#include <ScdElementData.hpp>

Inheritance diagram for moab::ScdElementData:

Collaboration diagram for moab::ScdElementData:

Classes
class	VertexDataRef
	structure to hold references to bounding vertex blocks More...
Public Member Functions
	ScdElementData (EntityHandle start_handle, const int imin, const int jmin, const int kmin, const int imax, const int jmax, const int kmax, int *is_periodic)
	constructor
virtual	~ScdElementData ()
EntityHandle	get_vertex (const HomCoord &coords) const
	get handle of vertex at homogeneous coords
EntityHandle	get_vertex (int i, int j, int k) const
EntityHandle	get_element (const int i, const int j, const int k) const
	get handle of element at i, j, k
const HomCoord &	min_params () const
	get min params for this element
const HomCoord &	max_params () const
	get max params for this element
void	param_extents (int &di, int &dj, int &dk) const
	get the number of vertices in each direction, inclusive
ErrorCode	get_params (const EntityHandle ehandle, int &i, int &j, int &k) const
	given a handle, get the corresponding parameters
int	is_periodic_i () const
	return whether rectangle is periodic in i
int	is_periodic_j () const
	return whether rectangle is periodic in j
void	is_periodic (int is_p[2]) const
int	i_min () const
	convenience functions for parameter extents
int	j_min () const
int	k_min () const
int	i_max () const
int	j_max () const
int	k_max () const
bool	boundary_complete () const
	test the bounding vertex sequences and determine whether they fully define the vertices covering this element block's parameter space
bool	contains (const HomCoord &coords) const
	test whether this sequence contains these parameters
bool	contains_vertex (const HomCoord &coords) const
	test whether vertex parameterization in this sequence contains these parameters
ErrorCode	get_params_connectivity (const int i, const int j, const int k, std::vector< EntityHandle > &connectivity) const
	get connectivity of an entity given entity's parameters
ErrorCode	add_vsequence (ScdVertexData *vseq, const HomCoord &p1, const HomCoord &q1, const HomCoord &p2, const HomCoord &q2, const HomCoord &p3, const HomCoord &q3, bool bb_input=false, const HomCoord &bb_min=HomCoord::unitv[0], const HomCoord &bb_max=HomCoord::unitv[0])
	add a vertex seq ref to this element sequence; if bb_input is true, bounding box (in eseq-local coords) of vseq being added is input in bb_min and bb_max (allows partial sharing of vseq rather than the whole vseq); if it's false, the whole vseq is referenced and the eseq-local coordinates is computed from the transformed bounding box of the vseq
SequenceData *	subset (EntityHandle start, EntityHandle end, const int sequence_data_sizes, const int tag_data_sizes) const
unsigned long	get_memory_use () const
Static Public Member Functions
static EntityID	calc_num_entities (EntityHandle start_handle, int irange, int jrange, int krange, int *is_periodic=NULL)
Private Member Functions
	ScdElementData ()
	bare constructor, so compiler doesn't create one for me
Private Attributes
HomCoord	boxParams [3]
	parameter min/max/stride for vertices, in homogeneous coords ijkh; elements are one less than max
int	dIJK [3]
	difference between max and min params plus one (i.e. # VERTICES in each parametric direction)
int	dIJKm1 [3]
	difference between max and min params (i.e. # ELEMENTS in each parametric direction)
int	isPeriodic [2]
	whether scd element rectangle is periodic in i and possibly j
std::vector< VertexDataRef >	vertexSeqRefs
	list of bounding vertex blocks

Detailed Description

Definition at line 43 of file ScdElementData.hpp.

Constructor & Destructor Documentation

moab::ScdElementData::ScdElementData ( ) [private]

bare constructor, so compiler doesn't create one for me

moab::ScdElementData::ScdElementData	(	EntityHandle	start_handle,
		const int	imin,
		const int	jmin,
		const int	kmin,
		const int	imax,
		const int	jmax,
		const int	kmax,
		int *	is_periodic
	)

constructor

Definition at line 54 of file ScdElementData.cpp.

References boxParams, dIJK, dIJKm1, and isPeriodic.

    : SequenceData( 0,
                    shandle,
                    shandle + calc_num_entities( shandle, imax - imin, jmax - jmin, kmax - kmin, is_p ) - 1 )
{
    // need to have meaningful parameters
    assert( imax >= imin && jmax >= jmin && kmax >= kmin );

    isPeriodic[0] = ( is_p ? is_p[0] : 0 );
    isPeriodic[1] = ( is_p ? is_p[1] : 0 );

    boxParams[0] = HomCoord( imin, jmin, kmin );
    boxParams[1] = HomCoord( imax, jmax, kmax );
    boxParams[2] = HomCoord( 1, 1, 1 );

    // assign and compute parameter stuff
    dIJK[0]   = boxParams[1][0] - boxParams[0][0] + 1;
    dIJK[1]   = boxParams[1][1] - boxParams[0][1] + 1;
    dIJK[2]   = boxParams[1][2] - boxParams[0][2] + 1;
    dIJKm1[0] = dIJK[0] - ( isPeriodic[0] ? 0 : 1 );
    dIJKm1[1] = dIJK[1] - ( isPeriodic[1] ? 0 : 1 );
    dIJKm1[2] = dIJK[2] - 1;
}

moab::ScdElementData::~ScdElementData ( ) [virtual]

Definition at line 85 of file ScdElementData.cpp.

{}

Member Function Documentation

ErrorCode moab::ScdElementData::add_vsequence	(	ScdVertexData *	vseq,
		const HomCoord &	p1,
		const HomCoord &	q1,
		const HomCoord &	p2,
		const HomCoord &	q2,
		const HomCoord &	p3,
		const HomCoord &	q3,
		bool	bb_input = `false`,
		const HomCoord &	bb_min = `HomCoord::unitv[0]`,
		const HomCoord &	bb_max = `HomCoord::unitv[0]`
	)		`[inline]`

add a vertex seq ref to this element sequence; if bb_input is true, bounding box (in eseq-local coords) of vseq being added is input in bb_min and bb_max (allows partial sharing of vseq rather than the whole vseq); if it's false, the whole vseq is referenced and the eseq-local coordinates is computed from the transformed bounding box of the vseq

Definition at line 312 of file ScdElementData.hpp.

References moab::ScdVertexData::max_params(), MB_SUCCESS, moab::ScdVertexData::min_params(), moab::HomXform::three_pt_xform(), and vertexSeqRefs.

Referenced by moab::ScdBox::add_vbox(), and moab::SequenceManager::add_vsequence().

{
    // compute the transform given the vseq-local parameters and the mapping to
    // this element sequence's parameters passed in minmax
    HomXform M;
    M.three_pt_xform( p1, q1, p2, q2, p3, q3 );

    // min and max in element seq's parameter system may not be same as those in
    // vseq's system, so need to take min/max

    HomCoord minmax[2];
    if( bb_input )
    {
        minmax[0] = bb_min;
        minmax[1] = bb_max;
    }
    else
    {
        minmax[0] = vseq->min_params() * M;
        minmax[1] = vseq->max_params() * M;
    }

    // check against other vseq's to make sure they don't overlap
    for( std::vector< VertexDataRef >::const_iterator vsit = vertexSeqRefs.begin(); vsit != vertexSeqRefs.end();
         ++vsit )
        if( ( *vsit ).contains( minmax[0] ) || ( *vsit ).contains( minmax[1] ) ) return MB_FAILURE;

    HomCoord tmp_min( std::min( minmax[0].i(), minmax[1].i() ), std::min( minmax[0].j(), minmax[1].j() ),
                      std::min( minmax[0].k(), minmax[1].k() ) );
    HomCoord tmp_max( std::max( minmax[0].i(), minmax[1].i() ), std::max( minmax[0].j(), minmax[1].j() ),
                      std::max( minmax[0].k(), minmax[1].k() ) );

    // set up a new vertex sequence reference
    VertexDataRef tmp_seq_ref( tmp_min, tmp_max, M, vseq );

    // add to the list
    vertexSeqRefs.push_back( tmp_seq_ref );

    return MB_SUCCESS;
}

bool moab::ScdElementData::boundary_complete ( ) const

test the bounding vertex sequences and determine whether they fully define the vertices covering this element block's parameter space

Definition at line 87 of file ScdElementData.cpp.

References boxParams, moab::HomCoord::unitv, and vertexSeqRefs.

Referenced by moab::SweptElementSeq::boundary_complete(), moab::StructuredElementSeq::boundary_complete(), and get_vertex().

{
    // test the bounding vertex sequences to see if they fully define the
    // vertex parameter space for this rectangular block of elements

    int p;
    std::vector< VertexDataRef > minlist, maxlist;

    // pseudo code:
    // for each vertex sequence v:
    for( std::vector< VertexDataRef >::const_iterator vseq = vertexSeqRefs.begin(); vseq != vertexSeqRefs.end();
         ++vseq )
    {
        //   test min corner mincorner:
        bool mincorner = true;
        //   for each p = (i-1,j,k), (i,j-1,k), (i,j,k-1):
        for( p = 0; p < 3; p++ )
        {

            //     for each vsequence v' != v:
            for( std::vector< VertexDataRef >::const_iterator othervseq = vertexSeqRefs.begin();
                 othervseq != vertexSeqRefs.end(); ++othervseq )
            {
                if( othervseq == vseq ) continue;
                //       if v.min-p contained in v'
                if( ( *othervseq ).contains( ( *vseq ).minmax[0] - HomCoord::unitv[p] ) )
                {
                    //         mincorner = false
                    mincorner = false;
                    break;
                }
            }
            if( !mincorner ) break;
        }

        bool maxcorner = true;
        //   for each p = (i-1,j,k), (i,j-1,k), (i,j,k-1):
        for( p = 0; p < 3; p++ )
        {

            //     for each vsequence v' != v:
            for( std::vector< VertexDataRef >::const_iterator othervseq = vertexSeqRefs.begin();
                 othervseq != vertexSeqRefs.end(); ++othervseq )
            {
                if( othervseq == vseq ) continue;
                //       if v.max+p contained in v'
                if( ( *othervseq ).contains( ( *vseq ).minmax[1] + HomCoord::unitv[p] ) )
                {
                    //         maxcorner = false
                    maxcorner = false;
                    break;
                }
            }
            if( !maxcorner ) break;
        }

        //   if mincorner add to min corner list minlist
        if( mincorner ) minlist.push_back( *vseq );
        //   if maxcorner add to max corner list maxlist
        if( maxcorner ) maxlist.push_back( *vseq );
    }

    //
    // if minlist.size = 1 & maxlist.size = 1 & minlist[0] = esequence.min &
    //         maxlist[0] = esequence.max+(1,1,1)
    if( minlist.size() == 1 && maxlist.size() == 1 && minlist[0].minmax[0] == boxParams[0] &&
        maxlist[0].minmax[1] == boxParams[1] )
        //   complete
        return true;
    // else

    return false;
}

EntityID moab::ScdElementData::calc_num_entities	(	EntityHandle	start_handle,
		int	irange,
		int	jrange,
		int	krange,
		int *	is_periodic = `NULL`
	)		`[static]`

Definition at line 27 of file ScdElementData.cpp.

References dim, moab::CN::Dimension(), and moab::TYPE_FROM_HANDLE().

{
    size_t result = 1;
    auto dim      = CN::Dimension( TYPE_FROM_HANDLE( start_handle ) );
    switch( dim )
    {
        case 3:
            result *= krange;
            // fall through
        case 2:
            result *= ( is_periodic && is_periodic[1] ? ( jrange + 1 ) : jrange );
            // fall through
        case 1:
            result *= ( is_periodic && is_periodic[0] ? ( irange + 1 ) : irange );
            break;
        default:
            result = 0;
            assert( false );
            break;
    }
    return result;
}

bool moab::ScdElementData::contains ( const HomCoord & coords ) const [inline]

test whether this sequence contains these parameters

Definition at line 254 of file ScdElementData.hpp.

References boxParams, dIJKm1, moab::HomCoord::i(), moab::HomCoord::j(), and moab::HomCoord::k().

Referenced by moab::SweptElementSeq::contains(), moab::StructuredElementSeq::contains(), and get_params_connectivity().

{
    // upper bound is < instead of <= because element params max is one less
    // than vertex params max, except in case of 2d or 1d sequence
    return ( ( dIJKm1[0] && temp.i() >= boxParams[0].i() && temp.i() < boxParams[0].i() + dIJKm1[0] ) &&
             ( ( !dIJKm1[1] && temp.j() == boxParams[1].j() ) ||
               ( dIJKm1[1] && temp.j() >= boxParams[0].j() && temp.j() < boxParams[0].j() + dIJKm1[1] ) ) &&
             ( ( !dIJKm1[2] && temp.k() == boxParams[1].k() ) ||
               ( dIJKm1[2] && temp.k() >= boxParams[0].k() && temp.k() < boxParams[0].k() + dIJKm1[2] ) ) );
}

bool moab::ScdElementData::contains_vertex ( const HomCoord & coords ) const [inline]

test whether *vertex parameterization* in this sequence contains these parameters

Definition at line 265 of file ScdElementData.hpp.

References boxParams, dIJK, moab::HomCoord::i(), moab::HomCoord::j(), and moab::HomCoord::k().

{
    // upper bound is < instead of <= because element params max is one less
    // than vertex params max, except in case of 2d or 1d sequence
    return ( ( dIJK[0] && temp.i() >= boxParams[0].i() && temp.i() < boxParams[0].i() + dIJK[0] ) &&
             ( ( !dIJK[1] && temp.j() == boxParams[1].j() ) ||
               ( dIJK[1] && temp.j() >= boxParams[0].j() && temp.j() < boxParams[0].j() + dIJK[1] ) ) &&
             ( ( !dIJK[2] && temp.k() == boxParams[1].k() ) ||
               ( dIJK[2] && temp.k() >= boxParams[0].k() && temp.k() < boxParams[0].k() + dIJK[2] ) ) );
}

EntityHandle moab::ScdElementData::get_element	(	const int	i,
		const int	j,
		const int	k
	)		const `[inline]`

get handle of element at i, j, k

Definition at line 209 of file ScdElementData.hpp.

References dIJKm1, i_min(), j_min(), k_min(), and moab::SequenceData::start_handle().

Referenced by moab::SweptElementSeq::get_element(), and moab::StructuredElementSeq::get_element().

{
    return start_handle() + ( i - i_min() ) + ( j - j_min() ) * dIJKm1[0] + ( k - k_min() ) * dIJKm1[0] * dIJKm1[1];
}

unsigned long moab::ScdElementData::get_memory_use ( ) const

Definition at line 169 of file ScdElementData.cpp.

References vertexSeqRefs.

Referenced by moab::SweptElementSeq::get_const_memory_use(), and moab::StructuredElementSeq::get_const_memory_use().

{
    return sizeof( *this ) + vertexSeqRefs.capacity() * sizeof( VertexDataRef );
}

ErrorCode moab::ScdElementData::get_params	(	const EntityHandle	ehandle,
		int &	i,
		int &	j,
		int &	k
	)		const `[inline]`

given a handle, get the corresponding parameters

Definition at line 232 of file ScdElementData.hpp.

References boxParams, dIJKm1, moab::HomCoord::i(), i_max(), i_min(), moab::HomCoord::j(), j_max(), j_min(), moab::HomCoord::k(), k_max(), k_min(), MB_SUCCESS, moab::SequenceData::size(), moab::SequenceData::start_handle(), and moab::TYPE_FROM_HANDLE().

Referenced by moab::SweptElementSeq::get_params(), and moab::StructuredElementSeq::get_params().

{
    if( TYPE_FROM_HANDLE( ehandle ) != TYPE_FROM_HANDLE( start_handle() ) ) return MB_FAILURE;

    int hdiff = ehandle - start_handle();

    // use double ?: test below because on some platforms, both sides of the : are
    // evaluated, and if dIJKm1[1] is zero, that'll generate a divide-by-zero
    k = ( dIJKm1[1] > 0 ? hdiff / ( dIJKm1[1] > 0 ? dIJKm1[0] * dIJKm1[1] : 1 ) : 0 );
    j = ( hdiff - ( k * dIJKm1[0] * dIJKm1[1] ) ) / dIJKm1[0];
    i = hdiff % dIJKm1[0];

    k += boxParams[0].k();
    j += boxParams[0].j();
    i += boxParams[0].i();

    return ( ehandle >= start_handle() && ehandle < start_handle() + size() && i >= i_min() && i <= i_max() &&
             j >= j_min() && j <= j_max() && k >= k_min() && k <= k_max() )
               ? MB_SUCCESS
               : MB_FAILURE;
}

ErrorCode moab::ScdElementData::get_params_connectivity	(	const int	i,
		const int	j,
		const int	k,
		std::vector< EntityHandle > &	connectivity
	)		const `[inline]`

get connectivity of an entity given entity's parameters

Definition at line 362 of file ScdElementData.hpp.

References contains(), dIJKm1, moab::CN::Dimension(), get_vertex(), isPeriodic, MB_SUCCESS, moab::SequenceData::start_handle(), and moab::TYPE_FROM_HANDLE().

Referenced by moab::SweptElementSeq::get_params_connectivity(), and moab::StructuredElementSeq::get_params_connectivity().

{
    if( contains( HomCoord( i, j, k ) ) == false ) return MB_FAILURE;

    int ip1 = ( isPeriodic[0] ? ( i + 1 ) % dIJKm1[0] : i + 1 ),
        jp1 = ( isPeriodic[1] ? ( j + 1 ) % dIJKm1[1] : j + 1 );

    connectivity.push_back( get_vertex( i, j, k ) );
    connectivity.push_back( get_vertex( ip1, j, k ) );
    if( CN::Dimension( TYPE_FROM_HANDLE( start_handle() ) ) < 2 ) return MB_SUCCESS;
    connectivity.push_back( get_vertex( ip1, jp1, k ) );
    connectivity.push_back( get_vertex( i, jp1, k ) );
    if( CN::Dimension( TYPE_FROM_HANDLE( start_handle() ) ) < 3 ) return MB_SUCCESS;
    connectivity.push_back( get_vertex( i, j, k + 1 ) );
    connectivity.push_back( get_vertex( ip1, j, k + 1 ) );
    connectivity.push_back( get_vertex( ip1, jp1, k + 1 ) );
    connectivity.push_back( get_vertex( i, jp1, k + 1 ) );
    return MB_SUCCESS;
}

EntityHandle moab::ScdElementData::get_vertex ( const HomCoord & coords ) const [inline]

get handle of vertex at homogeneous coords

Definition at line 291 of file ScdElementData.hpp.

References boundary_complete(), and vertexSeqRefs.

Referenced by get_params_connectivity(), moab::SweptElementSeq::get_vertex(), moab::StructuredElementSeq::get_vertex(), and get_vertex().

{
    assert( boundary_complete() );
    for( std::vector< VertexDataRef >::const_iterator it = vertexSeqRefs.begin(); it != vertexSeqRefs.end(); ++it )
    {
        if( ( *it ).minmax[0] <= coords && ( *it ).minmax[1] >= coords )
        {
            // first get the vertex block-local parameters
            HomCoord local_coords = coords / ( *it ).xform;

            assert( ( *it ).srcSeq->contains( local_coords ) );

            // now get the vertex handle for those coords
            return ( *it ).srcSeq->get_vertex( local_coords );
        }
    }

    // got here, it's an error
    return 0;
}

EntityHandle moab::ScdElementData::get_vertex	(	int	i,
		int	j,
		int	k
	)		const `[inline]`

Definition at line 99 of file ScdElementData.hpp.

References get_vertex().

    {
        return get_vertex( HomCoord( i, j, k ) );
    }

int moab::ScdElementData::i_max ( ) const [inline]

Definition at line 150 of file ScdElementData.hpp.

References boxParams.

Referenced by get_params().

    {
        return ( boxParams[1].hom_coord() )[0];
    }

int moab::ScdElementData::i_min ( ) const [inline]

convenience functions for parameter extents

Definition at line 138 of file ScdElementData.hpp.

References boxParams.

Referenced by get_element(), and get_params().

    {
        return ( boxParams[0].hom_coord() )[0];
    }

void moab::ScdElementData::is_periodic ( int is_p[2] ) const [inline]

Definition at line 131 of file ScdElementData.hpp.

References isPeriodic.

Referenced by moab::StructuredElementSeq::is_periodic().

    {
        is_p[0] = isPeriodic[0];
        is_p[1] = isPeriodic[1];
    }

int moab::ScdElementData::is_periodic_i ( ) const [inline]

return whether rectangle is periodic in i

Definition at line 120 of file ScdElementData.hpp.

References isPeriodic.

Referenced by moab::StructuredElementSeq::is_periodic_i().

    {
        return isPeriodic[0];
    };

int moab::ScdElementData::is_periodic_j ( ) const [inline]

return whether rectangle is periodic in j

Definition at line 126 of file ScdElementData.hpp.

References isPeriodic.

Referenced by moab::StructuredElementSeq::is_periodic_j().

    {
        return isPeriodic[1];
    };

int moab::ScdElementData::j_max ( ) const [inline]

Definition at line 154 of file ScdElementData.hpp.

References boxParams.

Referenced by get_params().

    {
        return ( boxParams[1].hom_coord() )[1];
    }

int moab::ScdElementData::j_min ( ) const [inline]

Definition at line 142 of file ScdElementData.hpp.

References boxParams.

Referenced by get_element(), and get_params().

    {
        return ( boxParams[0].hom_coord() )[1];
    }

int moab::ScdElementData::k_max ( ) const [inline]

Definition at line 158 of file ScdElementData.hpp.

References boxParams.

Referenced by get_params().

    {
        return ( boxParams[1].hom_coord() )[2];
    }

int moab::ScdElementData::k_min ( ) const [inline]

Definition at line 146 of file ScdElementData.hpp.

References boxParams.

Referenced by get_element(), and get_params().

    {
        return ( boxParams[0].hom_coord() )[2];
    }

const HomCoord & moab::ScdElementData::max_params ( ) const [inline]

get max params for this element

Definition at line 219 of file ScdElementData.hpp.

References boxParams.

Referenced by moab::SweptElementSeq::max_params(), moab::StructuredElementSeq::max_params(), and moab::ScdBox::ScdBox().

{
    return boxParams[1];
}

const HomCoord & moab::ScdElementData::min_params ( ) const [inline]

get min params for this element

Definition at line 214 of file ScdElementData.hpp.

References boxParams.

Referenced by moab::SweptElementSeq::min_params(), moab::StructuredElementSeq::min_params(), and moab::ScdBox::ScdBox().

{
    return boxParams[0];
}

void moab::ScdElementData::param_extents	(	int &	di,
		int &	dj,
		int &	dk
	)		const `[inline]`

get the number of vertices in each direction, inclusive

Definition at line 225 of file ScdElementData.hpp.

References dIJK.

Referenced by moab::SweptElementSeq::param_extents(), and moab::StructuredElementSeq::param_extents().

{
    di = dIJK[0];
    dj = dIJK[1];
    dk = dIJK[2];
}

SequenceData * moab::ScdElementData::subset	(	EntityHandle	start,
		EntityHandle	end,
		const int *	sequence_data_sizes,
		const int *	tag_data_sizes
	)		const

Definition at line 161 of file ScdElementData.cpp.

{
    return 0;
}

Member Data Documentation

HomCoord moab::ScdElementData::boxParams[3] [private]

parameter min/max/stride for vertices, in homogeneous coords ijkh; elements are one less than max

Definition at line 65 of file ScdElementData.hpp.

Referenced by boundary_complete(), contains(), contains_vertex(), get_params(), i_max(), i_min(), j_max(), j_min(), k_max(), k_min(), max_params(), min_params(), and ScdElementData().

int moab::ScdElementData::dIJK[3] [private]

difference between max and min params plus one (i.e. # VERTICES in each parametric direction)

Definition at line 69 of file ScdElementData.hpp.

Referenced by contains_vertex(), param_extents(), and ScdElementData().

int moab::ScdElementData::dIJKm1[3] [private]

difference between max and min params (i.e. # ELEMENTS in each parametric direction)

Definition at line 73 of file ScdElementData.hpp.

Referenced by contains(), get_element(), get_params(), get_params_connectivity(), and ScdElementData().

int moab::ScdElementData::isPeriodic[2] [private]

whether scd element rectangle is periodic in i and possibly j

Definition at line 76 of file ScdElementData.hpp.

Referenced by get_params_connectivity(), is_periodic(), is_periodic_i(), is_periodic_j(), and ScdElementData().

std::vector< VertexDataRef > moab::ScdElementData::vertexSeqRefs [private]

list of bounding vertex blocks

Definition at line 82 of file ScdElementData.hpp.

Referenced by add_vsequence(), boundary_complete(), get_memory_use(), and get_vertex().

List of all members.

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

Classes

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation