libvtk7-dev 7.1.1+dfsg1-2 / usr / include / vtk-7.1 / vtkverdict / verdict.h

/*=========================================================================

  Module:    verdict.h.in

  Copyright (c) 2006 Sandia Corporation.
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
     PURPOSE.  See the above copyright notice for more information.

=========================================================================*/


/*! \file verdict.h
  \brief Header file for verdict library that calculates metrics for finite elements.
    Also see: \ref index "Main Page" 
 *
 * verdict.h is the header file for applications/libraries to include
 *           to compute quality metrics.
 *
 * This file is part of VERDICT
 *
 */

// .SECTION Thanks
// Prior to its inclusion within VTK, this code was developed by the CUBIT
// project at Sandia National Laboratories. 

#ifndef __verdict_h
#define __verdict_h

#define VERDICT_VERSION 120

#define BUILD_SHARED_LIBS
#ifdef BUILD_SHARED_LIBS
# define VERDICT_SHARED_LIB
#endif

/*!\page VerdictAsASubProject Verdict as a Subproject
 *
 * Should a project wish to include a private version of verdict, it may
 * turn on the CMake \c VERDICT_MANGLE option and define \c VERDICT_MANGLE_PREFIX.
 * This will use the \c verdict_mangle.h file to define macros that rename all
 * verdict library symbols using the given prefix.
 *
 * This allows programs using the parent project to link to the parent project
 * as well as other versions of verdict than the one used by the parent project.
 * If you are using mangling, you should consider setting \c VERDICT_NO_LIBRARY_VERSION
 * to 1 and \c VERDICT_LIBRARY_PROPERTIES to include your parent project's shared
 * library version number.
 *
 * Here is an example. Assume we have a library named XXX which we would like to use
 * a private copy of the verdict library (instead of the version installed in a system
 * directory). The XXX project source directory would contain a copy of the verdict
 * source and the CMake file for XXX would include:\code
 *   set( VERDICT_MANGLE "ON" CACHE BOOL "XXX requires Verdict to be mangled" FORCE )
 *   set( VERDICT_MANGLE_PREFIX "xxx" CACHE STRING "Verdict routines prefixed with xxx_" FORCE )
 *   set( VERDICT_NO_LIBRARY_VERSION 1 )
 *   set( VERDICT_LIBRARY_PROPERTIES
 *     ${VERDICT_LIBRARY_PROPERTIES}
 *     VERSION "xxx${XXX_VERSION}"
 *   )
 *   add_subdirectory( verdict )
 * \endcode
 * By setting these variables before descending into the verdict directory,
 * we force all the symbol names in the library to be prefaced with \c xxx_
 * and the resulting library will be named \a xxxverdict instead of simply \a verdict.
 */
/* #undef VERDICT_MANGLE */
#ifdef VERDICT_MANGLE
#  include "verdict_mangle.h"
#endif

#define VERDICT_DBL_MIN 1.0E-30
#define VERDICT_DBL_MAX 1.0E+30
#define VERDICT_PI 3.1415926535897932384626

#if defined(_WIN32) || defined (__CYGWIN__)
# define VERDICT_ABI_IMPORT __declspec(dllimport)
# define VERDICT_ABI_EXPORT __declspec(dllexport)
#elif __GNUC__ >= 4
# define VERDICT_ABI_IMPORT __attribute__ ((visibility("default")))
# define VERDICT_ABI_EXPORT __attribute__ ((visibility("default")))
#else
# define VERDICT_ABI_IMPORT
# define VERDICT_ABI_EXPORT
#endif

#ifdef __cplusplus
# define VERDICT_EXTERN_C extern "C"
#endif

#if defined(VERDICT_SHARED_LIB)
# ifdef verdict_EXPORTS
#  define C_FUNC_DEF VERDICT_EXTERN_C  VERDICT_ABI_EXPORT
# else
#  define C_FUNC_DEF VERDICT_EXTERN_C  VERDICT_ABI_IMPORT
# endif
#else
# define C_FUNC_DEF VERDICT_EXTERN_C
#endif


/* typedef for the user if they want to use
 *    function pointers */
#ifdef __cplusplus
extern "C" {
#endif
  typedef double(*VerdictFunction)(int, double[][3]);
  typedef int(*ComputeNormal)(double point[3], double normal[3]); 
#ifdef __cplusplus
}
#endif


/**\brief A <em>struct</em> to hold values computed by \ref v_hex_quality.
  *
  * HexMetricVals is used just as QuadMetricVals.
  * For an example, see the \ref UsingQuadMetricVals.  
  */
struct HexMetricVals
{
  /** \sa v_hex_edge_ratio */
  double edge_ratio ;  
  /** \sa v_hex_max_edge_ratio */
  double max_edge_ratio ;  
  /** \sa v_hex_skew */
  double skew ;
  /** \sa v_hex_taper */
  double taper ;
  /** \sa v_hex_volume */
  double volume ;
  /** \sa v_hex_stretch */
  double stretch ;
  /** \sa v_hex_diagonal */
  double diagonal ;
  /** \sa v_hex_dimension */
  double dimension ;
  /** \sa v_hex_oddy */
  double oddy ;
  /** \sa v_hex_med_aspect_frobenius */
  double med_aspect_frobenius ;
  /** \sa v_hex_max_aspect_frobenius */
  double max_aspect_frobenius ;
  /** \sa v_hex_condition */
  double condition ;
  /** \sa v_hex_jacobian */
  double jacobian ;
  /** \sa v_hex_scaled_jacobian */
  double scaled_jacobian ;
  /** \sa v_hex_shear */
  double shear ;
  /** \sa v_hex_shape */
  double shape ;
  /** \sa v_hex_relative_size */
  double relative_size_squared;
  /** \sa v_hex_shape_and_size */
  double shape_and_size ; 
  /** \sa v_hex_shear_and_size */
  double shear_and_size ; 
  /** \sa v_hex_distortion */
  double distortion; 
};

/**\brief A <em>struct</em> to hold values computed by \ref v_edge_quality.
  *
  * EdgeMetricVals is used just as QuadMetricVals.
  * For an example, see the \ref UsingQuadMetricVals.  
  */
struct EdgeMetricVals
{
  double length ; 
};


/**\brief A <em>struct</em> to hold values computed by \ref v_knife_quality.
  *
  * KnifeMetricVals is used just as QuadMetricVals.
  * For an example, see the \ref UsingQuadMetricVals.  
  */
struct KnifeMetricVals
{
  double volume ; 
};

/**\brief A <em>struct</em> to hold values computed by \ref v_quad_quality.
  *
  * \section UsingQuadMetricVals Example Usage of the QuadMetricVals Structure
  *
  * The following is an example of how this struct is used with Verdict.
  *
  * Example: \code
  * QuadMetricVals quad_metrics = {0};
  * unsigned long metrics_flag = 0;
  * metrics_flag += V_QUAD_SHAPE;
  * metrics_flag += V_QUAD_DISTORTION;
  * metrics_flag += V_QUAD_AREA;   
  * double quad_nodes[4][3];
  * get_quad_nodes( quad_nodes );  //some user-defined function to load 
  *                                //xyz coordinate info. into array  
  * v_quad_quality( 4, quad_nodes, metrics_flag, quad_metrics );
  * double my_shape      = quad_metrics.shape; 
  * double my_distortion = quad_metrics.distortion; 
  * double my_area       = quad_metrics.area;  \endcode
  *  
  */
struct QuadMetricVals
{
  /** \sa v_quad_edge_ratio function */
  double edge_ratio ;
  /** \sa v_quad_max_edge_ratio function */
  double max_edge_ratio ;
  /** \sa v_quad_aspect_ratio function */
  double aspect_ratio ;
  /** \sa v_quad_radius_ratio function */
  double radius_ratio ;
  /** \sa v_quad_med_aspect_frobenius function */
  double med_aspect_frobenius ;
  /** \sa v_quad_max_aspect_frobenius function */
  double max_aspect_frobenius ;
  /** \sa v_quad_skew function */
  double skew ;
  /** \sa v_quad_taper function */
  double taper ;
  /** \sa v_quad_warpage function */
  double warpage ;
  /** \sa v_quad_area function */
  double area ;
  /** \sa v_quad_stretch function */
  double stretch ;
  /** \sa v_quad_smallest_angle function */
  double minimum_angle ;
  /** \sa v_quad_largest_angle function */
  double maximum_angle ;
  /** \sa v_quad_oddy function */
  double oddy ;
  /** \sa v_quad_condition function */
  double condition ;
  /** \sa v_quad_jacobian function */
  double jacobian ;
  /** \sa v_quad_scaled_jacobian function */
  double scaled_jacobian ;
  /** \sa v_quad_shear function */
  double shear ;
  /** \sa v_quad_shape function */
  double shape ;
  /** \sa v_quad_relative_size_squared function */
  double relative_size_squared ;
  /** \sa v_quad_shape_and_size function */
  double shape_and_size ; 
  /** \sa v_quad_shear_and_size function */
  double shear_and_size ;
  /** \sa v_quad_distortion function */
  double distortion; 
};

/**\brief A <em>struct</em> to hold values computed by \ref v_pyramid_quality.
  *
  * PyramidMetricVals is used just as QuadMetricVals.
  * For an example, see the \ref UsingQuadMetricVals.  
  */
struct PyramidMetricVals
{
  double volume ; 
};
   
/**\brief A <em>struct</em> to hold values computed by \ref v_wedge_quality.
  *
  * WedgeMetricVals is used just as QuadMetricVals.
  * For an example, see the \ref UsingQuadMetricVals.  
  */
struct WedgeMetricVals
{
  /** \sa v_wedge_volume */
  double volume ;
  /** \sa v_wedge_edge_ratio */
  double edge_ratio ;
  /** \sa v_wedge_max_aspect_frobenius */
  double max_aspect_frobenius;
  /** \sa v_wedge_mean_aspect_frobenius */
  double mean_aspect_frobenius;
  /** \sa v_wedge_jacobian */
  double jacobian;
  /** \sa v_wedge_distortion */
  double distortion;
  /** \sa v_wedge_max_stretch */
  double max_stretch;
  /** \sa v_wedge_scaled_jacobian */
  double scaled_jacobian;
  /** \sa v_wedge_shape */
  double shape;
  /** \sa v_wedge_condition */
  double condition;
};
     
/**\brief A <em>struct</em> to hold values computed by \ref v_tet_quality.
  *
  * TetMetricVals is used just as QuadMetricVals.
  * For an example, see the \ref UsingQuadMetricVals.  
  */
struct TetMetricVals
{
  /** \sa v_tet_edge_ratio*/
  double edge_ratio;
  /** \sa v_tet_radius_ratio*/
  double radius_ratio;
  /** \sa v_tet_aspect_beta*/
  double aspect_beta;
  /** \sa v_tet_aspect_ratio */
  double aspect_ratio ;
  /** \sa v_tet_aspect_gamma */
  double aspect_gamma ;
  /** \sa v_tet_aspect_frobenius */
  double aspect_frobenius ;
  /** \sa v_tet_minimum_angle */
  double minimum_angle ;
  /** \sa v_tet_collapse_ratio*/
  double collapse_ratio;
  /** \sa v_tet_volume */
  double volume ;
  /** \sa v_tet_condition */
  double condition ;
  /** \sa v_tet_jacobian */
  double jacobian ;
  /** \sa v_tet_scaled_jacobian */
  double scaled_jacobian ;
  /** \sa v_tet_shape */
  double shape ;
  /** \sa v_tet_relative_size */
  double relative_size_squared ;
  /** \sa v_tet_shape_and_size*/
  double shape_and_size ; 
  /** \sa v_tet_distortion */
  double distortion; 
  /** \sa v_tet_equivolume_skew */
  double equivolume_skew;
  /** \sa v_tet_squish_index */
  double squish_index;

};

/**\brief A <em>struct</em> to hold values computed by \ref v_tri_quality.
  *
  * TriMetricVals is used just as QuadMetricVals.
  * For an example, see the \ref UsingQuadMetricVals.  
  */
struct TriMetricVals
{
  /** \sa v_tri_edge_ratio */
  double edge_ratio ;
  /** \sa v_tri_aspect_ratio */
  double aspect_ratio ;
  /** \sa v_tri_radius_ratio */
  double radius_ratio ;
  /** \sa v_tri_aspect_frobenius */
  double aspect_frobenius ;
  /** \sa v_tri_area*/
  double area ;
  /** \sa v_tri_minimum_angle*/
  double minimum_angle ;
  /** \sa v_tri_maximum_angle */
  double maximum_angle ;
  /** \sa v_tri_condition */
  double condition ;
  /** \sa v_tri_scaled_jacobian */
  double scaled_jacobian ;
  /** \sa v_tri_shape */
  double shape ;
  /** \sa v_tri_relative_size_squared */
  double relative_size_squared ;
  /** \sa v_tri_shape_and_size */
  double shape_and_size ; 
  /** \sa v_tri_distortion */
  double distortion; 
};



/* definition of bit fields to determine which metrics to calculate */

//! \name Atomic hex quality flags
//! 
//@{

/*!\hideinitializer \brief Request that the maximum edge ratio be computed. \sa v_hex_max_edge_ratio */
#define V_HEX_MAX_EDGE_RATIO         1
/*!\hideinitializer \brief Request that skew be computed. \sa v_hex_skew */
#define V_HEX_SKEW                   2
/*!\hideinitializer \brief Request that taper be computed. \sa v_hex_taper */
#define V_HEX_TAPER                  4
/*!\hideinitializer \brief Request that volume be computed. \sa v_hex_volume */
#define V_HEX_VOLUME                 8
/*!\hideinitializer \brief Request that stretch be computed. \sa v_hex_stretch */
#define V_HEX_STRETCH                16
/*!\hideinitializer \brief Request that the diagonal be computed. \sa v_hex_diagonal */
#define V_HEX_DIAGONAL               32
/*!\hideinitializer \brief Request that the dimension be computed. \sa v_hex_dimension */
#define V_HEX_DIMENSION              64
/*!\hideinitializer \brief Request that the Oddy quality be computed. \sa v_hex_oddy */
#define V_HEX_ODDY                   128
/*!\hideinitializer \brief Request that maximum Frobenius aspect be computed. \sa v_hex_condition */
#define V_HEX_MAX_ASPECT_FROBENIUS   256
/*!\hideinitializer \brief Request that the condition be computed. \sa v_hex_condition */
#define V_HEX_CONDITION              256
/*!\hideinitializer \brief Request that the Jacobian be computed. \sa v_hex_jacobian */
#define V_HEX_JACOBIAN               512
/*!\hideinitializer \brief Request that the scaled Jacobian be computed. \sa v_hex_scaled_jacobian */
#define V_HEX_SCALED_JACOBIAN        1024
/*!\hideinitializer \brief Request that shear be computed. \sa v_hex_shear */
#define V_HEX_SHEAR                  2048
/*!\hideinitializer \brief Request that shape be computed. \sa v_hex_shape */
#define V_HEX_SHAPE                  4096
/*!\hideinitializer \brief Request that the square of the relative size be computed. \sa v_hex_relative_size_squared */
#define V_HEX_RELATIVE_SIZE_SQUARED  8192
/*!\hideinitializer \brief Request that the product of shape and size be computed. \sa v_hex_shape_and_size */
#define V_HEX_SHAPE_AND_SIZE         16384
/*!\hideinitializer \brief Request that the product of shear and size be computed. \sa v_hex_shear_and_size */
#define V_HEX_SHEAR_AND_SIZE         32768
/*!\hideinitializer \brief Request that distortion be computed. \sa v_hex_distortion */
#define V_HEX_DISTORTION             65536
/*!\hideinitializer \brief Request that the edge ratio be computed. \sa v_hex_edge_ratio */
#define V_HEX_EDGE_RATIO             131072
/*!\hideinitializer \brief Request that average Frobenius aspect be computed. \sa v_hex_med_aspect_frobenius */
#define V_HEX_MED_ASPECT_FROBENIUS   262144
//!\name Composite hex quality flags
//! These flags are bitwise combinations of the atomic flags above.
//@{
/*!\hideinitializer \brief Request that all hex metrics be computed. */
#define V_HEX_ALL                    524287
/*!\hideinitializer \brief Request the traditional hex qualities be computed.
 *                  
 * This includes
 * \ref V_HEX_MAX_EDGE_RATIO, \ref V_HEX_SKEW,     \ref V_HEX_TAPER
 * \ref V_HEX_STRETCH,        \ref V_HEX_DIAGONAL, \ref V_HEX_ODDY,
 * \ref V_HEX_CONDITION,      \ref V_HEX_JACOBIAN, \ref V_HEX_SCALED_JACOBIAN, and
 * \ref V_HEX_DIMENSION.
 */
#define V_HEX_TRADITIONAL \
  V_HEX_MAX_EDGE_RATIO + \
  V_HEX_SKEW            + \
  V_HEX_TAPER           + \
  V_HEX_STRETCH         + \
  V_HEX_DIAGONAL        + \
  V_HEX_ODDY            + \
  V_HEX_CONDITION       + \
  V_HEX_JACOBIAN        + \
  V_HEX_SCALED_JACOBIAN + \
  V_HEX_DIMENSION
/*!\hideinitializer \brief Request hex qualities used to diagnose mesh or solver problems.
 *
 * This is currently a synonym for \ref V_HEX_VOLUME but may include more qualities in the future.
 */
#define V_HEX_DIAGNOSTIC V_HEX_VOLUME
/*!\hideinitializer \brief Request hex qualities that have an algebraic expression be computed.
 *
 * This includes
 * \ref V_HEX_SHAPE, \ref V_HEX_SHEAR, \ref V_HEX_RELATIVE_SIZE_SQUARED,
 * \ref V_HEX_SHAPE_AND_SIZE, and \ref V_HEX_SHEAR_AND_SIZE.
 */
#define V_HEX_ALGEBRAIC \
  V_HEX_SHAPE                  + \
  V_HEX_SHEAR                  + \
  V_HEX_RELATIVE_SIZE_SQUARED  + \
  V_HEX_SHAPE_AND_SIZE         + \
  V_HEX_SHEAR_AND_SIZE
/*!\hideinitializer \brief Request hex qualities for Mr. Robinson.
 */
#define V_HEX_ROBINSON \
  V_HEX_SKEW + \
  V_HEX_TAPER
//@}
//@}

//! \name Atomic tetrahedral quality flags
//! 
//@{
/*!\hideinitializer \brief Request that the radius ratio be computed. \sa v_tet_radius_ratio */
#define V_TET_RADIUS_RATIO           1
/*!\hideinitializer \brief Request that the aspect ratio beta be computed. \sa v_tet_aspect_beta */
#define V_TET_ASPECT_BETA            2
/*!\hideinitializer \brief Request that the aspect ratio gamma be computed. \sa v_tet_aspect_gamma */
#define V_TET_ASPECT_GAMMA           4
/*!\hideinitializer \brief Request that the volume be computed. \sa v_tet_volume */
#define V_TET_VOLUME                 8
/*!\hideinitializer \brief Request that the condition be computed. \sa v_tet_condition */
#define V_TET_CONDITION              16
/*!\hideinitializer \brief Request that the Jacobian be computed. \sa v_tet_jacobian */
#define V_TET_JACOBIAN               32
/*!\hideinitializer \brief Request that the scaled Jacobian be computed. \sa v_tet_scaled_jacobian */
#define V_TET_SCALED_JACOBIAN        64
/*!\hideinitializer \brief Request that the shape be computed. \sa v_tet_shape */
#define V_TET_SHAPE                  128
/*!\hideinitializer \brief Request that the square of the relative size be computed. \sa v_tet_relative_size_squared */
#define V_TET_RELATIVE_SIZE_SQUARED  256
/*!\hideinitializer \brief Request that the product of shape and size be computed. \sa v_tet_shape_and_size */
#define V_TET_SHAPE_AND_SIZE         512
/*!\hideinitializer \brief Request that the distortion be computed. \sa v_tet_distortion */
#define V_TET_DISTORTION             1024
/*!\hideinitializer \brief Request that the ratio of edge lengths be computed. \sa v_tet_edge_ratio */
#define V_TET_EDGE_RATIO             2048
/*!\hideinitializer \brief Request that the aspect ratio be computed. \sa v_tet_aspect_ratio */
#define V_TET_ASPECT_RATIO           4096
/*!\hideinitializer \brief Request that the Frobenius aspect be computed. \sa v_tet_aspect_frobenius */
#define V_TET_ASPECT_FROBENIUS       8192
/*!\hideinitializer \brief Request that the minimum dihedral angle be computed. \sa v_tet_minimum_angle */
#define V_TET_MINIMUM_ANGLE          16384
/*!\hideinitializer \brief Request that the collapse ratio be computed. \sa v_tet_collapse_ratio */
#define V_TET_COLLAPSE_RATIO         32768
/*!\hideinitializer \brief Request that the equivolume skew as defined by Fluent be computed. \sa v_tet_equivolume_skew */
#define V_TET_EQUIVOLUME_SKEW        65536
/*!\hideinitializer \brief Request that the squish index as defined by Fluent be computed. \sa v_tet_squish_index */
#define V_TET_SQUISH_INDEX           131072

//! Composite tetrahedral quality flags
//! These flags are bitwise combinations of the atomic flags above.
//@{
/*!\hideinitializer \brief Request that the all tetrahedral qualities be computed. */
#define V_TET_ALL                    262143
/*!\hideinitializer \brief Request that the tradtional tetrahedral qualities be computed.
 *
 * This includes
 * \ref V_TET_ASPECT_BETA, \ref V_TET_ASPECT_GAMMA, \ref V_TET_CONDITION,
 * \ref V_TET_JACOBIAN, and \ref V_TET_SCALED_JACOBIAN.
 */
#define V_TET_TRADITIONAL            V_TET_ASPECT_BETA + \
                                     V_TET_ASPECT_GAMMA + \
                                     V_TET_CONDITION + \
                                     V_TET_JACOBIAN + \
                                     V_TET_SCALED_JACOBIAN  
/*!\hideinitializer \brief Request hex qualities used to diagnose mesh or solver problems.
 *
 * This is currently a synonym for \ref V_TET_VOLUME but may include more qualities in the future.
 */
#define V_TET_DIAGNOSTIC             V_TET_VOLUME
/*!\hideinitializer \brief Request hex qualities that have an algebraic expression be computed.
 *
 * This includes
 * \ref V_TET_SHAPE, \ref V_TET_RELATIVE_SIZE_SQUARED, and \ref V_TET_SHAPE_AND_SIZE.
 */
#define V_TET_ALGEBRAIC              V_TET_SHAPE                  + \
                                     V_TET_RELATIVE_SIZE_SQUARED  + \
                                     V_TET_SHAPE_AND_SIZE
//@}
//@}

 
//! \name Pyramid bit fields
//! 
//@{
/*!\hideinitializer \brief */
#define V_PYRAMID_VOLUME             1
/*!\hideinitializer \brief */
#define V_PYRAMID_ALL \
  V_PYRAMID_VOLUME
//@}

//! \name Wedge bit fields
//! 
//@{
/*!\hideinitializer \brief */
#define V_WEDGE_VOLUME                 1
#define V_WEDGE_EDGE_RATIO             2
#define V_WEDGE_MAX_ASPECT_FROBENIUS   4
#define V_WEDGE_MEAN_ASPECT_FROBENIUS  8
#define V_WEDGE_JACOBIAN               16
#define V_WEDGE_SCALED_JACOBIAN        32
#define V_WEDGE_DISTORTION             64
#define V_WEDGE_MAX_STRETCH            128
#define V_WEDGE_SHAPE                  256
#define V_WEDGE_CONDITION              512
/*!\hideinitializer \brief */
#define V_WEDGE_ALL \
  V_WEDGE_VOLUME
//@}
 
//! \name Knife bit fields
//! 
//@{
/*!\hideinitializer \brief */
#define V_KNIFE_VOLUME               1
/*!\hideinitializer \brief */
#define V_KNIFE_ALL \
  V_KNIFE_VOLUME
//@}
 
//! \name Quad bit fields
//! 
//@{
/*!\hideinitializer \brief */
#define V_QUAD_MAX_EDGE_RATIO        1
/*!\hideinitializer \brief */
#define V_QUAD_SKEW                  2
/*!\hideinitializer \brief */
#define V_QUAD_TAPER                 4
/*!\hideinitializer \brief */
#define V_QUAD_WARPAGE               8
/*!\hideinitializer \brief */
#define V_QUAD_AREA                  16
/*!\hideinitializer \brief */
#define V_QUAD_STRETCH               32
/*!\hideinitializer \brief */
#define V_QUAD_MINIMUM_ANGLE         64
/*!\hideinitializer \brief */
#define V_QUAD_MAXIMUM_ANGLE         128
/*!\hideinitializer \brief */
#define V_QUAD_ODDY                  256
/*!\hideinitializer \brief */
#define V_QUAD_CONDITION             512
/*!\hideinitializer \brief */
#define V_QUAD_JACOBIAN              1024
/*!\hideinitializer \brief */
#define V_QUAD_SCALED_JACOBIAN       2048
/*!\hideinitializer \brief */
#define V_QUAD_SHEAR                 4096
/*!\hideinitializer \brief */
#define V_QUAD_SHAPE                 8192
/*!\hideinitializer \brief */
#define V_QUAD_RELATIVE_SIZE_SQUARED 16384
/*!\hideinitializer \brief */
#define V_QUAD_SHAPE_AND_SIZE        32768
/*!\hideinitializer \brief */
#define V_QUAD_SHEAR_AND_SIZE        65536
/*!\hideinitializer \brief */
#define V_QUAD_DISTORTION            131072
/*!\hideinitializer \brief */
#define V_QUAD_EDGE_RATIO            262144
/*!\hideinitializer \brief */
#define V_QUAD_ASPECT_RATIO          524288
/*!\hideinitializer \brief */
#define V_QUAD_RADIUS_RATIO          1048576
/*!\hideinitializer \brief */
#define V_QUAD_MED_ASPECT_FROBENIUS  2097152
/*!\hideinitializer \brief */
#define V_QUAD_MAX_ASPECT_FROBENIUS  4194304
/*!\hideinitializer \brief */
#define V_QUAD_ALL                   8388607
/*!\hideinitializer \brief */
#define V_QUAD_TRADITIONAL \
  V_QUAD_MAX_EDGE_RATIO + \
  V_QUAD_SKEW            + \
  V_QUAD_TAPER           + \
  V_QUAD_WARPAGE         + \
  V_QUAD_STRETCH         + \
  V_QUAD_MINIMUM_ANGLE   + \
  V_QUAD_MAXIMUM_ANGLE   + \
  V_QUAD_ODDY            + \
  V_QUAD_CONDITION       + \
  V_QUAD_JACOBIAN        + \
  V_QUAD_SCALED_JACOBIAN 
/*!\hideinitializer \brief */
#define V_QUAD_DIAGNOSTIC \
  V_QUAD_AREA
/*!\hideinitializer \brief */
#define V_QUAD_ALGEBRAIC \
  V_QUAD_SHEAR                 + \
  V_QUAD_SHAPE                 + \
  V_QUAD_RELATIVE_SIZE_SQUARED + \
  V_QUAD_SHAPE_AND_SIZE     
/*!\hideinitializer \brief */
#define V_QUAD_ROBINSON \
  V_QUAD_MAX_EDGE_RATIO + \
  V_QUAD_SKEW   + \
  V_QUAD_TAPER
//@}


//! \name Tri bit fields
//! 
//@{
/*!\hideinitializer \brief */
#define V_TRI_ASPECT_FROBENIUS       1
/*!\hideinitializer \brief */
#define V_TRI_AREA                   2
/*!\hideinitializer \brief */
#define V_TRI_MINIMUM_ANGLE          4
/*!\hideinitializer \brief */
#define V_TRI_MAXIMUM_ANGLE          8
/*!\hideinitializer \brief */
#define V_TRI_CONDITION              16
/*!\hideinitializer \brief */
#define V_TRI_SCALED_JACOBIAN        32
/*!\hideinitializer \brief */
#define V_TRI_SHAPE                  64
/*!\hideinitializer \brief */
#define V_TRI_RELATIVE_SIZE_SQUARED  128
/*!\hideinitializer \brief */
#define V_TRI_SHAPE_AND_SIZE         256
/*!\hideinitializer \brief */
#define V_TRI_DISTORTION             512
/*!\hideinitializer \brief */
#define V_TRI_RADIUS_RATIO           1024
/*!\hideinitializer \brief */
#define V_TRI_EDGE_RATIO             2048
/*!\hideinitializer \brief */
#define V_TRI_ALL                    4095
/*!\hideinitializer \brief */
#define V_TRI_TRADITIONAL \
  V_TRI_ASPECT_FROBENIUS + \
  V_TRI_MINIMUM_ANGLE + \
  V_TRI_MAXIMUM_ANGLE + \
  V_TRI_CONDITION + \
  V_TRI_SCALED_JACOBIAN 
/*!\hideinitializer \brief */
#define V_TRI_DIAGNOSTIC \
  V_TRI_AREA
/*!\hideinitializer \brief */
#define V_TRI_ALGEBRAIC \
  V_TRI_SHAPE + \
  V_TRI_SHAPE_AND_SIZE + \
  V_TRI_RELATIVE_SIZE_SQUARED
//@}
 
//! \name Tri bit fields
//! 
//@{
/*!\hideinitializer \brief */
#define V_EDGE_LENGTH                1
/*!\hideinitializer \brief */
#define V_EDGE_ALL \
  V_EDGE_LENGTH
//@}

                                     
/*! \mainpage
  Verdict is a library used to calculate metrics on the following type of elements:

    \li Hexahedra
    \li Tetrahedra
    \li Pyramid 
    \li Wedge 
    \li Knife 
    \li Quadrilateral
    \li Triangle
    \li Edge 

  Verdict calculates individual or multiple metrics on a single elment.  
  The v_*_quality(...) functions allow for efficient calculations of 
  multiple metrics on a single element.  Individual metrics may be 
  calculated on a single element as well. 

  \section GetVerdict Obtaining, Configuring, Building, and Installing Verdict

  Since your are reading reference documentation generated from the source code,
  you ostensibly already have Verdict.
  Instructions for this are on a separate page: \ref ObtainConfigureBuildInstall .

  \section UsingVerdict Using Verdict

  The v_*_quality functions take the following parameters: 

  \param num_nodes Number of nodes in the element. 
  \param coordinates 2D array containing x,y,z coordinate data of the nodes.
  \param metrics_request_flag Bitfield to define which metrics to calculate.
  \param metric_vals Struct to hold the metric calculated values. 

  All other functions take these parameters below and return the calculated
  metric value.

  \param num_nodes Number of nodes in the element. 
  \param coordinates 2D array containing x,y,z coordinate data of the nodes.

  
  \par Setting the metrics_request_flag: 
  In order to use v_*_quality functions you must know how to set the bitfield argument 
  correctly.  To calculate aspect ratio, condition number, shape and shear metrics on a triangle, set
  the "metrics_request_flag" like so: 

  \code
  unsigned int metrics_request_flag = 0;
  metrics_request_flag += V_TRI_ASPECT_FROBENIUS;  
  metrics_request_flag += V_TRI_CONDITION;
  metrics_request_flag += V_TRI_SHAPE;
  metrics_request_flag += V_TRI_SHEAR;
  \endcode 

  The bitwise field can also be set for many metrics at once using summary tags such as \ref V_HEX_ALL,
  \ref V_HEX_DIAGNOSTIC, or \ref V_TRI_ALGEBRAIC.

  Below is an example of how use Verdict's functions:

    
    Example: \code
    QuadMetricVals quad_metrics = {0};
    unsigned long metrics_flag = 0;
    metrics_flag += V_QUAD_SHAPE;
    metrics_flag += V_QUAD_DISTORTION;
    metrics_flag += V_QUAD_AREA;
    double quad_nodes[4][3];
 
    //node 1
    quad_node[0][0] = 0;  //x
    quad_node[0][1] = 0;  //y
    quad_node[0][2] = 0;  //z

    //node 2
    quad_node[1][0] = 1; 
    quad_node[1][1] = 0.1;
    quad_node[1][2] = 0.1;

    //node 3
    quad_node[2][0] = 0.9; 
    quad_node[2][1] = 0.9;
    quad_node[2][2] = -0.1;

    //node 4
    quad_node[3][0] = -0.05; 
    quad_node[3][1] = 1;
    quad_node[3][2] = 0;

    //calculate multiple metrics with one call
    v_quad_quality( 4, quad_nodes, metrics_flag, quad_metrics );
    double my_shape      = quad_metrics.shape; 
    double my_distortion = quad_metrics.distortion; 
    double my_area       = quad_metrics.area;  
  
    //calculate an individual metric 
    double my_relative_size = v_quad_relative_size( 4, quad_nodes );
    \endcode

*/

/*!\page ObtainConfigureBuildInstall Obtain, Configure, Build, and Install Verdict

  \section ObtainVerdict Obtaining the Verdict Source Code

  The verdict source code repository is now maintained by <a href="http://www.kitware.com/">Kitware</a>.
  You can check out the source with \code
    cvs -d :pserver:anonymous@public.kitware.com:/cvsroot/Verdict login
    cvs -d :pserver:anonymous@public.kitware.com:/cvsroot/Verdict -z3 co Verdict
  \endcode
  When asked for a password, enter "verdict".

  \section ConfiguringVerdict Configuring Verdict

  Verdict uses <a href="http://www.cmake.org/">CMake</a> to create project files.
  To build Verdict from source, you will need to obtain CMake.
  
  We strongly suggest that you build Verdict in a separate directory tree from the source code.
  Life is just too short to explain why; if you're curious, search the CMake mailing list.
  To make the instructions clear, we'll assume that you have the Verdict source code in \c /tmp/Verdict.
  Configuring Verdict is then as simple as \code
    mkdir /tmp/VerdictBuild
    cd /tmp/VerdictBuild
    cmake ../Verdict
  \endcode
  At this point, you may wish to edit <tt>/tmp/VerdictBuild/CMakeCache.txt</tt> to change settings
  from their default values.
  
  If you are going to include Verdict inside another library, you might want to read
  how to use \ref VerdictAsASubProject.

  \section BuildingAndInstallingVerdict Building and Installing Verdict

  Assuming you are using CMake's Makefile generator, building and installing Verdict
  is accomplished with \code
    make
    make install
  \endcode
  By default, Verdict will be installed in \c /usr/local.
  If you wish to change the location, edit your <tt>CMakeCache.txt</tt> file so that
  \c CMAKE_INSTALL_PREFIX contains a different directory and re-run \c cmake.
 */

    //! Calculates quality metrics for hexahedral elements.
    C_FUNC_DEF void v_hex_quality( int num_nodes, double coordinates[][3], 
        unsigned int metrics_request_flag, struct HexMetricVals *metric_vals ); 
    
    //! Calculates quality metrics for tetrahedral elements.
    C_FUNC_DEF void v_tet_quality( int num_nodes, double coordinates[][3], 
        unsigned int metrics_request_flag, struct TetMetricVals *metric_vals ); 
    
    //! Calculates quality metrics for pyramid elements.
    C_FUNC_DEF void v_pyramid_quality( int num_nodes, double coordinates[][3], 
        unsigned int metrics_request_flag, struct PyramidMetricVals *metric_vals ); 

    //! Calculates quality metrics for wedge elements.
    C_FUNC_DEF void v_wedge_quality( int num_nodes, double coordinates[][3], 
        unsigned int metrics_request_flag, struct WedgeMetricVals *metric_vals ); 

    //! Calculates quality metrics for knife elements.
    C_FUNC_DEF void v_knife_quality( int num_nodes, double coordinates[][3], 
        unsigned int metrics_request_flag, struct KnifeMetricVals *metric_vals ); 

    //! Calculates quality metrics for quadralateral elements.
    C_FUNC_DEF void v_quad_quality( int num_nodes, double coordinates[][3], 
        unsigned int metrics_request_flag, struct QuadMetricVals *metric_vals ); 

    //! Calculates quality metrics for triangle elements.
    C_FUNC_DEF void v_tri_quality( int num_nodes, double coordinates[][3], 
        unsigned int metrics_request_flag, struct TriMetricVals *metric_vals );

    //! Calculates quality metrics for edge elements.
    C_FUNC_DEF void v_edge_quality( int num_nodes, double coordinates[][3], 
        unsigned int metrics_request_flag, struct EdgeMetricVals *metric_vals ); 



/* individual quality functions for hex elements */

    //! Sets average size (volume) of hex, needed for v_hex_relative_size(...)
    C_FUNC_DEF void v_set_hex_size( double size );

    //! Calculates hex edge ratio metric.
    /**  Hmax / Hmin where Hmax and Hmin are respectively the maximum and the
         minimum edge lengths */ 
    C_FUNC_DEF double v_hex_edge_ratio( int num_nodes, double coordinates[][3] );

    //! Calculates hex maximum of edge ratio
    /**Maximum edge length ratio at hex center.
      Reference --- L.M. Taylor, and D.P. Flanagan, Pronto3D - A Three Dimensional Transient
         Solid Dynamics Program, SAND87-1912, Sandia National Laboratories, 1989. */
    C_FUNC_DEF double v_hex_max_edge_ratio( int num_nodes, double coordinates[][3] );

    //! Calculates hex skew metric. 
    /** Maximum |cos A| where A is the angle between edges at hex center.   
      Reference --- L.M. Taylor, and D.P. Flanagan, Pronto3D - A Three Dimensional Transient
         Solid Dynamics Program, SAND87-1912, Sandia National Laboratories, 1989. */
    C_FUNC_DEF double v_hex_skew( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex taper metric 
    /**  Maximum ratio of lengths derived from opposite edges. 
      Reference --- L.M. Taylor, and D.P. Flanagan, Pronto3D - A Three Dimensional Transient
         Solid Dynamics Program, SAND87-1912, Sandia National Laboratories, 1989. */
    C_FUNC_DEF double v_hex_taper( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex volume 
    /**  Jacobian at hex center. 
      Reference --- L.M. Taylor, and D.P. Flanagan, Pronto3D - A Three Dimensional Transient
         Solid Dynamics Program, SAND87-1912, Sandia National Laboratories, 1989. */
    C_FUNC_DEF double v_hex_volume( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex stretch metric   
    /**  Sqrt(3) * minimum edge length / maximum diagonal length. 
      Reference --- FIMESH code */ 
    C_FUNC_DEF double v_hex_stretch( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex diagonal metric   
    /** Minimum diagonal length / maximum diagonal length. 
      Reference --- Unknown */ 
    C_FUNC_DEF double v_hex_diagonal( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex dimension metric   
    /** Pronto-specific characteristic length for stable time step calculation.  
        Char_length = Volume / 2 grad Volume. 
      Reference --- L.M. Taylor, and D.P. Flanagan, Pronto3D - A Three Dimensional Transient
         Solid Dynamics Program, SAND87-1912, Sandia National Laboratories, 1989. */
    C_FUNC_DEF double v_hex_dimension( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex oddy metric   
    C_FUNC_DEF double v_hex_oddy( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex condition metric   
    /** Average Frobenius condition number of the Jacobian matrix at 8 corners. */ 
    C_FUNC_DEF double v_hex_med_aspect_frobenius( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex condition metric   
    /** Maximum Frobenius condition number of the Jacobian matrix at 8 corners.
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities, 
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */ 
    C_FUNC_DEF double v_hex_max_aspect_frobenius( int num_nodes, double coordinates[][3] ); 
    //! Calculates hex condition metric. This is a synonym for \ref v_hex_max_aspect_frobenius.
    C_FUNC_DEF double v_hex_condition( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex jacobian metric   
    /** Minimum pointwise volume of local map at 8 corners & center of hex. 
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities, 
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */ 
    C_FUNC_DEF double v_hex_jacobian( int num_nodes, double coordinates[][3] ); 
    
    //! Calculates hex scaled jacobian metric   
    /** Minimum Jacobian divided by the lengths of the 3 edge vectors. 
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities, 
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */ 
    C_FUNC_DEF double v_hex_scaled_jacobian( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex shear metric   
    /** 3/Mean Ratio of Jacobian Skew matrix.
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication.  */
    C_FUNC_DEF double v_hex_shear( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex shape metric.
    /** 3/Mean Ratio of weighted Jacobian matrix. 
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication.  */
    C_FUNC_DEF double v_hex_shape( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex relative size metric. 
    /** 3/Mean Ratio of weighted Jacobian matrix.
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication.  */
    C_FUNC_DEF double v_hex_relative_size_squared( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex shape-size metric.
    /** Product of Shape and Relative Size.
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication.  */
    C_FUNC_DEF double v_hex_shape_and_size( int num_nodes, double coordinates[][3] ); 

    //! Calculates hex shear-size metric   
    /** Product of Shear and Relative Size.
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication.  */
    C_FUNC_DEF double v_hex_shear_and_size( int num_nodes, double coordinates[][3] );

    //! Calculates hex distortion metric   
    /** {min(|J|)/actual volume}*parent volume, parent volume = 8 for hex.
       Reference --- SDRC/IDEAS Simulation: Finite Element Modeling--User's Guide */
    C_FUNC_DEF double v_hex_distortion( int num_nodes, double coordinates[][3] );

/* individual quality functions for tet elements */

    //! Sets average size (volume) of tet, needed for v_tet_relative_size(...)
    C_FUNC_DEF void v_set_tet_size( double size );

    //! Calculates tet edge ratio metric.
    /**  Hmax / Hmin where Hmax and Hmin are respectively the maximum and the
       minimum edge lengths */ 
    C_FUNC_DEF double v_tet_edge_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet radius ratio metric.
    /** CR / (3.0 * IR)  where CR = circumsphere radius, IR = inscribed sphere radius.
        Reference ---  V. N. Parthasarathy et al, A comparison of tetrahedron 
        quality measures, Finite Elem. Anal. Des., Vol 15(1993), 255-261. */ 
    C_FUNC_DEF double v_tet_radius_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates the radius ratio metric of a positively oriented tet.
    /** CR / (3.0 * IR)  where CR = circumsphere radius, IR = inscribed sphere radius
        if the element is positively-oriented.
        Reference ---  V. N. Parthasarathy et al, A comparison of tetrahedron 
        quality measures, Finite Elem. Anal. Des., Vol 15(1993), 255-261. */ 
    C_FUNC_DEF double v_tet_aspect_beta( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet aspect ratio metric.
    /**  Hmax / (2 sqrt(6) r) where Hmax and r respectively denote the greatest edge 
       length and the inradius of the tetrahedron
       Reference ---  P. Frey and P.-L. George, Meshing, Hermes (2000). */ 
    C_FUNC_DEF double v_tet_aspect_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet aspect gamma metric.
    /**  Srms**3 / (8.479670*V) where Srms = sqrt(Sum(Si**2)/6), Si = edge length. 
       Reference ---  V. N. Parthasarathy et al, A comparison of tetrahedron 
       quality measures, Finite Elem. Anal. Des., Vol 15(1993), 255-261. */ 
    C_FUNC_DEF double v_tet_aspect_gamma( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet aspect frobenius metric.
    /** Frobenius condition number when the reference element is regular
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */
    C_FUNC_DEF double v_tet_aspect_frobenius( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet minimum dihedral angle.
    /** Minimum (nonoriented) dihedral angle of a tetrahedron, expressed in degrees. */
    C_FUNC_DEF double v_tet_minimum_angle( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet collapse ratio metric.
    /**  Collapse ratio */ 
    C_FUNC_DEF double v_tet_collapse_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet volume.
    /** (1/6) * Jacobian at corner node.
       Reference ---  V. N. Parthasarathy et al, A comparison of tetrahedron 
       quality measures, Finite Elem. Anal. Des., Vol 15(1993), 255-261. */ 
    C_FUNC_DEF double v_tet_volume( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet condition metric.
    /** Condition number of the Jacobian matrix at any corner. 
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */
    C_FUNC_DEF double v_tet_condition( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet jacobian. 
    /** Minimum pointwise volume at any corner. 
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */
    C_FUNC_DEF double v_tet_jacobian( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet scaled jacobian. 
    /** Minimum Jacobian divided by the lengths of 3 edge vectors 
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */
    C_FUNC_DEF double v_tet_scaled_jacobian( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet shape metric.
    /** 3/Mean Ratio of weighted Jacobian matrix.
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */ 
    C_FUNC_DEF double v_tet_shape( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet relative size metric.
    /** Min( J, 1/J ), where J is determinant of weighted Jacobian matrix.
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */ 
    C_FUNC_DEF double v_tet_relative_size_squared( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet shape-size metric.
    /** Product of Shape and Relative Size. 
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */ 
    C_FUNC_DEF double v_tet_shape_and_size( int num_nodes, double coordinates[][3] ); 

    //! Calculates tet distortion metric.
    /** {min(|J|)/actual volume}*parent volume, parent volume = 1/6 for tet.
       Reference --- SDRC/IDEAS Simulation: Finite Element Modeling--User's Guide */ 
    C_FUNC_DEF double v_tet_distortion( int num_nodes, double coordinates[][3] ); 
    
/* individual quality functions for pyramid elements */ 

    //! Calculates pyramid volume.
    C_FUNC_DEF double v_pyramid_volume( int num_nodes, double coordinates[][3] ); 


/* individual quality functions for wedge elements */

    //! Calculates wedge volume.
    C_FUNC_DEF double v_wedge_volume( int num_nodes, double coordinates[][3] ); 

    //! Calculates wedge edge ratio metric.
    /**  Hmax / Hmin where Hmax and Hmin are respectively the maximum and the
       minimum edge lengths */
    C_FUNC_DEF double v_wedge_edge_ratio( int num_nodes, double coordinates[][3] );

    //! Calculates wedge max aspect forbenius.
    /** max(F_0123, F_1204, F_2015, F_3540, F_4351, F_5432)
      Reference --- Adaptation of hex max aspect frobenius */
    C_FUNC_DEF double v_wedge_max_aspect_frobenius( int num_nodes, double coordinates[][3] );

    //! Calculates wedge mean aspect forbenius.
    /** 1/6 * (F_0123 + F_1204 + F+2015 + F_3540 + F_4351 + F_5432)
      Reference --- Adaptation of hex mean aspect frobenius */
    C_FUNC_DEF double v_wedge_mean_aspect_frobenius( int num_nodes, double coordinates[][3] );

    //! Calculates wedge jacobian metric.
    /** min{((L_2 X L_0) * L_3)_k}
       Reference --- Adaptation of Tet jacobian metric. */
    C_FUNC_DEF double v_wedge_jacobian( int num_nodes, double coordinates[][3]);

    //! Calculates wedge distortion metric.
    /** {min(|J|)/actual volume}*parent volume.
       Reference --- Adaptation of Hex distortion metric. */
    C_FUNC_DEF double v_wedge_distortion( int num_nodes, double coordinates[][3] );

    //! Calculates the wedge stretch
    /** Minimum of the stretch of each quadrilateral face.
        Reference -- See quadrilateral stretch */
    C_FUNC_DEF double v_wedge_max_stretch( int num_nodes, double coordinates[][3] );

    //! Calculates wedge scaled jacobian metric.
    /** Reference --- Adaptation of Hex and Tet scaled jacobian metric. */
    C_FUNC_DEF double v_wedge_scaled_jacobian( int num_nodes, double coordinates[][3] );

    //! Calculates the wedge shape metric.
    /** 3 divided by the minimum mean ratio of the Jacobian matrix at each
        element corner.
        Reference -- Adaptaation of Hex shape metric. */
    C_FUNC_DEF double v_wedge_shape( int num_nodes, double coordinates[][3] );

    //! Calculates wedge max aspect forbenius.
    /** max(F_0123, F_1204, F_2015, F_3540, F_4351, F_5432)
      Reference --- Adaptation of hex max aspect frobenius */
    C_FUNC_DEF double v_wedge_condition( int num_nodes, double coordinates[][3] );


/* individual quality functions for knife elements */

    //! Calculates knife volume.
    C_FUNC_DEF double v_knife_volume( int num_nodes, double coordinates[][3] ); 

    
/* individual quality functions for edge elements */

    //! Calculates edge length. 
    C_FUNC_DEF double v_edge_length( int num_nodes, double coordinates[][3] ); 

    
/* individual quality functions for quad elements */
    //! Sets average size (area) of quad, needed for v_quad_relative_size(...)
    C_FUNC_DEF void v_set_quad_size( double size );

    //! Calculates quad edge ratio
    /** edge ratio
        Reference --- P. P. Pebay, Planar Quadrangle Quality
        Measures, Eng. Comp., 2004, 20(2):157-173 */
    C_FUNC_DEF double v_quad_edge_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad maximum of edge ratio.
    /** Maximum edge length ratio at quad center.
       Reference --- J. Robinson, CRE Method of element testing and the 
       Jacobian shape parameters, Eng. Comput., Vol 4, 1987. */ 
    C_FUNC_DEF double v_quad_max_edge_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad aspect ratio
    /** aspect ratio
        Reference --- P. P. Pebay, Planar Quadrangle Quality
        Measures, Eng. Comp., 2004, 20(2):157-173 */
    C_FUNC_DEF double v_quad_aspect_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad radius ratio
    /** radius ratio
        Reference --- P. P. Pebay, Planar Quadrangle Quality
        Measures, Eng. Comp., 2004, 20(2):157-173 */
    C_FUNC_DEF double v_quad_radius_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad average Frobenius aspect
    /** average Frobenius aspect
        Reference --- P. P. Pebay, Planar Quadrangle Quality
        Measures, Eng. Comp., 2004, 20(2):157-173 */
    C_FUNC_DEF double v_quad_med_aspect_frobenius( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad maximum Frobenius aspect
    /** average Frobenius aspect
        Reference --- P. P. Pebay, Planar Quadrangle Quality
        Measures, Eng. Comp., 2004, 20(2):157-173 */
    C_FUNC_DEF double v_quad_max_aspect_frobenius( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad skew metric.
    /** Maximum |cos A| where A is the angle between edges at quad center. 
       Reference --- J. Robinson, CRE Method of element testing and the 
       Jacobian shape parameters, Eng. Comput., Vol 4, 1987. */ 
    C_FUNC_DEF double v_quad_skew( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad taper metric.
    /** Maximum ratio of lengths derived from opposite edges. 
       Reference --- J. Robinson, CRE Method of element testing and the 
       Jacobian shape parameters, Eng. Comput., Vol 4, 1987. */ 
    C_FUNC_DEF double v_quad_taper( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad warpage metric.
    /** Cosine of Minimum Dihedral Angle formed by Planes Intersecting in Diagonals. 
       Reference --- J. Robinson, CRE Method of element testing and the 
       Jacobian shape parameters, Eng. Comput., Vol 4, 1987. */ 
    C_FUNC_DEF double v_quad_warpage( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad area.
    /** Jacobian at quad center.
       Reference --- J. Robinson, CRE Method of element testing and the 
       Jacobian shape parameters, Eng. Comput., Vol 4, 1987. */ 
    C_FUNC_DEF double v_quad_area( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad strech metric.
    /** Sqrt(2) * minimum edge length / maximum diagonal length.
       Reference --- FIMESH code. */
    C_FUNC_DEF double v_quad_stretch( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad's smallest angle.
    /** Smallest included quad angle (degrees).
       Reference --- Unknown. */ 
    C_FUNC_DEF double v_quad_minimum_angle( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad's largest angle.
    /** Largest included quad angle (degrees). 
       Reference --- Unknown. */ 
    C_FUNC_DEF double v_quad_maximum_angle( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad oddy metric.
    C_FUNC_DEF double v_quad_oddy( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad condition number metric.
    /** Maximum condition number of the Jacobian matrix at 4 corners.
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */
    C_FUNC_DEF double v_quad_condition( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad jacobian.
    /** Minimum pointwise volume of local map at 4 corners & center of quad. 
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */
    C_FUNC_DEF double v_quad_jacobian( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad scaled jacobian.
    /** Minimum Jacobian divided by the lengths of the 2 edge vectors. 
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */
    C_FUNC_DEF double v_quad_scaled_jacobian( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad shear metric.
    /** 2/Condition number of Jacobian Skew matrix.
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */
    C_FUNC_DEF double v_quad_shear( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad shape metric.
    /** 2/Condition number of weighted Jacobian matrix. 
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */
    C_FUNC_DEF double v_quad_shape( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad relative size metric.
    /** Min( J, 1/J ), where J is determinant of weighted Jacobian matrix. 
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */
    C_FUNC_DEF double v_quad_relative_size_squared( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad shape-size metric.
    /** Product of Shape and Relative Size. 
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */
    C_FUNC_DEF double v_quad_shape_and_size( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad shear-size metric.
    /** Product of Shear and Relative Size. 
       Reference --- P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */
    C_FUNC_DEF double v_quad_shear_and_size( int num_nodes, double coordinates[][3] ); 

    //! Calculates quad distortion metric.
    /** {min(|J|)/actual area}*parent area, parent area = 4 for quad.
       Reference --- SDRC/IDEAS Simulation: Finite Element Modeling--User's Guide */
    C_FUNC_DEF double v_quad_distortion( int num_nodes, double coordinates[][3] ); 


/* individual quality functions for triangle elements */

    //! Sets average size (area) of tri, needed for v_tri_relative_size(...) 
    C_FUNC_DEF void  v_set_tri_size( double size );

    //! Sets function pointer to calculate triangle normal wrt surface 
    C_FUNC_DEF void v_set_tri_normal_func( ComputeNormal func );

    //! Calculates triangle metric.
    /** edge ratio
        Reference --- P. P. Pebay & T. J. Baker, Analysis of Triangle Quality
        Measures, AMS Math. Comp., 2003, 72(244):1817-1839 */
    C_FUNC_DEF double v_tri_edge_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** aspect ratio
        Reference --- P. P. Pebay & T. J. Baker, Analysis of Triangle Quality
        Measures, AMS Math. Comp., 2003, 72(244):1817-1839 */
    C_FUNC_DEF double v_tri_aspect_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** radius ratio
        Reference --- P. P. Pebay & T. J. Baker, Analysis of Triangle Quality
        Measures, AMS Math. Comp., 2003, 72(244):1817-1839 */
    C_FUNC_DEF double v_tri_radius_ratio( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** Frobenius aspect */
    C_FUNC_DEF double v_tri_aspect_frobenius( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** Maximum included angle in triangle */
    C_FUNC_DEF double v_tri_area( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** Minimum included angle in triangle */
    C_FUNC_DEF double v_tri_minimum_angle( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** Maximum included angle in triangle */
    C_FUNC_DEF double v_tri_maximum_angle( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** Condition number of the Jacobian matrix.
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */ 
    C_FUNC_DEF double v_tri_condition( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** Minimum Jacobian divided by the lengths of 2 edge vectors. 
       Reference --- P. Knupp, Achieving Finite Element Mesh Quality via 
       Optimization of the Jacobian Matrix Norm and Associated Quantities,
       Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. */ 
    C_FUNC_DEF double v_tri_scaled_jacobian( int num_nodes, double coordinates[][3] );

    //! Calculates triangle metric.
    /**  */
    C_FUNC_DEF double v_tri_shear( int num_nodes, double coordinates[][3] ); 
    
    //! Calculates triangle metric.
    /** Min( J, 1/J ), where J is determinant of weighted Jacobian matrix. 
       Reference ---  P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */
    C_FUNC_DEF double v_tri_relative_size_squared( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /** 2/Condition number of weighted Jacobian matrix. 
       Reference ---  P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */
    C_FUNC_DEF double v_tri_shape( int num_nodes, double coordinates[][3] ); 

    //! Calculates triangle metric.
    /**  Product of Shape and Relative Size. 
       Reference ---  P. Knupp, Algebraic Mesh Quality Metrics for
       Unstructured Initial Meshes, submitted for publication. */
    C_FUNC_DEF double v_tri_shape_and_size( int num_nodes, double coordinates[][3] );

    //! Calculates triangle metric.
    /** {min(|J|)/actual area}*parent area, parent area = 1/2 for triangular element. 
       Reference --- SDRC/IDEAS Simulation: Finite Element Modeling--User's Guide */
    C_FUNC_DEF double v_tri_distortion( int num_nodes, double coordinates[][3] );



#endif  /* __verdict_h */