22)
void	inverse (const VerdictVector &x1, const VerdictVector &x2, const VerdictVector &x3, VerdictVector &u1, VerdictVector &u2, VerdictVector &u3)
void	form_Q (const VerdictVector &v1, const VerdictVector &v2, const VerdictVector &v3, VerdictVector &q1, VerdictVector &q2, VerdictVector &q3)
void	product (VerdictVector &a1, VerdictVector &a2, VerdictVector &a3, VerdictVector &b1, VerdictVector &b2, VerdictVector &b3, VerdictVector &c1, VerdictVector &c2, VerdictVector &c3)
double	norm_squared (VerdictVector &x1, VerdictVector &x2, VerdictVector &x3)
double	skew_x (VerdictVector &q1, VerdictVector &q2, VerdictVector &q3, VerdictVector &qw1, VerdictVector &qw2, VerdictVector &qw3)

Variables
double	verdictSqrt2

Macro Definition Documentation

form_t

#define form_t	(		m11,
			m21,
			m12,
			m22,
			mw11,
			mw21,
			mw12,
			mw22,
			detmw,
			xm11,
			xm21,
			xm12,
			xm22
	)

Value:

 xm11 = ( ( m11 ) * ( mw22 ) - ( m12 ) * ( mw21 ) ) / ( detmw ); \
 ( xm21 ) = ( ( m21 ) * ( mw22 ) - ( m22 ) * ( mw21 ) ) / ( detmw ); \
 ( xm12 ) = ( ( m12 ) * ( mw11 ) - ( m11 ) * ( mw12 ) ) / ( detmw ); \
 ( xm22 ) = ( ( m22 ) * ( mw11 ) - ( m21 ) * ( mw12 ) ) / ( detmw );

Definition at line 67 of file verdict_defines.hpp.

jacobian_matrix

#define jacobian_matrix	(		a,
			b,
			c,
			d,
			e,
			f,
			g
	)

Value:

 double jac_mat_tmp; \
 jac_mat_tmp = sqrt( a ); \
 if( jac_mat_tmp == 0 ) \
 { \
 ( d ) = 0; \
 ( e ) = 0; \
 ( f ) = 0; \
 ( g ) = 0; \
 } \
 else \
 { \
 ( d ) = jac_mat_tmp; \
 ( e ) = 0; \
 ( f ) = ( b ) / jac_mat_tmp; \
 ( g ) = ( c ) / jac_mat_tmp; \
 }

Definition at line 48 of file verdict_defines.hpp.

metric_matrix

#define metric_matrix	(		m11,
			m21,
			m12,
			m22,
			gm11,
			gm12,
			gm22
	)

Value:

 gm11 = ( m11 ) * ( m11 ) + ( m21 ) * ( m21 ); \
 ( gm12 ) = ( m11 ) * ( m12 ) + ( m21 ) * ( m22 ); \
 ( gm22 ) = ( m12 ) * ( m12 ) + ( m22 ) * ( m22 );

Definition at line 116 of file verdict_defines.hpp.

VERDICT_MAX

#define VERDICT_MAX	(		a,
			b
	)		( ( a ) > ( b ) ? ( a ) : ( b ) )

Definition at line 36 of file verdict_defines.hpp.

VERDICT_MIN

#define VERDICT_MIN	(		a,
			b
	)		( ( a ) < ( b ) ? ( a ) : ( b ) )

Definition at line 35 of file verdict_defines.hpp.

Enumeration Type Documentation

VerdictBoolean

enum VerdictBoolean

Enumerator
VERDICT_FALSE
VERDICT_TRUE

Definition at line 29 of file verdict_defines.hpp.

{
 VERDICT_FALSE = 0,
 VERDICT_TRUE = 1
};

Function Documentation

determinant() [1/2]

double determinant ( const VerdictVector &  v1, const VerdictVector &  v2, const VerdictVector &  v3  )

inline

Definition at line 43 of file verdict_defines.hpp.

{
 return v1 % ( v2 * v3 );
}

determinant() [2/2]

double determinant ( double  a, double  b, double  c, double  d  )

inline

Definition at line 38 of file verdict_defines.hpp.

{
 return ( ( a ) * ( d ) - ( b ) * ( c ) );
}

Referenced by get_weight(), inverse(), v_quad_quality(), v_quad_relative_size_squared(), v_tri_quality(), and v_tri_relative_size_squared().

form_Q()

void form_Q ( const VerdictVector &  v1, const VerdictVector &  v2, const VerdictVector &  v3, VerdictVector &  q1, VerdictVector &  q2, VerdictVector &  q3  )

inline

Definition at line 210 of file verdict_defines.hpp.

{
 
 double g11, g12, g13, g22, g23, g33;
 
 g11 = v1 % v1;
 g12 = v1 % v2;
 g13 = v1 % v3;
 g22 = v2 % v2;
 g23 = v2 % v3;
 g33 = v3 % v3;
 
 double rtg11 = sqrt( g11 );
 double rtg22 = sqrt( g22 );
 double rtg33 = sqrt( g33 );
 VerdictVector temp1;
 
 temp1 = v1 * v2;
 
 double cross = sqrt( temp1 % temp1 );
 
 double q11, q21, q31;
 double q12, q22, q32;
 double q13, q23, q33;
 
 q11 = 1;
 q21 = 0;
 q31 = 0;
 
 q12 = g12 / rtg11 / rtg22;
 q22 = cross / rtg11 / rtg22;
 q32 = 0;
 
 q13 = g13 / rtg11 / rtg33;
 q23 = ( g11 * g23 - g12 * g13 ) / rtg11 / rtg33 / cross;
 temp1 = v2 * v3;
 q33 = ( v1 % temp1 ) / rtg33 / cross;
 
 q1.set( q11, q21, q31 );
 q2.set( q12, q22, q32 );
 q3.set( q13, q23, q33 );
}

References moab::cross(), and VerdictVector::set().

inverse()

void inverse ( const VerdictVector &  x1, const VerdictVector &  x2, const VerdictVector &  x3, VerdictVector &  u1, VerdictVector &  u2, VerdictVector &  u3  )

inline

Definition at line 143 of file verdict_defines.hpp.

{
 double detx = determinant( x1, x2, x3 );
 VerdictVector rx1, rx2, rx3;
 
 rx1.set( x1.x(), x2.x(), x3.x() );
 rx2.set( x1.y(), x2.y(), x3.y() );
 rx3.set( x1.z(), x2.z(), x3.z() );
 
 u1 = rx2 * rx3;
 u2 = rx3 * rx1;
 u3 = rx1 * rx2;
 
 u1 /= detx;
 u2 /= detx;
 u3 /= detx;
}

References determinant(), VerdictVector::set(), VerdictVector::x(), VerdictVector::y(), and VerdictVector::z().

Referenced by skew_x(), and test_spectral_hex().

norm_squared() [1/2]

double norm_squared ( double  m11, double  m21, double  m12, double  m22  )

inline

Definition at line 111 of file verdict_defines.hpp.

{
 return m11 * m11 + m21 * m21 + m12 * m12 + m22 * m22;
}

Referenced by skew_x().

norm_squared() [2/2]

double norm_squared ( VerdictVector &  x1, VerdictVector &  x2, VerdictVector &  x3  )

inline

Definition at line 280 of file verdict_defines.hpp.

{
 return ( x1 % x1 ) + ( x2 % x2 ) + ( x3 % x3 );
}

normalize_jacobian()

double normalize_jacobian ( double  jacobi, VerdictVector &  v1, VerdictVector &  v2, VerdictVector &  v3, int  tet_flag = 0  )

inline

Definition at line 75 of file verdict_defines.hpp.

{
 double return_value = 0.0;
 
 if( jacobi != 0.0 )
 {
 
 double l1, l2, l3, length_product;
 // Note: there may be numerical problems if one is a lot shorter
 // than the others this way. But scaling each vector before the
 // triple product would involve 3 square roots instead of just
 // one.
 l1 = v1.length_squared();
 l2 = v2.length_squared();
 l3 = v3.length_squared();
 length_product = sqrt( l1 * l2 * l3 );
 
 // if some numerical scaling problem, or just plain roundoff,
 // then push back into range [-1,1].
 if( length_product < fabs( jacobi ) )
 {
 length_product = fabs( jacobi );
 }
 
 if( tet_flag == 1 )
 return_value = verdictSqrt2 * jacobi / length_product;
 else
 return_value = jacobi / length_product;
 }
 return return_value;
}

References VerdictVector::length_squared(), and verdictSqrt2.

product()

void product ( VerdictVector &  a1, VerdictVector &  a2, VerdictVector &  a3, VerdictVector &  b1, VerdictVector &  b2, VerdictVector &  b3, VerdictVector &  c1, VerdictVector &  c2, VerdictVector &  c3  )

inline

Definition at line 258 of file verdict_defines.hpp.

{
 
 VerdictVector x1, x2, x3;
 
 x1.set( a1.x(), a2.x(), a3.x() );
 x2.set( a1.y(), a2.y(), a3.y() );
 x3.set( a1.z(), a2.z(), a3.z() );
 
 c1.set( x1 % b1, x2 % b1, x3 % b1 );
 c2.set( x1 % b2, x2 % b2, x3 % b2 );
 c3.set( x1 % b3, x2 % b3, x3 % b3 );
}

References VerdictVector::set(), VerdictVector::x(), VerdictVector::y(), and VerdictVector::z().

Referenced by skew_x().

skew_matrix()

int skew_matrix ( double  gm11, double  gm12, double  gm22, double  det, double &  qm11, double &  qm21, double &  qm12, double &  qm22  )

inline

Definition at line 121 of file verdict_defines.hpp.

{
 double tmp = sqrt( gm11 * gm22 );
 if( tmp == 0 )
 {
 return false;
 }
 
 qm11 = 1;
 qm21 = 0;
 qm12 = gm12 / tmp;
 qm22 = det / tmp;
 return true;
}

skew_x()

double skew_x ( VerdictVector &  q1, VerdictVector &  q2, VerdictVector &  q3, VerdictVector &  qw1, VerdictVector &  qw2, VerdictVector &  qw3  )

inline

Definition at line 286 of file verdict_defines.hpp.

{
 double normsq1, normsq2, kappa;
 VerdictVector u1, u2, u3;
 VerdictVector x1, x2, x3;
 
 inverse( qw1, qw2, qw3, u1, u2, u3 );
 product( q1, q2, q3, u1, u2, u3, x1, x2, x3 );
 inverse( x1, x2, x3, u1, u2, u3 );
 normsq1 = norm_squared( x1, x2, x3 );
 normsq2 = norm_squared( u1, u2, u3 );
 kappa = sqrt( normsq1 * normsq2 );
 
 double skew = 0;
 if( kappa > VERDICT_DBL_MIN ) skew = 3 / kappa;
 
 return skew;
}

References inverse(), norm_squared(), product(), and VERDICT_DBL_MIN.

Variable Documentation

verdictSqrt2

double verdictSqrt2

extern

Definition at line 30 of file V_GaussIntegration.cpp.

Referenced by normalize_jacobian().