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.

   30 {
   31     VERDICT_FALSE = 0,
   32     VERDICT_TRUE  = 1
   33 };

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.

   44 {
   45     return v1 % ( v2 * v3 );
   46 }

determinant() [2/2]

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

inline

Definition at line 38 of file verdict_defines.hpp.

   39 {
   40     return ( ( a ) * ( d ) - ( b ) * ( c ) );
   41 }

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.

  216 {
  217  
  218     double g11, g12, g13, g22, g23, g33;
  219  
  220     g11 = v1 % v1;
  221     g12 = v1 % v2;
  222     g13 = v1 % v3;
  223     g22 = v2 % v2;
  224     g23 = v2 % v3;
  225     g33 = v3 % v3;
  226  
  227     double rtg11 = sqrt( g11 );
  228     double rtg22 = sqrt( g22 );
  229     double rtg33 = sqrt( g33 );
  230     VerdictVector temp1;
  231  
  232     temp1 = v1 * v2;
  233  
  234     double cross = sqrt( temp1 % temp1 );
  235  
  236     double q11, q21, q31;
  237     double q12, q22, q32;
  238     double q13, q23, q33;
  239  
  240     q11 = 1;
  241     q21 = 0;
  242     q31 = 0;
  243  
  244     q12 = g12 / rtg11 / rtg22;
  245     q22 = cross / rtg11 / rtg22;
  246     q32 = 0;
  247  
  248     q13   = g13 / rtg11 / rtg33;
  249     q23   = ( g11 * g23 - g12 * g13 ) / rtg11 / rtg33 / cross;
  250     temp1 = v2 * v3;
  251     q33   = ( v1 % temp1 ) / rtg33 / cross;
  252  
  253     q1.set( q11, q21, q31 );
  254     q2.set( q12, q22, q32 );
  255     q3.set( q13, q23, q33 );
  256 }

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.

  149 {
  150     double detx = determinant( x1, x2, x3 );
  151     VerdictVector rx1, rx2, rx3;
  152  
  153     rx1.set( x1.x(), x2.x(), x3.x() );
  154     rx2.set( x1.y(), x2.y(), x3.y() );
  155     rx3.set( x1.z(), x2.z(), x3.z() );
  156  
  157     u1 = rx2 * rx3;
  158     u2 = rx3 * rx1;
  159     u3 = rx1 * rx2;
  160  
  161     u1 /= detx;
  162     u2 /= detx;
  163     u3 /= detx;
  164 }

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.

  112 {
  113     return m11 * m11 + m21 * m21 + m12 * m12 + m22 * m22;
  114 }

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.

  282 {
  283     return ( x1 % x1 ) + ( x2 % x2 ) + ( x3 % x3 );
  284 }

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.

   80 {
   81     double return_value = 0.0;
   82  
   83     if( jacobi != 0.0 )
   84     {
   85  
   86         double l1, l2, l3, length_product;
   87         // Note: there may be numerical problems if one is a lot shorter
   88         // than the others this way. But scaling each vector before the
   89         // triple product would involve 3 square roots instead of just
   90         // one.
   91         l1             = v1.length_squared();
   92         l2             = v2.length_squared();
   93         l3             = v3.length_squared();
   94         length_product = sqrt( l1 * l2 * l3 );
   95  
   96         // if some numerical scaling problem, or just plain roundoff,
   97         // then push back into range [-1,1].
   98         if( length_product < fabs( jacobi ) )
   99         {
  100             length_product = fabs( jacobi );
  101         }
  102  
  103         if( tet_flag == 1 )
  104             return_value = verdictSqrt2 * jacobi / length_product;
  105         else
  106             return_value = jacobi / length_product;
  107     }
  108     return return_value;
  109 }

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.

  267 {
  268  
  269     VerdictVector x1, x2, x3;
  270  
  271     x1.set( a1.x(), a2.x(), a3.x() );
  272     x2.set( a1.y(), a2.y(), a3.y() );
  273     x3.set( a1.z(), a2.z(), a3.z() );
  274  
  275     c1.set( x1 % b1, x2 % b1, x3 % b1 );
  276     c2.set( x1 % b2, x2 % b2, x3 % b2 );
  277     c3.set( x1 % b3, x2 % b3, x3 % b3 );
  278 }

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.

  129 {
  130     double tmp = sqrt( gm11 * gm22 );
  131     if( tmp == 0 )
  132     {
  133         return false;
  134     }
  135  
  136     qm11 = 1;
  137     qm21 = 0;
  138     qm12 = gm12 / tmp;
  139     qm22 = det / tmp;
  140     return true;
  141 }

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.

  292 {
  293     double normsq1, normsq2, kappa;
  294     VerdictVector u1, u2, u3;
  295     VerdictVector x1, x2, x3;
  296  
  297     inverse( qw1, qw2, qw3, u1, u2, u3 );
  298     product( q1, q2, q3, u1, u2, u3, x1, x2, x3 );
  299     inverse( x1, x2, x3, u1, u2, u3 );
  300     normsq1 = norm_squared( x1, x2, x3 );
  301     normsq2 = norm_squared( u1, u2, u3 );
  302     kappa   = sqrt( normsq1 * normsq2 );
  303  
  304     double skew = 0;
  305     if( kappa > VERDICT_DBL_MIN ) skew = 3 / kappa;
  306  
  307     return skew;
  308 }

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().