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

Include dependency graph for verdict_defines.hpp:

This graph shows which files directly or indirectly include this file:

Defines
#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

Define Documentation

#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.

#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.

#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.

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

Definition at line 36 of file verdict_defines.hpp.

Referenced by diag_length(), hex_edge_length(), v_hex_diagonal(), v_hex_edge_ratio(), v_hex_jacobian(), v_hex_max_aspect_frobenius(), v_hex_max_edge_ratio(), v_hex_med_aspect_frobenius(), v_hex_oddy(), v_hex_quality(), v_hex_relative_size_squared(), v_hex_scaled_jacobian(), v_hex_shape(), v_hex_shape_and_size(), v_hex_shear(), v_hex_shear_and_size(), v_hex_skew(), v_hex_stretch(), v_hex_taper(), v_hex_volume(), v_quad_area(), v_quad_aspect_ratio(), v_quad_condition(), v_quad_edge_ratio(), v_quad_jacobian(), v_quad_max_aspect_frobenius(), v_quad_max_edge_ratio(), v_quad_maximum_angle(), v_quad_med_aspect_frobenius(), v_quad_minimum_angle(), v_quad_oddy(), v_quad_quality(), v_quad_radius_ratio(), v_quad_relative_size_squared(), v_quad_scaled_jacobian(), v_quad_shape(), v_quad_shape_and_size(), v_quad_shear_and_size(), v_quad_stretch(), v_quad_warpage(), v_tet_aspect_frobenius(), v_tet_aspect_ratio(), v_tet_collapse_ratio(), v_tet_edge_ratio(), v_tet_minimum_angle(), v_tet_quality(), v_tet_shape(), v_tri_area(), v_tri_aspect_frobenius(), v_tri_aspect_ratio(), v_tri_distortion(), v_tri_edge_ratio(), v_tri_maximum_angle(), v_tri_minimum_angle(), v_tri_quality(), v_tri_radius_ratio(), v_tri_relative_size_squared(), v_tri_scaled_jacobian(), v_tri_shape(), and v_tri_shape_and_size().

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

Definition at line 35 of file verdict_defines.hpp.

Referenced by diag_length(), hex_edge_length(), v_hex_diagonal(), v_hex_edge_ratio(), v_hex_jacobian(), v_hex_max_aspect_frobenius(), v_hex_max_edge_ratio(), v_hex_med_aspect_frobenius(), v_hex_oddy(), v_hex_quality(), v_hex_relative_size_squared(), v_hex_scaled_jacobian(), v_hex_shape(), v_hex_shape_and_size(), v_hex_shear(), v_hex_shear_and_size(), v_hex_skew(), v_hex_stretch(), v_hex_taper(), v_hex_volume(), v_quad_area(), v_quad_aspect_ratio(), v_quad_condition(), v_quad_distortion(), v_quad_edge_ratio(), v_quad_jacobian(), v_quad_max_aspect_frobenius(), v_quad_max_edge_ratio(), v_quad_maximum_angle(), v_quad_med_aspect_frobenius(), v_quad_minimum_angle(), v_quad_oddy(), v_quad_quality(), v_quad_radius_ratio(), v_quad_relative_size_squared(), v_quad_scaled_jacobian(), v_quad_shape(), v_quad_shape_and_size(), v_quad_shear(), v_quad_shear_and_size(), v_quad_skew(), v_quad_stretch(), v_quad_taper(), v_quad_warpage(), v_tet_aspect_beta(), v_tet_aspect_frobenius(), v_tet_aspect_ratio(), v_tet_collapse_ratio(), v_tet_edge_ratio(), v_tet_minimum_angle(), v_tet_quality(), v_tet_radius_ratio(), v_tri_area(), v_tri_aspect_frobenius(), v_tri_aspect_ratio(), v_tri_condition(), v_tri_distortion(), v_tri_edge_ratio(), v_tri_maximum_angle(), v_tri_minimum_angle(), v_tri_quality(), v_tri_radius_ratio(), v_tri_relative_size_squared(), v_tri_scaled_jacobian(), v_tri_shape(), and v_tri_shape_and_size().

Enumeration Type Documentation

enum VerdictBoolean

Enumerator:

VERDICT_FALSE
VERDICT_TRUE

Definition at line 29 of file verdict_defines.hpp.

{
    VERDICT_FALSE = 0,
    VERDICT_TRUE  = 1
};

Function Documentation

double determinant	(	double	a,
		double	b,
		double	c,
		double	d
	)		`[inline]`

Definition at line 38 of file verdict_defines.hpp.

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

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

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 );
}

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.

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

{

    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 );
}

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.

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

Referenced by moab::element_utility::Linear_tet_map< Entity_handle, moab::Matrix3 >::set_tet(), skew_x(), moab::element_utility::Linear_hex_map< moab::Matrix3 >::solve_inverse(), and test_spectral_hex().

{
    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;
}

double norm_squared	(	double	m11,
		double	m21,
		double	m12,
		double	m22
	)		`[inline]`

Definition at line 111 of file verdict_defines.hpp.

Referenced by skew_x().

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

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 );
}

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.

References VerdictVector::length_squared(), and verdictSqrt2.

{
    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;
}

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.

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

Referenced by skew_x().

{

    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 );
}

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;
}

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.

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

{
    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;
}

Variable Documentation

double verdictSqrt2

Definition at line 30 of file V_GaussIntegration.cpp.

Referenced by normalize_jacobian().

Defines

Enumerations

Functions

Variables

Define Documentation

Enumeration Type Documentation

Function Documentation

Variable Documentation