findpt.c File Reference

#include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>
#include <math.h>
#include <float.h>
#include <string.h>
#include "moab/FindPtFuncs.h"

Include dependency graph for findpt.c:

Go to the source code of this file.

Classes
struct	lob_bnd_base
struct	lob_bnd_ext
struct	obbox_data_2
struct	obbox_data_3
Defines
#define	DIAGNOSTICS   0
#define	DIAGNOSTICS   0
#define	DIAGNOSTICS   0
Functions
static void	lob_bnd_base_alloc (lob_bnd_base *p, unsigned n, unsigned m)
static void	lob_bnd_base_free (lob_bnd_base *p)
static void	lob_bnd_ext_alloc (lob_bnd_ext *p, unsigned n, unsigned m)
static void	lob_bnd_ext_free (lob_bnd_ext *p)
static void	lob_bnd_base_setup (lob_bnd_base *p, const realType *z, const realType *w)
static void	lob_bnd_ext_setup (lob_bnd_ext *p, const realType *z, const realType *w)
static void	lob_bnd_lines (const lob_bnd_base *p, const realType *u, realType *a, realType *b)
static void	lob_bnd_1 (const lob_bnd_base *p, const realType *u, realType bnd[2], realType *work)
static void	lob_bnd_2 (const lob_bnd_base *pr, const lob_bnd_ext *ps, const realType *u, realType bnd[2], realType *work)
static void	mat_inv_2 (const realType A[4], realType inv[4])
static void	mat_inv_3 (const realType A[9], realType inv[9])
static void	mat_app_2r (realType y[2], const realType A[4], const realType x[2])
static void	mat_app_2c (realType y[2], const realType A[4], const realType x[2])
static void	mat_app_3r (realType y[3], const realType A[9], const realType x[3])
static void	mat_app_3c (realType y[3], const realType A[9], const realType x[3])
static void	tinyla_solve_2 (realType x[2], const realType A[4], const realType b[2])
static void	tinyla_solve_3 (realType x[3], const realType A[9], const realType b[3])
static void	tinyla_solve_sym_2 (realType *x0, realType *x1, const realType A[3], realType b0, realType b1)
static void	obbox_data_alloc_2 (obbox_data_2 *p, const unsigned n[2], const unsigned m[2])
static void	obbox_data_free_2 (obbox_data_2 *p)
static void	obbox_data_alloc_3 (obbox_data_3 *p, const unsigned n[3], const unsigned m[3])
static void	obbox_data_free_3 (obbox_data_3 *p)
static obbox_data_2 *	obbox_setup_2 (const realType *const z[2], const realType *const w[2], const unsigned n[2], const unsigned m[2])
static obbox_data_3 *	obbox_setup_3 (const realType *const z[3], const realType *const w[3], const unsigned n[3], const unsigned m[3])
static void	obbox_free_2 (obbox_data_2 *p)
static void	obbox_free_3 (obbox_data_3 *p)
int	obbox_axis_test_2 (const obbox_2 *p, const realType x[2])
int	obbox_axis_test_3 (const obbox_3 *p, const realType x[3])
int	obbox_test_2 (const obbox_2 *p, const realType x[2], realType r[2])
int	obbox_test_3 (const obbox_3 *p, const realType x[3], realType r[3])
void	obbox_calc_tfm_2 (const realType *x, const realType *y, unsigned n, unsigned s, const realType c0[2], const realType A[4], realType *u)
void	obbox_calc_tfm_3 (const realType *x, const realType *y, const realType *z, unsigned nr, unsigned sr, unsigned ns, unsigned ss, const realType c0[3], const realType A[9], realType *u)
void	obbox_merge_2 (realType *b, const realType *ob)
void	obbox_merge_3 (realType *b, const realType *ob)
void	obbox_side_2 (const realType *x, const realType *y, unsigned n, unsigned s, const realType c0[2], const realType A[4], realType *work, const lob_bnd_base *lbd, realType bnd[4])
void	obbox_side_3 (const realType *x, const realType *y, const realType *z, unsigned nr, unsigned sr, unsigned ns, unsigned ss, const realType c0[3], const realType A[9], realType *work, const lob_bnd_base *dr, const lob_bnd_ext *ds, realType bnd[6])
void	obbox_bnd_2 (const obbox_data_2 *p, const realType *x, const realType *y, const realType c0[2], const realType A[4], realType bnd[4])
void	obbox_bnd_3 (const obbox_data_3 *p, const realType *x, const realType *y, const realType *z, const realType c0[3], const realType A[9], realType bnd[6])
void	obbox_calc_2 (const obbox_data_2 *p, realType tol, const realType *x, const realType *y, obbox_2 *b)
void	obbox_calc_3 (const obbox_data_3 *p, realType tol, const realType *x, const realType *y, const realType *z, obbox_3 *b)
static int	ifloor (realType x)
static int	iceil (realType x)
static unsigned	hash_index_helper (realType low, realType fac, unsigned n, realType x)
static uint	hash_index_2 (const hash_data_2 *p, const realType x[2])
static uint	hash_index_3 (const hash_data_3 *p, const realType x[3])
static void	hash_setfac_2 (hash_data_2 *p, unsigned n)
static void	hash_setfac_3 (hash_data_3 *p, unsigned n)
static void	hash_range_2 (const hash_data_2 *p, uint i, unsigned d, unsigned *ia, unsigned *ib)
static void	hash_range_3 (const hash_data_3 *p, uint i, unsigned d, unsigned *ia, unsigned *ib)
static uint	hash_count_2 (hash_data_2 *p, uint nel, unsigned n)
static uint	hash_count_3 (hash_data_3 *p, uint nel, unsigned n)
static uint	hash_opt_size_2 (hash_data_2 *p, uint nel, uint max_size)
static uint	hash_opt_size_3 (hash_data_3 *p, uint nel, uint max_size)
static void	hash_getbb_2 (hash_data_2 *p, const realType *const elx[2], const unsigned n[2], uint nel, realType tol)
static void	hash_getbb_3 (hash_data_3 *p, const realType *const elx[3], const unsigned n[3], uint nel, realType tol)
static void	hash_build_2 (hash_data_2 *p, const realType *const x[2], const unsigned n[2], uint nel, uint max_hash_size, realType tol)
static void	hash_build_3 (hash_data_3 *p, const realType *const x[3], const unsigned n[3], uint nel, uint max_hash_size, realType tol)
static void	hash_free_2 (hash_data_2 *p)
static void	hash_free_3 (hash_data_3 *p)
static unsigned	opt_constr (unsigned constraints, unsigned d)
static void	opt_constr_unpack_2 (unsigned constraints, unsigned *c)
static void	opt_constr_unpack_3 (unsigned constraints, unsigned *c)
static unsigned	opt_constr_pack_2 (const unsigned *c)
static unsigned	opt_constr_pack_3 (const unsigned *c)
void	opt_alloc_3 (opt_data_3 *p, lagrange_data *ld)
void	opt_free_3 (opt_data_3 *p)
static void	opt_vol_set_3 (opt_data_3 *p, const realType r[3])
static void	opt_vol_intp_3 (opt_data_3 *p)
void	opt_vol_set_intp_3 (opt_data_3 *p, const realType r[3])
static void	opt_face_proj_3 (opt_data_3 *p)
static void	opt_face_set_3 (opt_data_3 *p, const realType r[3], unsigned constr)
static void	opt_face_intp_3 (opt_data_3 *p)
static void	opt_face_set_intp_3 (opt_data_3 *p, const realType r[3], unsigned constr)
static void	opt_face_hess_3 (opt_data_3 *p, realType hess[9])
static void	opt_edge_proj_3 (opt_data_3 *p)
static void	opt_edge_set_3 (opt_data_3 *p, const realType r[3], unsigned constr)
static void	opt_edge_intp_3 (opt_data_3 *p)
static void	opt_edge_set_intp_3 (opt_data_3 *p, const realType r[3], unsigned constr)
static void	opt_edge_hess_3 (opt_data_3 *p, realType hess[3])
static void	opt_point_proj_3 (opt_data_3 *p)
static void	opt_point_set_3 (opt_data_3 *p, unsigned constr)
static void	opt_point_intp_3 (opt_data_3 *p)
static void	opt_point_set_intp_3 (opt_data_3 *p, unsigned constr)
double	opt_findpt_3 (opt_data_3 *p, const realType *const elx[3], const realType xstar[3], realType r[3], unsigned *constr)
void	opt_alloc_2 (opt_data_2 *p, lagrange_data *ld)
void	opt_free_2 (opt_data_2 *p)
static void	opt_area_set_2 (opt_data_2 *p, const realType r[2])
static void	opt_area_intp_2 (opt_data_2 *p)
static void	opt_area_set_intp_2 (opt_data_2 *p, const realType r[2])
static void	opt_edge_proj_2 (opt_data_2 *p)
static void	opt_edge_set_2 (opt_data_2 *p, const realType r[2], unsigned constr)
static void	opt_edge_intp_2 (opt_data_2 *p)
static void	opt_edge_set_intp_2 (opt_data_2 *p, const realType r[2], unsigned constr)
static void	opt_edge_hess_2 (opt_data_2 *p, realType hess[2])
static void	opt_point_proj_2 (opt_data_2 *p)
static void	opt_point_set_2 (opt_data_2 *p, unsigned constr)
static void	opt_point_intp_2 (opt_data_2 *p)
static void	opt_point_set_intp_2 (opt_data_2 *p, unsigned constr)
double	opt_findpt_2 (opt_data_2 *p, const realType *const elx[2], const realType xstar[2], realType r[2], unsigned *constr)
static void	findpt_list_sort (findpt_listel **A, unsigned n)
findpt_data_2 *	findpt_setup_2 (const realType *const xw[2], const unsigned n[2], uint nel, uint max_hash_size, realType bbox_tol)
findpt_data_3 *	findpt_setup_3 (const realType *const xw[3], const unsigned n[3], uint nel, uint max_hash_size, realType bbox_tol)
void	findpt_free_2 (findpt_data_2 *p)
void	findpt_free_3 (findpt_data_3 *p)
const realType *	findpt_allbnd_2 (const findpt_data_2 *p)
const realType *	findpt_allbnd_3 (const findpt_data_3 *p)
static void	findpt_hash_2 (findpt_data_2 *p, const realType x[2])
static void	findpt_hash_3 (findpt_data_3 *p, const realType x[3])
static int	findpt_guess_2 (findpt_data_2 *p, const realType x[2], uint el, realType r[2], realType *dist)
static int	findpt_guess_3 (findpt_data_3 *p, const realType x[3], uint el, realType r[3], realType *dist)
static int	findpt_pass_2 (findpt_data_2 *p, const realType x[2], uint *el, realType r[2], realType *dist_min)
static int	findpt_pass_3 (findpt_data_3 *p, const realType x[3], uint *el, realType r[3], realType *dist_min)
int	findpt_2 (findpt_data_2 *p, const realType x[2], int guess, uint *el, realType r[2], realType *dist)
int	findpt_3 (findpt_data_3 *p, const realType x[3], int guess, uint *el, realType r[3], realType *dist)
void	findpt_weights_2 (findpt_data_2 *p, const realType r[2])
void	findpt_weights_3 (findpt_data_3 *p, const realType r[3])
double	findpt_eval_2 (findpt_data_2 *p, const realType *u)
double	findpt_eval_3 (findpt_data_3 *p, const realType *u)
Variables
const unsigned	opt_no_constraints_2 = 3 + 1
const unsigned	opt_no_constraints_3 = 9 + 3 + 1
static const char	opt_constr_num_2 [9] = { 2, 1, 2, 1, 0, 1, 2, 1, 2 }
static const char	opt_constr_num_3 [27]
static const char	opt_constr_dir_3 [27]
static const char	opt_constr_not [27]
static const char	opt_constr_wide [27]
static const unsigned	opt_other1_3 [3] = { 1, 0, 0 }
static const unsigned	opt_other2_3 [3] = { 2, 2, 1 }

---

Define Documentation

#define DIAGNOSTICS   0

Definition at line 2125 of file findpt.c.

Referenced by opt_findpt_2(), and opt_findpt_3().

#define DIAGNOSTICS   0

Definition at line 2125 of file findpt.c.

#define DIAGNOSTICS   0

Definition at line 2125 of file findpt.c.

---

Function Documentation

int findpt_2	(	findpt_data_2 *	p,
		const realType	x[2],
		int	guess,
		uint *	el,
		realType	r[2],
		realType *	dist
	)

Definition at line 2186 of file findpt.c.

References findpt_data_2::end, findpt_guess_2(), findpt_hash_2(), findpt_pass_2(), and findpt_data_2::sorted.

{
    if( guess && findpt_guess_2( p, x, *el, r, dist ) ) return 0;
    findpt_hash_2( p, x );
    if( p->sorted == p->end ) return -1;
    return findpt_pass_2( p, x, el, r, dist );
}

int findpt_3	(	findpt_data_3 *	p,
		const realType	x[3],
		int	guess,
		uint *	el,
		realType	r[3],
		realType *	dist
	)

Definition at line 2194 of file findpt.c.

References findpt_data_3::end, findpt_guess_3(), findpt_hash_3(), findpt_pass_3(), and findpt_data_3::sorted.

{
    if( guess && findpt_guess_3( p, x, *el, r, dist ) ) return 0;
    findpt_hash_3( p, x );
#if DIAGNOSTICS
    printf( "hashing leaves %d elements to consider\n", p->end - p->sorted );
#endif
    if( p->sorted == p->end ) return -1;
    return findpt_pass_3( p, x, el, r, dist );
}

const realType* findpt_allbnd_2

(

const findpt_data_2 *

p

)

Definition at line 2042 of file findpt.c.

References hash_data_2::bnd, and findpt_data_2::hash.

{
    return p->hash->bnd;
}

const realType* findpt_allbnd_3

(

const findpt_data_3 *

p

)

Definition at line 2047 of file findpt.c.

References hash_data_3::bnd, and findpt_data_3::hash.

{
    return p->hash->bnd;
}

double findpt_eval_2	(	findpt_data_2 *	p,
		const realType *	u
	)

Definition at line 2218 of file findpt.c.

{
    return tensor_i2( p->ld[ 0 ].J, p->ld[ 0 ].n, p->ld[ 1 ].J, p->ld[ 1 ].n, u, p->od_work );
}

double findpt_eval_3	(	findpt_data_3 *	p,
		const realType *	u
	)

Definition at line 2223 of file findpt.c.

{
    return tensor_i3( p->ld[ 0 ].J, p->ld[ 0 ].n, p->ld[ 1 ].J, p->ld[ 1 ].n, p->ld[ 2 ].J, p->ld[ 2 ].n, u,
                      p->od_work );
}

void findpt_free_2

(

findpt_data_2 *

p

)

Definition at line 2014 of file findpt.c.

References findpt_data_2::hash, hash_free_2(), findpt_data_2::list, findpt_data_2::od, opt_free_2(), findpt_data_2::sorted, and findpt_data_2::z.

{
    unsigned d;
    opt_free_2( p->od );
    free( p->od );
    hash_free_2( p->hash );
    free( p->hash );
    free( p->list );
    free( p->sorted );
    for( d = 0; d < 2; ++d )
        free( p->z[ d ] );
    free( p );
}

void findpt_free_3

(

findpt_data_3 *

p

)

Definition at line 2028 of file findpt.c.

References findpt_data_3::hash, hash_free_3(), findpt_data_3::list, findpt_data_3::od, opt_free_3(), findpt_data_3::sorted, and findpt_data_3::z.

{
    unsigned d;
    opt_free_3( p->od );
    free( p->od );
    hash_free_3( p->hash );
    free( p->hash );
    free( p->list );
    free( p->sorted );
    for( d = 0; d < 3; ++d )
        free( p->z[ d ] );
    free( p );
}

static int findpt_guess_2	(	findpt_data_2 *	p,
		const realType	x[2],
		uint	el,
		realType	r[2],
		realType *	dist
	)		[static]

Definition at line 2096 of file findpt.c.

References findpt_data_2::hash, findpt_data_2::nptel, hash_data_2::obb, obbox_axis_test_2(), obbox_test_2(), findpt_data_2::od, opt_findpt_2(), opt_no_constraints_2, and findpt_data_2::xw.

Referenced by findpt_2().

{
    const uint      arrindex = p->nptel * el;
    const realType* elx[ 2 ];
    realType        g[ 2 ];
    unsigned        c = opt_no_constraints_2;
    const obbox_2*  obb = &p->hash->obb[ el ];
    elx[ 0 ] = p->xw[ 0 ] + arrindex;
    elx[ 1 ] = p->xw[ 1 ] + arrindex;
    if( obbox_axis_test_2( obb, x ) || obbox_test_2( obb, x, g ) ) return 0;
    *dist = opt_findpt_2( p->od, elx, x, r, &c );
    return c == opt_no_constraints_2;
}

static int findpt_guess_3	(	findpt_data_3 *	p,
		const realType	x[3],
		uint	el,
		realType	r[3],
		realType *	dist
	)		[static]

Definition at line 2110 of file findpt.c.

References findpt_data_3::hash, findpt_data_3::nptel, hash_data_3::obb, obbox_axis_test_3(), obbox_test_3(), findpt_data_3::od, opt_findpt_3(), opt_no_constraints_3, and findpt_data_3::xw.

Referenced by findpt_3().

{
    const uint      arrindex = p->nptel * el;
    const realType* elx[ 3 ];
    realType        g[ 3 ];
    unsigned        c = opt_no_constraints_3;
    const obbox_3*  obb = &p->hash->obb[ el ];
    elx[ 0 ] = p->xw[ 0 ] + arrindex;
    elx[ 1 ] = p->xw[ 1 ] + arrindex;
    elx[ 2 ] = p->xw[ 2 ] + arrindex;
    if( obbox_axis_test_3( obb, x ) || obbox_test_3( obb, x, g ) ) return 0;
    *dist = opt_findpt_3( p->od, elx, x, r, &c );
    return c == opt_no_constraints_3;
}

static void findpt_hash_2	(	findpt_data_2 *	p,
		const realType	x[2]
	)		[static]

Definition at line 2052 of file findpt.c.

References b, findpt_listel::dist, findpt_listel::el, findpt_data_2::end, findpt_list_sort(), findpt_data_2::hash, hash_index_2(), findpt_data_2::list, hash_data_2::obb, obbox_axis_test_2(), obbox_test_2(), hash_data_2::offset, findpt_listel::r, r1norm_2(), and findpt_data_2::sorted.

Referenced by findpt_2().

{
    findpt_listel *list = p->list, **sorted = p->sorted;
    const uint     hi = hash_index_2( p->hash, x );
    const uint*    offset = p->hash->offset;
    uint           i;
    const uint     b = offset[ hi ], e = offset[ hi + 1 ];
    for( i = b; i != e; ++i )
    {
        const uint     el = offset[ i ];
        realType*      r = &list->r[ 0 ];
        const obbox_2* obb = &p->hash->obb[ el ];
        if( obbox_axis_test_2( obb, x ) ) continue;
        if( obbox_test_2( obb, x, r ) ) continue;
        list->el = el;
        list->dist = r1norm_2( r[ 0 ], r[ 1 ] );
        *sorted++ = list++;
    }
    p->end = sorted;
    if( p->end != p->sorted ) findpt_list_sort( p->sorted, p->end - p->sorted );
}

static void findpt_hash_3	(	findpt_data_3 *	p,
		const realType	x[3]
	)		[static]

Definition at line 2074 of file findpt.c.

References b, findpt_listel::dist, findpt_listel::el, findpt_data_3::end, findpt_list_sort(), findpt_data_3::hash, hash_index_3(), findpt_data_3::list, hash_data_3::obb, obbox_axis_test_3(), obbox_test_3(), hash_data_3::offset, findpt_listel::r, r1norm_3(), and findpt_data_3::sorted.

Referenced by findpt_3().

{
    findpt_listel *list = p->list, **sorted = p->sorted;
    const uint     hi = hash_index_3( p->hash, x );
    const uint*    offset = p->hash->offset;
    uint           i;
    const uint     b = offset[ hi ], e = offset[ hi + 1 ];
    for( i = b; i != e; ++i )
    {
        const uint     el = offset[ i ];
        realType*      r = &list->r[ 0 ];
        const obbox_3* obb = &p->hash->obb[ el ];
        if( obbox_axis_test_3( obb, x ) ) continue;
        if( obbox_test_3( obb, x, r ) ) continue;
        list->el = el;
        list->dist = r1norm_3( r[ 0 ], r[ 1 ], r[ 2 ] );
        *sorted++ = list++;
    }
    p->end = sorted;
    if( p->end != p->sorted ) findpt_list_sort( p->sorted, p->end - p->sorted );
}

static void findpt_list_sort	(	findpt_listel **	A,
		unsigned	n
	)		[static]

Definition at line 1916 of file findpt.c.

References dist(), findpt_listel::dist, and n.

Referenced by findpt_hash_2(), and findpt_hash_3().

{
    unsigned i;
    --A; /* make A have a base index of 1 */
    /* build heap */
    for( i = 2; i <= n; ++i )
    {
        findpt_listel* item = A[ i ];
        unsigned       hole = i, parent = hole >> 1;
        if( A[ parent ]->dist >= item->dist ) continue;
        do
        {
            A[ hole ] = A[ parent ];
            hole = parent;
            parent >>= 1;
        } while( parent && A[ parent ]->dist < item->dist );
        A[ hole ] = item;
    }
    /* extract */
    for( i = n - 1; i; --i )
    {
        findpt_listel* item = A[ i + 1 ];
        unsigned       hole = 1;
        A[ i + 1 ] = A[ 1 ];
        for( ;; )
        {
            unsigned ch = hole << 1, r = ch + 1;
            if( r <= i && A[ ch ]->dist < A[ r ]->dist ) ch = r;
            if( ch > i || item->dist >= A[ ch ]->dist ) break;
            A[ hole ] = A[ ch ];
            hole = ch;
        }
        A[ hole ] = item;
    }
}

static int findpt_pass_2	(	findpt_data_2 *	p,
		const realType	x[2],
		uint *	el,
		realType	r[2],
		realType *	dist_min
	)		[static]

Definition at line 2127 of file findpt.c.

References obbox_2::axis_bnd, dist(), findpt_listel::el, findpt_data_2::end, findpt_data_2::hash, findpt_data_2::nptel, hash_data_2::obb, findpt_data_2::od, opt_findpt_2(), opt_no_constraints_2, findpt_listel::r, r2norm_2(), findpt_data_2::sorted, and findpt_data_2::xw.

Referenced by findpt_2().

{
    findpt_listel** qq = p->sorted;
    const realType* bnd;
    realType        dist;
    do
    {
        findpt_listel*  q = *qq;
        const uint      arrindex = p->nptel * q->el;
        const realType* elx[ 2 ];
        unsigned        c = opt_no_constraints_2;
        elx[ 0 ] = p->xw[ 0 ] + arrindex;
        elx[ 1 ] = p->xw[ 1 ] + arrindex;
        dist = opt_findpt_2( p->od, elx, x, q->r, &c );
        if( qq == p->sorted || dist < *dist_min || c == opt_no_constraints_2 )
        {
            *dist_min = dist;
            *el = q->el;
            memcpy( r, q->r, 2 * sizeof( realType ) );
            if( c == opt_no_constraints_2 ) return 0;
        }
    } while( ++qq != p->end );
    bnd = p->hash->obb[ *el ].axis_bnd;
    return *dist_min > r2norm_2( bnd[ 1 ] - bnd[ 0 ], bnd[ 3 ] - bnd[ 2 ] ) ? -1 : 1;
}

static int findpt_pass_3	(	findpt_data_3 *	p,
		const realType	x[3],
		uint *	el,
		realType	r[3],
		realType *	dist_min
	)		[static]

Definition at line 2153 of file findpt.c.

References obbox_3::axis_bnd, dist(), findpt_listel::el, findpt_data_3::end, findpt_data_3::hash, findpt_data_3::nptel, hash_data_3::obb, findpt_data_3::od, opt_findpt_3(), opt_no_constraints_3, findpt_listel::r, r2norm_3(), findpt_data_3::sorted, and findpt_data_3::xw.

Referenced by findpt_3().

{
    findpt_listel** qq = p->sorted;
    const realType* bnd;
    realType        dist;
    do
    {
        findpt_listel*  q = *qq;
        const uint      arrindex = p->nptel * q->el;
        const realType* elx[ 3 ];
        unsigned        c = opt_no_constraints_3;
        elx[ 0 ] = p->xw[ 0 ] + arrindex;
        elx[ 1 ] = p->xw[ 1 ] + arrindex;
        elx[ 2 ] = p->xw[ 2 ] + arrindex;
        dist = opt_findpt_3( p->od, elx, x, q->r, &c );
        if( qq == p->sorted || dist < *dist_min || c == opt_no_constraints_3 )
        {
            *dist_min = dist;
            *el = q->el;
            memcpy( r, q->r, 3 * sizeof( realType ) );
            if( c == opt_no_constraints_3 )
            {
#if DIAGNOSTICS
                printf( "point found in element #%d\n", qq - p->sorted );
#endif
                return 0;
            }
        }
    } while( ++qq != p->end );
    bnd = p->hash->obb[ *el ].axis_bnd;
    return *dist_min > r2norm_3( bnd[ 1 ] - bnd[ 0 ], bnd[ 3 ] - bnd[ 2 ], bnd[ 5 ] - bnd[ 4 ] ) ? -1 : 1;
}

findpt_data_2* findpt_setup_2	(	const realType *const	xw[2],
		const unsigned	n[2],
		uint	nel,
		uint	max_hash_size,
		realType	bbox_tol
	)

Definition at line 1952 of file findpt.c.

References findpt_data_2::hash, hash_build_2(), lagrange_setup(), findpt_data_2::ld, findpt_data_2::list, lobatto_nodes(), hash_data_2::max, findpt_data_2::nptel, findpt_data_2::od, findpt_data_2::od_work, opt_alloc_2(), findpt_data_2::sorted, tmalloc, opt_data_2::work, findpt_data_2::xw, and findpt_data_2::z.

{
    unsigned       d;
    findpt_data_2* p = tmalloc( findpt_data_2, 1 );

    p->hash = tmalloc( hash_data_2, 1 );
    p->od = tmalloc( opt_data_2, 1 );

    for( d = 0; d < 2; ++d )
        p->xw[ d ] = xw[ d ];
    p->nptel = n[ 0 ] * n[ 1 ];

    hash_build_2( p->hash, xw, n, nel, max_hash_size, bbox_tol );

    for( d = 0; d < 2; ++d )
    {
        p->z[ d ] = tmalloc( realType, n[ d ] );
        lobatto_nodes( p->z[ d ], n[ d ] );
        lagrange_setup( &p->ld[ d ], p->z[ d ], n[ d ] );
    }

    p->list = tmalloc( findpt_listel, p->hash->max );
    p->sorted = tmalloc( findpt_listel*, p->hash->max );

    opt_alloc_2( p->od, p->ld );
    p->od_work = p->od->work;

    return p;
}

findpt_data_3* findpt_setup_3	(	const realType *const	xw[3],
		const unsigned	n[3],
		uint	nel,
		uint	max_hash_size,
		realType	bbox_tol
	)

Definition at line 1983 of file findpt.c.

References findpt_data_3::hash, hash_build_3(), lagrange_setup(), findpt_data_3::ld, findpt_data_3::list, lobatto_nodes(), hash_data_3::max, findpt_data_3::nptel, findpt_data_3::od, findpt_data_3::od_work, opt_alloc_3(), findpt_data_3::sorted, tmalloc, opt_data_3::work, findpt_data_3::xw, and findpt_data_3::z.

{
    unsigned       d;
    findpt_data_3* p = tmalloc( findpt_data_3, 1 );

    p->hash = tmalloc( hash_data_3, 1 );
    p->od = tmalloc( opt_data_3, 1 );

    for( d = 0; d < 3; ++d )
        p->xw[ d ] = xw[ d ];
    p->nptel = n[ 0 ] * n[ 1 ] * n[ 2 ];

    hash_build_3( p->hash, xw, n, nel, max_hash_size, bbox_tol );

    for( d = 0; d < 3; ++d )
    {
        p->z[ d ] = tmalloc( realType, n[ d ] );
        lobatto_nodes( p->z[ d ], n[ d ] );
        lagrange_setup( &p->ld[ d ], p->z[ d ], n[ d ] );
    }

    p->list = tmalloc( findpt_listel, p->hash->max );
    p->sorted = tmalloc( findpt_listel*, p->hash->max );

    opt_alloc_3( p->od, p->ld );
    p->od_work = p->od->work;

    return p;
}

void findpt_weights_2	(	findpt_data_2 *	p,
		const realType	r[2]
	)

Definition at line 2205 of file findpt.c.

{
    lagrange_0( &p->ld[ 0 ], r[ 0 ] );
    lagrange_0( &p->ld[ 1 ], r[ 1 ] );
}

void findpt_weights_3	(	findpt_data_3 *	p,
		const realType	r[3]
	)

Definition at line 2211 of file findpt.c.

{
    lagrange_0( &p->ld[ 0 ], r[ 0 ] );
    lagrange_0( &p->ld[ 1 ], r[ 1 ] );
    lagrange_0( &p->ld[ 2 ], r[ 2 ] );
}

static void hash_build_2	(	hash_data_2 *	p,
		const realType *const	x[2],
		const unsigned	n[2],
		uint	nel,
		uint	max_hash_size,
		realType	tol
	)		[static]

Definition at line 969 of file findpt.c.

References hash_getbb_2(), hash_data_2::hash_n, hash_opt_size_2(), hash_range_2(), hash_data_2::max, hash_data_2::obb, hash_data_2::offset, size, moab::sum(), tcalloc, tmalloc, and uint.

Referenced by findpt_setup_2().

{
    uint      i, el, size, hn2, sum;
    unsigned  hn;
    unsigned* count;
    p->obb = tmalloc( obbox_2, nel );
    hash_getbb_2( p, x, n, nel, tol );
    size = hash_opt_size_2( p, nel, max_hash_size );
    p->offset = tmalloc( uint, size );
    hn = p->hash_n;
    hn2 = (uint)hn * hn;
    count = tcalloc( unsigned, hn2 );
    for( el = 0; el < nel; ++el )
    {
        unsigned ia, ib, j, ja, jb;
        hash_range_2( p, el, 0, &ia, &ib );
        hash_range_2( p, el, 1, &ja, &jb );
        for( j = ja; j < jb; ++j )
            for( i = ia; i < ib; ++i )
                ++count[ (uint)j * hn + i ];
    }
    sum = hn2 + 1, p->max = count[ 0 ];
    p->offset[ 0 ] = sum;
    for( i = 0; i < hn2; ++i )
    {
        if( count[ i ] > p->max ) p->max = count[ i ];
        sum += count[ i ];
        p->offset[ i + 1 ] = sum;
    }
    for( el = 0; el < nel; ++el )
    {
        unsigned ia, ib, j, ja, jb;
        hash_range_2( p, el, 0, &ia, &ib );
        hash_range_2( p, el, 1, &ja, &jb );
        for( j = ja; j < jb; ++j )
            for( i = ia; i < ib; ++i )
            {
                uint arrindex = (uint)j * hn + i;
                p->offset[ p->offset[ arrindex + 1 ] - count[ arrindex ] ] = el;
                --count[ arrindex ];
            }
    }
    free( count );
}

static void hash_build_3	(	hash_data_3 *	p,
		const realType *const	x[3],
		const unsigned	n[3],
		uint	nel,
		uint	max_hash_size,
		realType	tol
	)		[static]

Definition at line 1015 of file findpt.c.

References hash_getbb_3(), hash_data_3::hash_n, hash_opt_size_3(), hash_range_3(), hash_data_3::max, hash_data_3::obb, hash_data_3::offset, size, moab::sum(), tcalloc, tmalloc, and uint.

Referenced by findpt_setup_3().

{
    uint      i, el, size, hn3, sum;
    unsigned  hn;
    unsigned* count;
    p->obb = tmalloc( obbox_3, nel );
    hash_getbb_3( p, x, n, nel, tol );
    size = hash_opt_size_3( p, nel, max_hash_size );
    p->offset = tmalloc( uint, size );
    hn = p->hash_n;
    hn3 = (uint)hn * hn * hn;
    count = tcalloc( unsigned, hn3 );
    for( el = 0; el < nel; ++el )
    {
        unsigned ia, ib, j, ja, jb, k, ka, kb;
        hash_range_3( p, el, 0, &ia, &ib );
        hash_range_3( p, el, 1, &ja, &jb );
        hash_range_3( p, el, 2, &ka, &kb );
        for( k = ka; k < kb; ++k )
            for( j = ja; j < jb; ++j )
                for( i = ia; i < ib; ++i )
                    ++count[ ( (uint)k * hn + j ) * hn + i ];
    }
    sum = hn3 + 1, p->max = count[ 0 ];
    p->offset[ 0 ] = sum;
    for( i = 0; i < hn3; ++i )
    {
        if( count[ i ] > p->max ) p->max = count[ i ];
        sum += count[ i ];
        p->offset[ i + 1 ] = sum;
    }
    for( el = 0; el < nel; ++el )
    {
        unsigned ia, ib, j, ja, jb, k, ka, kb;
        hash_range_3( p, el, 0, &ia, &ib );
        hash_range_3( p, el, 1, &ja, &jb );
        hash_range_3( p, el, 2, &ka, &kb );
        for( k = ka; k < kb; ++k )
            for( j = ja; j < jb; ++j )
                for( i = ia; i < ib; ++i )
                {
                    uint arrindex = ( (uint)k * hn + j ) * hn + i;
                    p->offset[ p->offset[ arrindex + 1 ] - count[ arrindex ] ] = el;
                    --count[ arrindex ];
                }
    }
    free( count );
}

static uint hash_count_2	(	hash_data_2 *	p,
		uint	nel,
		unsigned	n
	)		[static]

Definition at line 830 of file findpt.c.

References hash_range_2(), and hash_setfac_2().

Referenced by hash_opt_size_2().

{
    uint i, count = 0;
    hash_setfac_2( p, n );
    for( i = 0; i < nel; ++i )
    {
        unsigned ia, ib;
        uint     ci;
        hash_range_2( p, i, 0, &ia, &ib );
        ci = ib - ia;
        hash_range_2( p, i, 1, &ia, &ib );
        ci *= ib - ia;
        count += ci;
    }
    return count;
}

static uint hash_count_3	(	hash_data_3 *	p,
		uint	nel,
		unsigned	n
	)		[static]

Definition at line 847 of file findpt.c.

References hash_range_3(), and hash_setfac_3().

Referenced by hash_opt_size_3().

{
    uint i, count = 0;
    hash_setfac_3( p, n );
    for( i = 0; i < nel; ++i )
    {
        unsigned ia, ib;
        uint     ci;
        hash_range_3( p, i, 0, &ia, &ib );
        ci = ib - ia;
        hash_range_3( p, i, 1, &ia, &ib );
        ci *= ib - ia;
        hash_range_3( p, i, 2, &ia, &ib );
        ci *= ib - ia;
        count += ci;
    }
    return count;
}

static void hash_free_2

(

hash_data_2 *

p

)

[static]

Definition at line 1065 of file findpt.c.

References hash_data_2::obb, and hash_data_2::offset.

Referenced by findpt_free_2().

{
    free( p->obb );
    free( p->offset );
}

static void hash_free_3

(

hash_data_3 *

p

)

[static]

Definition at line 1071 of file findpt.c.

References hash_data_3::obb, and hash_data_3::offset.

Referenced by findpt_free_3().

{
    free( p->obb );
    free( p->offset );
}

static void hash_getbb_2	(	hash_data_2 *	p,
		const realType *const	elx[2],
		const unsigned	n[2],
		uint	nel,
		realType	tol
	)		[static]

Definition at line 900 of file findpt.c.

References obbox_2::axis_bnd, hash_data_2::bnd, lobatto_nodes(), lobatto_weights(), hash_data_2::obb, obbox_calc_2(), obbox_free_2(), obbox_merge_2(), obbox_setup_2(), tmalloc, and z.

Referenced by hash_build_2().

{
    obbox_data_2*   data;
    realType *      z[ 2 ], *w[ 2 ];
    uint            i;
    unsigned        d;
    const unsigned  nn = n[ 0 ] * n[ 1 ];
    unsigned int    m[ 2 ];
    const realType* x[ 2 ];

    for( i = 0; i < 2; ++i )
    {
        x[ i ] = elx[ i ];
        m[ i ] = 2 * n[ i ];
    }

    z[ 0 ] = tmalloc( realType, 2 * ( n[ 0 ] + n[ 1 ] ) );
    w[ 0 ] = z[ 0 ] + n[ 0 ];
    z[ 1 ] = w[ 0 ] + n[ 0 ], w[ 1 ] = z[ 1 ] + n[ 1 ];
    for( d = 0; d < 2; ++d )
        lobatto_nodes( z[ d ], n[ d ] ), lobatto_weights( z[ d ], w[ d ], n[ d ] );
    data = obbox_setup_2( (const realType* const*)z, (const realType* const*)w, n, m );
    obbox_calc_2( data, tol, x[ 0 ], x[ 1 ], &p->obb[ 0 ] );
    memcpy( &p->bnd[ 0 ], (const realType*)&p->obb[ 0 ].axis_bnd[ 0 ], 4 * sizeof( realType ) );
    for( i = 0; i < nel; ++i, x[ 0 ] += nn, x[ 1 ] += nn )
    {
        obbox_calc_2( data, tol, x[ 0 ], x[ 1 ], &p->obb[ i ] );
        obbox_merge_2( &p->bnd[ 0 ], (const realType*)&p->obb[ i ].axis_bnd[ 0 ] );
    }
    obbox_free_2( data );
    free( z[ 0 ] );
}

static void hash_getbb_3	(	hash_data_3 *	p,
		const realType *const	elx[3],
		const unsigned	n[3],
		uint	nel,
		realType	tol
	)		[static]

Definition at line 934 of file findpt.c.

References obbox_3::axis_bnd, hash_data_3::bnd, lobatto_nodes(), lobatto_weights(), hash_data_3::obb, obbox_calc_3(), obbox_free_3(), obbox_merge_3(), obbox_setup_3(), tmalloc, and z.

Referenced by hash_build_3().

{
    obbox_data_3*   data;
    const realType* x[ 3 ];
    realType *      z[ 3 ], *w[ 3 ];
    uint            i;
    unsigned        d;
    const unsigned  nn = n[ 0 ] * n[ 1 ] * n[ 2 ];
    unsigned int    m[ 3 ];

    for( i = 0; i < 3; ++i )
    {
        x[ i ] = elx[ i ];
        m[ i ] = 2 * n[ i ];
    }

    z[ 0 ] = tmalloc( realType, 2 * ( n[ 0 ] + n[ 1 ] + n[ 2 ] ) );
    w[ 0 ] = z[ 0 ] + n[ 0 ];
    for( d = 1; d < 3; ++d )
        z[ d ] = w[ d - 1 ] + n[ d - 1 ], w[ d ] = z[ d ] + n[ d ];
    for( d = 0; d < 3; ++d )
        lobatto_nodes( z[ d ], n[ d ] ), lobatto_weights( z[ d ], w[ d ], n[ d ] );
    data = obbox_setup_3( (const realType* const*)z, (const realType* const*)w, n, m );
    obbox_calc_3( data, tol, x[ 0 ], x[ 1 ], x[ 2 ], &p->obb[ 0 ] );
    memcpy( &p->bnd[ 0 ], (const realType*)&p->obb[ 0 ].axis_bnd[ 0 ], 6 * sizeof( realType ) );
    for( i = 0; i < nel; ++i, x[ 0 ] += nn, x[ 1 ] += nn, x[ 2 ] += nn )
    {
        obbox_calc_3( data, tol, x[ 0 ], x[ 1 ], x[ 2 ], &p->obb[ i ] );
        obbox_merge_3( &p->bnd[ 0 ], (const realType*)&p->obb[ i ].axis_bnd[ 0 ] );
    }
    obbox_free_3( data );
    free( z[ 0 ] );
}

static uint hash_index_2	(	const hash_data_2 *	p,
		const realType	x[2]
	)		[static]

Definition at line 777 of file findpt.c.

References hash_data_2::bnd, hash_data_2::fac, hash_index_helper(), hash_data_2::hash_n, and n.

Referenced by findpt_hash_2().

{
    const unsigned n = p->hash_n;
    return (uint)hash_index_helper( p->bnd[ 2 ], p->fac[ 1 ], n, x[ 1 ] ) * n +
           hash_index_helper( p->bnd[ 0 ], p->fac[ 0 ], n, x[ 0 ] );
}

static uint hash_index_3	(	const hash_data_3 *	p,
		const realType	x[3]
	)		[static]

Definition at line 784 of file findpt.c.

References hash_data_3::bnd, hash_data_3::fac, hash_index_helper(), hash_data_3::hash_n, and n.

Referenced by findpt_hash_3().

{
    const unsigned n = p->hash_n;
    return ( (uint)hash_index_helper( p->bnd[ 4 ], p->fac[ 2 ], n, x[ 2 ] ) * n +
             hash_index_helper( p->bnd[ 2 ], p->fac[ 1 ], n, x[ 1 ] ) ) *
               n +
           hash_index_helper( p->bnd[ 0 ], p->fac[ 0 ], n, x[ 0 ] );
}

static unsigned hash_index_helper	(	realType	low,
		realType	fac,
		unsigned	n,
		realType	x
	)		[static]

Definition at line 770 of file findpt.c.

References ifloor().

Referenced by hash_index_2(), and hash_index_3().

{
    const int i = ifloor( ( x - low ) * fac );
    if( i < 0 ) return 0;
    return umin_2( i, n - 1 );
}

static uint hash_opt_size_2	(	hash_data_2 *	p,
		uint	nel,
		uint	max_size
	)		[static]

Definition at line 866 of file findpt.c.

References hash_count_2(), hash_setfac_2(), nl, size, and uint.

Referenced by hash_build_2().

{
    unsigned nl = 1, nu = ceil( sqrt( max_size - nel ) );
    uint     size_low = 2 + nel;
    while( nu - nl > 1 )
    {
        unsigned nm = nl + ( nu - nl ) / 2;
        uint     size = (uint)nm * nm + 1 + hash_count_2( p, nel, nm );
        if( size <= max_size )
            nl = nm, size_low = size;
        else
            nu = nm;
    }
    hash_setfac_2( p, nl );
    return size_low;
}

static uint hash_opt_size_3	(	hash_data_3 *	p,
		uint	nel,
		uint	max_size
	)		[static]

Definition at line 883 of file findpt.c.

References hash_count_3(), hash_setfac_3(), nl, size, and uint.

Referenced by hash_build_3().

{
    unsigned nl = 1, nu = ceil( pow( max_size - nel, 1.0 / 3 ) );
    uint     size_low = 2 + nel;
    while( nu - nl > 1 )
    {
        unsigned nm = nl + ( nu - nl ) / 2;
        uint     size = (uint)nm * nm * nm + 1 + hash_count_3( p, nel, nm );
        if( size <= max_size )
            nl = nm, size_low = size;
        else
            nu = nm;
    }
    hash_setfac_3( p, nl );
    return size_low;
}

static void hash_range_2	(	const hash_data_2 *	p,
		uint	i,
		unsigned	d,
		unsigned *	ia,
		unsigned *	ib
	)		[static]

Definition at line 808 of file findpt.c.

References obbox_2::axis_bnd, b, hash_data_2::bnd, hash_data_2::fac, hash_data_2::hash_n, iceil(), ifloor(), and hash_data_2::obb.

Referenced by hash_build_2(), and hash_count_2().

{
    const realType a = p->obb[ i ].axis_bnd[ d * 2 ];
    const realType b = p->obb[ i ].axis_bnd[ d * 2 + 1 ];
    const int      i0 = ifloor( ( a - p->bnd[ d * 2 ] ) * p->fac[ d ] );
    const unsigned i1 = iceil( ( b - p->bnd[ d * 2 ] ) * p->fac[ d ] );
    *ia = imax_2( 0, i0 );
    *ib = imin_2( i1, p->hash_n );
    if( *ib == *ia ) ++( *ib );
}

static void hash_range_3	(	const hash_data_3 *	p,
		uint	i,
		unsigned	d,
		unsigned *	ia,
		unsigned *	ib
	)		[static]

Definition at line 819 of file findpt.c.

References obbox_3::axis_bnd, b, hash_data_3::bnd, hash_data_3::fac, hash_data_3::hash_n, iceil(), ifloor(), and hash_data_3::obb.

Referenced by hash_build_3(), and hash_count_3().

{
    const realType a = p->obb[ i ].axis_bnd[ d * 2 ];
    const realType b = p->obb[ i ].axis_bnd[ d * 2 + 1 ];
    const int      i0 = ifloor( ( a - p->bnd[ d * 2 ] ) * p->fac[ d ] );
    const unsigned i1 = iceil( ( b - p->bnd[ d * 2 ] ) * p->fac[ d ] );
    *ia = imax_2( 0, i0 );
    *ib = imin_2( i1, p->hash_n );
    if( *ib == *ia ) ++( *ib );
}

static void hash_setfac_2	(	hash_data_2 *	p,
		unsigned	n
	)		[static]

Definition at line 793 of file findpt.c.

References hash_data_2::bnd, hash_data_2::fac, hash_data_2::hash_n, and n.

Referenced by hash_count_2(), and hash_opt_size_2().

{
    p->hash_n = n;
    p->fac[ 0 ] = n / ( p->bnd[ 1 ] - p->bnd[ 0 ] );
    p->fac[ 1 ] = n / ( p->bnd[ 3 ] - p->bnd[ 2 ] );
}

static void hash_setfac_3	(	hash_data_3 *	p,
		unsigned	n
	)		[static]

Definition at line 800 of file findpt.c.

References hash_data_3::bnd, hash_data_3::fac, hash_data_3::hash_n, and n.

Referenced by hash_count_3(), and hash_opt_size_3().

{
    p->hash_n = n;
    p->fac[ 0 ] = n / ( p->bnd[ 1 ] - p->bnd[ 0 ] );
    p->fac[ 1 ] = n / ( p->bnd[ 3 ] - p->bnd[ 2 ] );
    p->fac[ 2 ] = n / ( p->bnd[ 5 ] - p->bnd[ 4 ] );
}

static int iceil

(

realType

x

)

[static]

Definition at line 761 of file findpt.c.

References mbceil.

Referenced by hash_range_2(), and hash_range_3().

{
    /*
    int y = x;
    return (double)y < x ? y+1 : y;
    */
    return mbceil( x );
}

static int ifloor

(

realType

x

)

[static]

Definition at line 752 of file findpt.c.

References mbfloor.

Referenced by hash_index_helper(), hash_range_2(), and hash_range_3().

{
    /*
    int y = x;
    return (double)y > x ? y-1 : y;
    */
    return mbfloor( x );
}

static void lob_bnd_1	(	const lob_bnd_base *	p,
		const realType *	u,
		realType	bnd[2],
		realType *	work
	)		[static]

Definition at line 186 of file findpt.c.

References b, lob_bnd_lines(), and lob_bnd_base::m.

Referenced by obbox_side_2().

{
    unsigned  j;
    realType *a = work, *b = work + p->m;
    lob_bnd_lines( p, u, a, b );
    bnd[ 0 ] = a[ 0 ], bnd[ 1 ] = b[ 0 ];
    for( j = 1; j < p->m; ++j )
    {
        if( a[ j ] < bnd[ 0 ] ) bnd[ 0 ] = a[ j ];
        if( b[ j ] > bnd[ 1 ] ) bnd[ 1 ] = b[ j ];
    }
}

static void lob_bnd_2	(	const lob_bnd_base *	pr,
		const lob_bnd_ext *	ps,
		const realType *	u,
		realType	bnd[2],
		realType *	work
	)		[static]

Definition at line 200 of file findpt.c.

References lob_bnd_ext::b, b, b1, lob_bnd_base::h, lob_bnd_lines(), lob_bnd_base::m, lob_bnd_base::n, nr, lob_bnd_ext::ovn, lob_bnd_ext::ovp, lob_bnd_base::Q0, lob_bnd_base::Q1, t, lob_bnd_ext::uvn, lob_bnd_ext::uvp, and lob_bnd_base::z.

Referenced by obbox_side_3().

{
    unsigned  nr = pr->n, mr = pr->m, ns = ps->b.n, ms = ps->b.m;
    realType *a0 = work, *a1 = a0 + mr, *ar_ = a1 + mr, *ar = ar_, *br_ = ar + mr * ns, *br = br_, *a_ = br + mr * ns,
             *a = a_, *b_ = a + mr * ms, *b = b_, *uvp, *ovp, *uvn, *ovn;
    realType b0, b1;
    unsigned i, j, k;
    for( i = 0; i < mr; ++i )
        a0[ i ] = a1[ i ] = 0;
    for( j = 0; j < ns; ++j, u += nr )
    {
        realType q0 = ps->b.Q0[ j ], q1 = ps->b.Q1[ j ];
        lob_bnd_lines( pr, u, ar, br );
        for( i = 0; i < mr; ++i )
        {
            realType t = ( *ar++ + *br++ ) / 2;
            a0[ i ] += q0 * t, a1[ i ] += q1 * t;
        }
    }
    for( i = 0; i < mr; ++i )
    {
        realType a0i = a0[ i ], a1i = a1[ i ];
        for( k = 0; k < ms; ++k )
            *b++ = *a++ = a0i + a1i * ps->b.h[ k ];
    }
    ar = ar_, br = br_;
    uvp = ps->uvp, ovp = ps->ovp, uvn = ps->uvn, ovn = ps->ovn;
    for( j = 0; j < ns; ++j, uvp += ms, uvn += ms, ovp += ms, ovn += ms )
    {
        realType zj = ps->b.z[ j ];
        a = a_, b = b_;
        for( i = 0; i < mr; ++i )
        {
            realType t = a0[ i ] + a1[ i ] * zj;
            realType uw = *ar++ - t;
            realType ow = *br++ - t;
            if( uw >= 0 ) /* 0  <= uw <= ow */
                for( k = 0; k < ms; ++k )
                    *a++ += uw * uvp[ k ] + ow * uvn[ k ], *b++ += ow * ovp[ k ] + uw * ovn[ k ];
            else if( ow <= 0 ) /* uw <= ow <= 0  */
                for( k = 0; k < ms; ++k )
                    *a++ += uw * ovp[ k ] + ow * ovn[ k ], *b++ += ow * uvp[ k ] + uw * uvn[ k ];
            else /* uw <  0  <  ow */
                for( k = 0; k < ms; ++k )
                    *a++ += uw * ovp[ k ] + ow * uvn[ k ], *b++ += ow * ovp[ k ] + uw * uvn[ k ];
        }
    }
    b0 = a_[ 0 ], b1 = b_[ 0 ];
    for( i = 1; i < mr * ms; ++i )
    {
        if( a_[ i ] < b0 ) b0 = a_[ i ];
        if( b_[ i ] > b1 ) b1 = b_[ i ];
    }
    bnd[ 0 ] = b0, bnd[ 1 ] = b1;
}

static void lob_bnd_base_alloc	(	lob_bnd_base *	p,
		unsigned	n,
		unsigned	m
	)		[static]

Definition at line 80 of file findpt.c.

References lob_bnd_base::h, lob_bnd_base::m, lob_bnd_base::n, n, lob_bnd_base::ov, lob_bnd_base::Q0, lob_bnd_base::Q1, tmalloc, and lob_bnd_base::uv.

Referenced by obbox_data_alloc_2(), and obbox_data_alloc_3().

{
    p->n = n, p->m = m;
    p->Q0 = tmalloc( realType, 2 * n + m + 2 * n * m );
    p->Q1 = p->Q0 + n;
    p->h = p->Q1 + n;
    p->uv = p->h + m;
    p->ov = p->uv + n * m;
}

static void lob_bnd_base_free

(

lob_bnd_base *

p

)

[static]

Definition at line 90 of file findpt.c.

References lob_bnd_base::Q0.

Referenced by obbox_data_free_2(), and obbox_data_free_3().

{
    free( p->Q0 );
}

static void lob_bnd_base_setup	(	lob_bnd_base *	p,
		const realType *	z,
		const realType *	w
	)		[static]

Definition at line 114 of file findpt.c.

References lob_bnd_base::h, lagrange_weights_deriv(), lob_bnd_base::m, mbcos, MOAB_POLY_PI, lob_bnd_base::n, n, lob_bnd_base::ov, lob_bnd_base::Q0, lob_bnd_base::Q1, tmalloc, lob_bnd_base::uv, z, and lob_bnd_base::z.

Referenced by lob_bnd_ext_setup(), obbox_setup_2(), and obbox_setup_3().

{
    unsigned  i, j, m = p->m, n = p->n, mm = 2 * m - 1;
    realType *q = tmalloc( realType, ( 2 * n + 1 ) * mm + 6 * n ), *J = q + mm, *D = J + n * mm, *work = D + n * mm;
    p->z = z;
    for( i = 0; i < n; ++i )
        p->Q0[ i ] = w[ i ] / 2, p->Q1[ i ] = 3 * p->Q0[ i ] * z[ i ];
    p->h[ 0 ] = -1, p->h[ m - 1 ] = 1;
    for( j = 1; j < m - 1; ++j )
        p->h[ j ] = mbcos( ( m - j - 1 ) * MOAB_POLY_PI / ( m - 1 ) );
    for( j = 0; j < m - 1; ++j )
        q[ 2 * j ] = p->h[ j ], q[ 2 * j + 1 ] = ( p->h[ j ] + p->h[ j + 1 ] ) / 2;
    q[ mm - 1 ] = p->h[ m - 1 ];
    lagrange_weights_deriv( z, n, q, mm, J, D, work );
    for( i = 0; i < n; ++i )
    {
        realType *uv = p->uv + i * m, *ov = p->ov + i * m;
        ov[ 0 ] = uv[ 0 ] = J[ i ];
        ov[ m - 1 ] = uv[ m - 1 ] = J[ ( mm - 1 ) * n + i ];
        for( j = 1; j < m - 1; ++j )
        {
            unsigned jj = 2 * j;
            realType c0 = J[ ( jj - 1 ) * n + i ] + ( q[ jj ] - q[ jj - 1 ] ) * D[ ( jj - 1 ) * n + i ];
            realType c1 = J[ ( jj + 1 ) * n + i ] + ( q[ jj ] - q[ jj + 1 ] ) * D[ ( jj + 1 ) * n + i ];
            realType c2 = J[ jj * n + i ];
            rminmax_3( &uv[ j ], &ov[ j ], c0, c1, c2 );
        }
    }
    free( q );
}

static void lob_bnd_ext_alloc	(	lob_bnd_ext *	p,
		unsigned	n,
		unsigned	m
	)		[static]

Definition at line 95 of file findpt.c.

References lob_bnd_ext::b, lob_bnd_base::h, lob_bnd_base::m, lob_bnd_base::n, n, lob_bnd_base::ov, lob_bnd_ext::ovn, lob_bnd_ext::ovp, lob_bnd_base::Q0, lob_bnd_base::Q1, tmalloc, lob_bnd_base::uv, lob_bnd_ext::uvn, and lob_bnd_ext::uvp.

Referenced by obbox_data_alloc_3().

{
    p->b.n = n, p->b.m = m;
    p->b.Q0 = tmalloc( realType, 2 * n + m + 6 * n * m );
    p->b.Q1 = p->b.Q0 + n;
    p->b.h = p->b.Q1 + n;
    p->b.uv = p->b.h + m;
    p->b.ov = p->b.uv + n * m;
    p->uvp = p->b.ov + n * m;
    p->uvn = p->uvp + n * m;
    p->ovp = p->uvn + n * m;
    p->ovn = p->ovp + n * m;
}

static void lob_bnd_ext_free

(

lob_bnd_ext *

p

)

[static]

Definition at line 109 of file findpt.c.

References lob_bnd_ext::b, and lob_bnd_base::Q0.

Referenced by obbox_data_free_3().

{
    free( p->b.Q0 );
}

static void lob_bnd_ext_setup	(	lob_bnd_ext *	p,
		const realType *	z,
		const realType *	w
	)		[static]

Definition at line 145 of file findpt.c.

References lob_bnd_ext::b, lob_bnd_base_setup(), lob_bnd_base::m, lob_bnd_base::n, lob_bnd_base::ov, lob_bnd_ext::ovn, lob_bnd_ext::ovp, lob_bnd_base::uv, lob_bnd_ext::uvn, and lob_bnd_ext::uvp.

Referenced by obbox_setup_3().

{
    unsigned i, mn = p->b.m * p->b.n;
    lob_bnd_base_setup( &p->b, z, w );
    for( i = 0; i < mn; ++i )
    {
        realType uvi = p->b.uv[ i ], ovi = p->b.ov[ i ];
        p->uvp[ i ] = p->uvn[ i ] = p->ovp[ i ] = p->ovn[ i ] = 0;
        if( uvi > 0 )
            p->uvp[ i ] = uvi;
        else
            p->uvn[ i ] = uvi;
        if( ovi > 0 )
            p->ovp[ i ] = ovi;
        else
            p->ovn[ i ] = ovi;
    }
}

static void lob_bnd_lines	(	const lob_bnd_base *	p,
		const realType *	u,
		realType *	a,
		realType *	b
	)		[static]

Definition at line 164 of file findpt.c.

References lob_bnd_base::h, lob_bnd_base::m, lob_bnd_base::n, lob_bnd_base::ov, lob_bnd_base::Q0, lob_bnd_base::Q1, lob_bnd_base::uv, and lob_bnd_base::z.

Referenced by lob_bnd_1(), and lob_bnd_2().

{
    unsigned        i, j;
    realType        a0 = 0, a1 = 0;
    const realType *uv = p->uv, *ov = p->ov;
    for( i = 0; i < p->n; ++i )
        a0 += p->Q0[ i ] * u[ i ], a1 += p->Q1[ i ] * u[ i ];
    for( j = 0; j < p->m; ++j )
        b[ j ] = a[ j ] = a0 + a1 * p->h[ j ];
    for( i = 0; i < p->n; ++i )
    {
        realType w = u[ i ] - ( a0 + a1 * p->z[ i ] );
        if( w >= 0 )
            for( j = 0; j < p->m; ++j )
                a[ j ] += w * ( *uv++ ), b[ j ] += w * ( *ov++ );
        else
            for( j = 0; j < p->m; ++j )
                a[ j ] += w * ( *ov++ ), b[ j ] += w * ( *uv++ );
    }
}

static void mat_app_2c	(	realType	y[2],
		const realType	A[4],
		const realType	x[2]
	)		[static]

Definition at line 291 of file findpt.c.

Referenced by opt_findpt_2().

{
    y[ 0 ] = A[ 0 ] * x[ 0 ] + A[ 2 ] * x[ 1 ];
    y[ 1 ] = A[ 1 ] * x[ 0 ] + A[ 3 ] * x[ 1 ];
}

static void mat_app_2r	(	realType	y[2],
		const realType	A[4],
		const realType	x[2]
	)		[static]

Definition at line 285 of file findpt.c.

Referenced by tinyla_solve_2().

{
    y[ 0 ] = A[ 0 ] * x[ 0 ] + A[ 1 ] * x[ 1 ];
    y[ 1 ] = A[ 2 ] * x[ 0 ] + A[ 3 ] * x[ 1 ];
}

static void mat_app_3c	(	realType	y[3],
		const realType	A[9],
		const realType	x[3]
	)		[static]

Definition at line 304 of file findpt.c.

Referenced by opt_findpt_3().

{
    y[ 0 ] = A[ 0 ] * x[ 0 ] + A[ 3 ] * x[ 1 ] + A[ 6 ] * x[ 2 ];
    y[ 1 ] = A[ 1 ] * x[ 0 ] + A[ 4 ] * x[ 1 ] + A[ 7 ] * x[ 2 ];
    y[ 2 ] = A[ 2 ] * x[ 0 ] + A[ 5 ] * x[ 1 ] + A[ 8 ] * x[ 2 ];
}

static void mat_app_3r	(	realType	y[3],
		const realType	A[9],
		const realType	x[3]
	)		[static]

Definition at line 297 of file findpt.c.

Referenced by tinyla_solve_3().

{
    y[ 0 ] = A[ 0 ] * x[ 0 ] + A[ 1 ] * x[ 1 ] + A[ 2 ] * x[ 2 ];
    y[ 1 ] = A[ 3 ] * x[ 0 ] + A[ 4 ] * x[ 1 ] + A[ 5 ] * x[ 2 ];
    y[ 2 ] = A[ 6 ] * x[ 0 ] + A[ 7 ] * x[ 1 ] + A[ 8 ] * x[ 2 ];
}

static void mat_inv_2	(	const realType	A[4],
		realType	inv[4]
	)		[static]

Definition at line 261 of file findpt.c.

Referenced by obbox_calc_2(), and tinyla_solve_2().

{
    const realType idet = 1 / ( A[ 0 ] * A[ 3 ] - A[ 1 ] * A[ 2 ] );
    inv[ 0 ] = idet * A[ 3 ];
    inv[ 1 ] = -( idet * A[ 1 ] );
    inv[ 2 ] = -( idet * A[ 2 ] );
    inv[ 3 ] = idet * A[ 0 ];
}

static void mat_inv_3	(	const realType	A[9],
		realType	inv[9]
	)		[static]

Definition at line 270 of file findpt.c.

References b.

Referenced by obbox_calc_3(), and tinyla_solve_3().

{
    const realType a = A[ 4 ] * A[ 8 ] - A[ 5 ] * A[ 7 ], b = A[ 5 ] * A[ 6 ] - A[ 3 ] * A[ 8 ],
                   c = A[ 3 ] * A[ 7 ] - A[ 4 ] * A[ 6 ], idet = 1 / ( A[ 0 ] * a + A[ 1 ] * b + A[ 2 ] * c );
    inv[ 0 ] = idet * a;
    inv[ 1 ] = idet * ( A[ 2 ] * A[ 7 ] - A[ 1 ] * A[ 8 ] );
    inv[ 2 ] = idet * ( A[ 1 ] * A[ 5 ] - A[ 2 ] * A[ 4 ] );
    inv[ 3 ] = idet * b;
    inv[ 4 ] = idet * ( A[ 0 ] * A[ 8 ] - A[ 2 ] * A[ 6 ] );
    inv[ 5 ] = idet * ( A[ 2 ] * A[ 3 ] - A[ 0 ] * A[ 5 ] );
    inv[ 6 ] = idet * c;
    inv[ 7 ] = idet * ( A[ 1 ] * A[ 6 ] - A[ 0 ] * A[ 7 ] );
    inv[ 8 ] = idet * ( A[ 0 ] * A[ 4 ] - A[ 1 ] * A[ 3 ] );
}

int obbox_axis_test_2	(	const obbox_2 *	p,
		const realType	x[2]
	)

Definition at line 497 of file findpt.c.

References obbox_2::axis_bnd.

Referenced by findpt_guess_2(), and findpt_hash_2().

{
    return ( x[ 0 ] < p->axis_bnd[ 0 ] || x[ 0 ] > p->axis_bnd[ 1 ] || x[ 1 ] < p->axis_bnd[ 2 ] ||
             x[ 1 ] > p->axis_bnd[ 3 ] );
}

int obbox_axis_test_3	(	const obbox_3 *	p,
		const realType	x[3]
	)

Definition at line 503 of file findpt.c.

References obbox_3::axis_bnd.

Referenced by findpt_guess_3(), and findpt_hash_3().

{
    return ( x[ 0 ] < p->axis_bnd[ 0 ] || x[ 0 ] > p->axis_bnd[ 1 ] || x[ 1 ] < p->axis_bnd[ 2 ] ||
             x[ 1 ] > p->axis_bnd[ 3 ] || x[ 2 ] < p->axis_bnd[ 4 ] || x[ 2 ] > p->axis_bnd[ 5 ] );
}

void obbox_bnd_2	(	const obbox_data_2 *	p,
		const realType *	x,
		const realType *	y,
		const realType	c0[2],
		const realType	A[4],
		realType	bnd[4]
	)

Definition at line 605 of file findpt.c.

References obbox_data_2::dr, obbox_data_2::ds, lob_bnd_base::n, nr, obbox_merge_2(), obbox_side_2(), and obbox_data_2::work.

Referenced by obbox_calc_2().

{
    unsigned i, nr = p->dr.n, ns = p->ds.n;
    realType obnd[ 4 ];

    i = nr * ( ns - 1 );
    obbox_side_2( x, y, nr, 1, c0, A, p->work, &p->dr, bnd );
    obbox_side_2( x + i, y + i, nr, 1, c0, A, p->work, &p->dr, obnd );
    obbox_merge_2( bnd, obnd );

    i = nr - 1;
    obbox_side_2( x, y, ns, nr, c0, A, p->work, &p->ds, obnd );
    obbox_merge_2( bnd, obnd );
    obbox_side_2( x + i, y + i, nr, nr, c0, A, p->work, &p->ds, obnd );
    obbox_merge_2( bnd, obnd );
}

void obbox_bnd_3	(	const obbox_data_3 *	p,
		const realType *	x,
		const realType *	y,
		const realType *	z,
		const realType	c0[3],
		const realType	A[9],
		realType	bnd[6]
	)

Definition at line 627 of file findpt.c.

References lob_bnd_ext::b, obbox_data_3::dr, obbox_data_3::ds, obbox_data_3::dt, lob_bnd_base::n, nr, obbox_merge_3(), obbox_side_3(), and obbox_data_3::work.

Referenced by obbox_calc_3().

{
    unsigned i, nr = p->dr.n, ns = p->ds.b.n, nt = p->dt.b.n;
    realType obnd[ 6 ];

    i = nr * ns * ( nt - 1 );
    obbox_side_3( x, y, z, nr, 1, ns, 0, c0, A, p->work, &p->dr, &p->ds, bnd );
    obbox_side_3( x + i, y + i, z + i, nr, 1, ns, 0, c0, A, p->work, &p->dr, &p->ds, obnd );
    obbox_merge_3( bnd, obnd );

    i = nr * ( ns - 1 );
    obbox_side_3( x, y, z, nr, 1, nt, i, c0, A, p->work, &p->dr, &p->dt, obnd );
    obbox_merge_3( bnd, obnd );
    obbox_side_3( x + i, y + i, z + i, nr, 1, nt, i, c0, A, p->work, &p->dr, &p->dt, obnd );
    obbox_merge_3( bnd, obnd );

    i = nr - 1;
    obbox_side_3( x, y, z, ns, nr, nt, 0, c0, A, p->work, &p->ds.b, &p->dt, obnd );
    obbox_merge_3( bnd, obnd );
    obbox_side_3( x + i, y + i, z + i, ns, nr, nt, 0, c0, A, p->work, &p->ds.b, &p->dt, obnd );
    obbox_merge_3( bnd, obnd );
}

void obbox_calc_2	(	const obbox_data_2 *	p,
		realType	tol,
		const realType *	x,
		const realType *	y,
		obbox_2 *	b
	)

Definition at line 651 of file findpt.c.

References obbox_2::A, obbox_2::axis_bnd, obbox_data_2::dr, obbox_data_2::Dr0, obbox_data_2::ds, obbox_data_2::Ds0, MBMesquite::inv(), obbox_data_2::Jr0, obbox_data_2::Js0, mat_inv_2(), lob_bnd_base::n, obbox_bnd_2(), tensor_ig2(), obbox_data_2::work, and obbox_2::x.

Referenced by hash_getbb_2().

{
    const realType zero[ 2 ] = { 0, 0 }, id[ 4 ] = { 1, 0, 0, 1 };
    realType       c0[ 2 ], jac[ 4 ], inv[ 4 ], bnd[ 4 ], u0[ 2 ], d[ 2 ];

    obbox_bnd_2( p, x, y, zero, id, b->axis_bnd );
    d[ 0 ] = b->axis_bnd[ 1 ] - b->axis_bnd[ 0 ];
    d[ 1 ] = b->axis_bnd[ 3 ] - b->axis_bnd[ 2 ];
    b->axis_bnd[ 0 ] -= tol * d[ 0 ], b->axis_bnd[ 1 ] += tol * d[ 0 ];
    b->axis_bnd[ 2 ] -= tol * d[ 1 ], b->axis_bnd[ 3 ] += tol * d[ 1 ];

    c0[ 0 ] = tensor_ig2( p->Jr0, p->Dr0, p->dr.n, p->Js0, p->Ds0, p->ds.n, x, jac, p->work );
    c0[ 1 ] = tensor_ig2( p->Jr0, p->Dr0, p->dr.n, p->Js0, p->Ds0, p->ds.n, y, jac + 2, p->work );
    mat_inv_2( jac, inv );

    obbox_bnd_2( p, x, y, c0, inv, bnd );

    u0[ 0 ] = ( bnd[ 0 ] + bnd[ 1 ] ) / 2;
    u0[ 1 ] = ( bnd[ 2 ] + bnd[ 3 ] ) / 2;
    d[ 0 ] = 2 / ( ( 1 + tol ) * ( bnd[ 1 ] - bnd[ 0 ] ) );
    d[ 1 ] = 2 / ( ( 1 + tol ) * ( bnd[ 3 ] - bnd[ 2 ] ) );
    b->x[ 0 ] = c0[ 0 ] + jac[ 0 ] * u0[ 0 ] + jac[ 1 ] * u0[ 1 ];
    b->x[ 1 ] = c0[ 1 ] + jac[ 2 ] * u0[ 0 ] + jac[ 3 ] * u0[ 1 ];
    b->A[ 0 ] = d[ 0 ] * inv[ 0 ], b->A[ 1 ] = d[ 0 ] * inv[ 1 ];
    b->A[ 2 ] = d[ 1 ] * inv[ 2 ], b->A[ 3 ] = d[ 1 ] * inv[ 3 ];
}

void obbox_calc_3	(	const obbox_data_3 *	p,
		realType	tol,
		const realType *	x,
		const realType *	y,
		const realType *	z,
		obbox_3 *	b
	)

Definition at line 678 of file findpt.c.

References obbox_3::A, obbox_3::axis_bnd, lob_bnd_ext::b, obbox_data_3::dr, obbox_data_3::Dr0, obbox_data_3::ds, obbox_data_3::Ds0, obbox_data_3::dt, obbox_data_3::Dt0, MBMesquite::inv(), obbox_data_3::Jr0, obbox_data_3::Js0, obbox_data_3::Jt0, mat_inv_3(), lob_bnd_base::n, obbox_bnd_3(), tensor_ig3(), obbox_data_3::work, and obbox_3::x.

Referenced by hash_getbb_3().

{
    const realType zero[ 3 ] = { 0, 0 }, id[ 9 ] = { 1, 0, 0, 0, 1, 0, 0, 0, 1 };
    realType       c0[ 3 ], jac[ 9 ], inv[ 9 ], bnd[ 6 ], u0[ 3 ], d[ 3 ];

    obbox_bnd_3( p, x, y, z, zero, id, b->axis_bnd );
    d[ 0 ] = b->axis_bnd[ 1 ] - b->axis_bnd[ 0 ];
    d[ 1 ] = b->axis_bnd[ 3 ] - b->axis_bnd[ 2 ];
    d[ 2 ] = b->axis_bnd[ 5 ] - b->axis_bnd[ 4 ];
    b->axis_bnd[ 0 ] -= tol * d[ 0 ], b->axis_bnd[ 1 ] += tol * d[ 0 ];
    b->axis_bnd[ 2 ] -= tol * d[ 1 ], b->axis_bnd[ 3 ] += tol * d[ 1 ];
    b->axis_bnd[ 4 ] -= tol * d[ 2 ], b->axis_bnd[ 5 ] += tol * d[ 2 ];

    c0[ 0 ] =
        tensor_ig3( p->Jr0, p->Dr0, p->dr.n, p->Js0, p->Ds0, p->ds.b.n, p->Jt0, p->Dt0, p->dt.b.n, x, jac, p->work );
    c0[ 1 ] = tensor_ig3( p->Jr0, p->Dr0, p->dr.n, p->Js0, p->Ds0, p->ds.b.n, p->Jt0, p->Dt0, p->dt.b.n, y, jac + 3,
                          p->work );
    c0[ 2 ] = tensor_ig3( p->Jr0, p->Dr0, p->dr.n, p->Js0, p->Ds0, p->ds.b.n, p->Jt0, p->Dt0, p->dt.b.n, z, jac + 6,
                          p->work );
    mat_inv_3( jac, inv );

    obbox_bnd_3( p, x, y, z, c0, inv, bnd );

    u0[ 0 ] = ( bnd[ 0 ] + bnd[ 1 ] ) / 2;
    u0[ 1 ] = ( bnd[ 2 ] + bnd[ 3 ] ) / 2;
    u0[ 2 ] = ( bnd[ 4 ] + bnd[ 5 ] ) / 2;
    d[ 0 ] = 2 / ( ( 1 + tol ) * ( bnd[ 1 ] - bnd[ 0 ] ) );
    d[ 1 ] = 2 / ( ( 1 + tol ) * ( bnd[ 3 ] - bnd[ 2 ] ) );
    d[ 2 ] = 2 / ( ( 1 + tol ) * ( bnd[ 5 ] - bnd[ 4 ] ) );
    b->x[ 0 ] = c0[ 0 ] + jac[ 0 ] * u0[ 0 ] + jac[ 1 ] * u0[ 1 ] + jac[ 2 ] * u0[ 2 ];
    b->x[ 1 ] = c0[ 1 ] + jac[ 3 ] * u0[ 0 ] + jac[ 4 ] * u0[ 1 ] + jac[ 5 ] * u0[ 2 ];
    b->x[ 2 ] = c0[ 2 ] + jac[ 6 ] * u0[ 0 ] + jac[ 7 ] * u0[ 1 ] + jac[ 8 ] * u0[ 2 ];
    b->A[ 0 ] = d[ 0 ] * inv[ 0 ], b->A[ 1 ] = d[ 0 ] * inv[ 1 ], b->A[ 2 ] = d[ 0 ] * inv[ 2 ];
    b->A[ 3 ] = d[ 1 ] * inv[ 3 ], b->A[ 4 ] = d[ 1 ] * inv[ 4 ], b->A[ 5 ] = d[ 1 ] * inv[ 5 ];
    b->A[ 6 ] = d[ 2 ] * inv[ 6 ], b->A[ 7 ] = d[ 2 ] * inv[ 7 ], b->A[ 8 ] = d[ 2 ] * inv[ 8 ];
}

void obbox_calc_tfm_2	(	const realType *	x,
		const realType *	y,
		unsigned	n,
		unsigned	s,
		const realType	c0[2],
		const realType	A[4],
		realType *	u
	)

Definition at line 534 of file findpt.c.

References n.

Referenced by obbox_side_2().

{
    unsigned  i;
    realType* v = u + n;
    for( i = 0; i < n; ++i, x += s, y += s )
    {
        const realType xt = *x - c0[ 0 ], yt = *y - c0[ 1 ];
        u[ i ] = A[ 0 ] * xt + A[ 1 ] * yt;
        v[ i ] = A[ 2 ] * xt + A[ 3 ] * yt;
    }
}

void obbox_calc_tfm_3	(	const realType *	x,
		const realType *	y,
		const realType *	z,
		unsigned	nr,
		unsigned	sr,
		unsigned	ns,
		unsigned	ss,
		const realType	c0[3],
		const realType	A[9],
		realType *	u
	)

Definition at line 547 of file findpt.c.

References nr.

Referenced by obbox_side_3().

{
    unsigned  i, j;
    realType *v = u + nr * ns, *w = v + nr * ns;
    for( j = 0; j < ns; ++j, x += ss, y += ss, z += ss )
    {
        for( i = 0; i < nr; ++i, x += sr, y += sr, z += sr )
        {
            const realType xt = *x - c0[ 0 ], yt = *y - c0[ 1 ], zt = *z - c0[ 2 ];
            *u++ = A[ 0 ] * xt + A[ 1 ] * yt + A[ 2 ] * zt;
            *v++ = A[ 3 ] * xt + A[ 4 ] * yt + A[ 5 ] * zt;
            *w++ = A[ 6 ] * xt + A[ 7 ] * yt + A[ 8 ] * zt;
        }
    }
}

static void obbox_data_alloc_2	(	obbox_data_2 *	p,
		const unsigned	n[2],
		const unsigned	m[2]
	)		[static]

Definition at line 406 of file findpt.c.

References obbox_data_2::dr, obbox_data_2::Dr0, obbox_data_2::ds, obbox_data_2::Ds0, obbox_data_2::Jr0, obbox_data_2::Js0, lob_bnd_base_alloc(), tmalloc, umax_2, and obbox_data_2::work.

Referenced by obbox_setup_2().

{
    const unsigned max_npm = umax_2( n[ 0 ] + m[ 0 ], n[ 1 ] + m[ 1 ] );
    lob_bnd_base_alloc( &p->dr, n[ 0 ], m[ 0 ] );
    lob_bnd_base_alloc( &p->ds, n[ 1 ], m[ 1 ] );
    p->Jr0 = tmalloc( realType, 2 * n[ 0 ] + 2 * n[ 1 ] + 2 * max_npm );
    p->Dr0 = p->Jr0 + n[ 0 ];
    p->Js0 = p->Dr0 + n[ 0 ];
    p->Ds0 = p->Js0 + n[ 1 ];
    p->work = p->Ds0 + n[ 1 ];
}

static void obbox_data_alloc_3	(	obbox_data_3 *	p,
		const unsigned	n[3],
		const unsigned	m[3]
	)		[static]

Definition at line 425 of file findpt.c.

References obbox_data_3::dr, obbox_data_3::Dr0, obbox_data_3::ds, obbox_data_3::Ds0, obbox_data_3::dt, obbox_data_3::Dt0, obbox_data_3::Jr0, obbox_data_3::Js0, obbox_data_3::Jt0, lob_bnd_base_alloc(), lob_bnd_ext_alloc(), tmalloc, and obbox_data_3::work.

Referenced by obbox_setup_3().

{
    const unsigned wk1 = 3 * n[ 0 ] * n[ 1 ] + 2 * m[ 0 ] + 2 * m[ 0 ] * n[ 1 ] + 2 * m[ 0 ] * m[ 1 ];
    const unsigned wk2 = 3 * n[ 0 ] * n[ 2 ] + 2 * m[ 0 ] + 2 * m[ 0 ] * n[ 2 ] + 2 * m[ 0 ] * m[ 2 ];
    const unsigned wk3 = 3 * n[ 1 ] * n[ 2 ] + 2 * m[ 1 ] + 2 * m[ 1 ] * n[ 2 ] + 2 * m[ 1 ] * m[ 2 ];
    const unsigned wk_max = umax_3( wk1, wk2, wk3 );
    lob_bnd_base_alloc( &p->dr, n[ 0 ], m[ 0 ] );
    lob_bnd_ext_alloc( &p->ds, n[ 1 ], m[ 1 ] );
    lob_bnd_ext_alloc( &p->dt, n[ 2 ], m[ 2 ] );
    p->Jr0 = tmalloc( realType, 2 * n[ 0 ] + 2 * n[ 1 ] + 2 * n[ 2 ] + wk_max );
    p->Dr0 = p->Jr0 + n[ 0 ];
    p->Js0 = p->Dr0 + n[ 0 ];
    p->Ds0 = p->Js0 + n[ 1 ];
    p->Jt0 = p->Ds0 + n[ 1 ];
    p->Dt0 = p->Jt0 + n[ 2 ];
    p->work = p->Dt0 + n[ 2 ];
}

static void obbox_data_free_2

(

obbox_data_2 *

p

)

[static]

Definition at line 418 of file findpt.c.

References obbox_data_2::dr, obbox_data_2::ds, obbox_data_2::Jr0, and lob_bnd_base_free().

Referenced by obbox_free_2().

{
    lob_bnd_base_free( &p->dr );
    lob_bnd_base_free( &p->ds );
    free( p->Jr0 );
}

static void obbox_data_free_3

(

obbox_data_3 *

p

)

[static]

Definition at line 443 of file findpt.c.

References obbox_data_3::dr, obbox_data_3::ds, obbox_data_3::dt, obbox_data_3::Jr0, lob_bnd_base_free(), and lob_bnd_ext_free().

Referenced by obbox_free_3().

{
    lob_bnd_base_free( &p->dr );
    lob_bnd_ext_free( &p->ds );
    lob_bnd_ext_free( &p->dt );
    free( p->Jr0 );
}

static void obbox_free_2

(

obbox_data_2 *

p

)

[static]

Definition at line 485 of file findpt.c.

References obbox_data_free_2().

Referenced by hash_getbb_2().

{
    obbox_data_free_2( p );
    free( p );
}

static void obbox_free_3

(

obbox_data_3 *

p

)

[static]

Definition at line 491 of file findpt.c.

References obbox_data_free_3().

Referenced by hash_getbb_3().

{
    obbox_data_free_3( p );
    free( p );
}

void obbox_merge_2	(	realType *	b,
		const realType *	ob
	)

Definition at line 564 of file findpt.c.

Referenced by hash_getbb_2(), and obbox_bnd_2().

{
    if( ob[ 0 ] < b[ 0 ] ) b[ 0 ] = ob[ 0 ];
    if( ob[ 1 ] > b[ 1 ] ) b[ 1 ] = ob[ 1 ];
    if( ob[ 2 ] < b[ 2 ] ) b[ 2 ] = ob[ 2 ];
    if( ob[ 3 ] > b[ 3 ] ) b[ 3 ] = ob[ 3 ];
}

void obbox_merge_3	(	realType *	b,
		const realType *	ob
	)

Definition at line 572 of file findpt.c.

Referenced by hash_getbb_3(), and obbox_bnd_3().

{
    if( ob[ 0 ] < b[ 0 ] ) b[ 0 ] = ob[ 0 ];
    if( ob[ 1 ] > b[ 1 ] ) b[ 1 ] = ob[ 1 ];
    if( ob[ 2 ] < b[ 2 ] ) b[ 2 ] = ob[ 2 ];
    if( ob[ 3 ] > b[ 3 ] ) b[ 3 ] = ob[ 3 ];
    if( ob[ 4 ] < b[ 4 ] ) b[ 4 ] = ob[ 4 ];
    if( ob[ 5 ] > b[ 5 ] ) b[ 5 ] = ob[ 5 ];
}

static obbox_data_2* obbox_setup_2	(	const realType *const	z[2],
		const realType *const	w[2],
		const unsigned	n[2],
		const unsigned	m[2]
	)		[static]

Definition at line 451 of file findpt.c.

References obbox_data_2::dr, obbox_data_2::Dr0, obbox_data_2::ds, obbox_data_2::Ds0, obbox_data_2::Jr0, obbox_data_2::Js0, lagrange_weights_deriv(), lob_bnd_base_setup(), obbox_data_alloc_2(), tmalloc, and umax_2.

Referenced by hash_getbb_2().

{
    const realType zero = 0;
    realType*      work;
    obbox_data_2*  p = tmalloc( obbox_data_2, 1 );
    obbox_data_alloc_2( p, n, m );
    lob_bnd_base_setup( &p->dr, z[ 0 ], w[ 0 ] );
    lob_bnd_base_setup( &p->ds, z[ 1 ], w[ 1 ] );
    work = tmalloc( realType, 6 * umax_2( n[ 0 ], n[ 1 ] ) );
    lagrange_weights_deriv( z[ 0 ], n[ 0 ], &zero, 1, p->Jr0, p->Dr0, work );
    lagrange_weights_deriv( z[ 1 ], n[ 1 ], &zero, 1, p->Js0, p->Ds0, work );
    free( work );
    return p;
}

static obbox_data_3* obbox_setup_3	(	const realType *const	z[3],
		const realType *const	w[3],
		const unsigned	n[3],
		const unsigned	m[3]
	)		[static]

Definition at line 467 of file findpt.c.

References obbox_data_3::dr, obbox_data_3::Dr0, obbox_data_3::ds, obbox_data_3::Ds0, obbox_data_3::dt, obbox_data_3::Dt0, obbox_data_3::Jr0, obbox_data_3::Js0, obbox_data_3::Jt0, lagrange_weights_deriv(), lob_bnd_base_setup(), lob_bnd_ext_setup(), obbox_data_alloc_3(), and tmalloc.

Referenced by hash_getbb_3().

{
    const realType zero = 0;
    realType*      work;
    obbox_data_3*  p = tmalloc( obbox_data_3, 1 );
    obbox_data_alloc_3( p, n, m );
    lob_bnd_base_setup( &p->dr, z[ 0 ], w[ 0 ] );
    lob_bnd_ext_setup( &p->ds, z[ 1 ], w[ 1 ] );
    lob_bnd_ext_setup( &p->dt, z[ 2 ], w[ 2 ] );
    work = tmalloc( realType, 6 * umax_3( n[ 0 ], n[ 1 ], n[ 2 ] ) );
    lagrange_weights_deriv( z[ 0 ], n[ 0 ], &zero, 1, p->Jr0, p->Dr0, work );
    lagrange_weights_deriv( z[ 1 ], n[ 1 ], &zero, 1, p->Js0, p->Ds0, work );
    lagrange_weights_deriv( z[ 2 ], n[ 2 ], &zero, 1, p->Jt0, p->Dt0, work );
    free( work );
    return p;
}

void obbox_side_2	(	const realType *	x,
		const realType *	y,
		unsigned	n,
		unsigned	s,
		const realType	c0[2],
		const realType	A[4],
		realType *	work,
		const lob_bnd_base *	lbd,
		realType	bnd[4]
	)

Definition at line 583 of file findpt.c.

References lob_bnd_1(), and obbox_calc_tfm_2().

Referenced by obbox_bnd_2().

{
    obbox_calc_tfm_2( x, y, n, s, c0, A, work );
    lob_bnd_1( lbd, work, bnd, work + 2 * n );
    lob_bnd_1( lbd, work + n, bnd + 2, work + 2 * n );
}

void obbox_side_3	(	const realType *	x,
		const realType *	y,
		const realType *	z,
		unsigned	nr,
		unsigned	sr,
		unsigned	ns,
		unsigned	ss,
		const realType	c0[3],
		const realType	A[9],
		realType *	work,
		const lob_bnd_base *	dr,
		const lob_bnd_ext *	ds,
		realType	bnd[6]
	)

Definition at line 592 of file findpt.c.

References lob_bnd_2(), and obbox_calc_tfm_3().

Referenced by obbox_bnd_3().

{
    obbox_calc_tfm_3( x, y, z, nr, sr, ns, ss, c0, A, work );
    lob_bnd_2( dr, ds, work, bnd, work + 3 * nr * ns );
    lob_bnd_2( dr, ds, work + nr * ns, bnd + 2, work + 3 * nr * ns );
    lob_bnd_2( dr, ds, work + 2 * nr * ns, bnd + 4, work + 3 * nr * ns );
}

int obbox_test_2	(	const obbox_2 *	p,
		const realType	x[2],
		realType	r[2]
	)

Definition at line 509 of file findpt.c.

References obbox_2::A, mbabs, and obbox_2::x.

Referenced by findpt_guess_2(), and findpt_hash_2().

{
    realType xt[ 2 ];
    xt[ 0 ] = x[ 0 ] - p->x[ 0 ];
    xt[ 1 ] = x[ 1 ] - p->x[ 1 ];
    r[ 0 ] = p->A[ 0 ] * xt[ 0 ] + p->A[ 1 ] * xt[ 1 ];
    if( mbabs( r[ 0 ] ) > 1 ) return 1;
    r[ 1 ] = p->A[ 2 ] * xt[ 0 ] + p->A[ 3 ] * xt[ 1 ];
    return mbabs( r[ 1 ] ) > 1;
}

int obbox_test_3	(	const obbox_3 *	p,
		const realType	x[3],
		realType	r[3]
	)

Definition at line 520 of file findpt.c.

References obbox_3::A, mbabs, and obbox_3::x.

Referenced by findpt_guess_3(), and findpt_hash_3().

{
    realType xt[ 3 ];
    xt[ 0 ] = x[ 0 ] - p->x[ 0 ];
    xt[ 1 ] = x[ 1 ] - p->x[ 1 ];
    xt[ 2 ] = x[ 2 ] - p->x[ 2 ];
    r[ 0 ] = p->A[ 0 ] * xt[ 0 ] + p->A[ 1 ] * xt[ 1 ] + p->A[ 2 ] * xt[ 2 ];
    if( mbabs( r[ 0 ] ) > 1 ) return 1;
    r[ 1 ] = p->A[ 3 ] * xt[ 0 ] + p->A[ 4 ] * xt[ 1 ] + p->A[ 5 ] * xt[ 2 ];
    if( mbabs( r[ 1 ] ) > 1 ) return 1;
    r[ 2 ] = p->A[ 6 ] * xt[ 0 ] + p->A[ 7 ] * xt[ 1 ] + p->A[ 8 ] * xt[ 2 ];
    return mbabs( r[ 2 ] ) > 1;
}

void opt_alloc_2	(	opt_data_2 *	p,
		lagrange_data *	ld
	)

Definition at line 1605 of file findpt.c.

References opt_data_2::ed, opt_edge_data_2::fd1, opt_data_2::ld, lagrange_data::n, nr, opt_data_2::size, tmalloc, umax_2, opt_data_2::work, and opt_edge_data_2::x.

Referenced by findpt_setup_2(), and moab::Element::SpectralQuad::Init().

{
    const unsigned nr = ld[ 0 ].n, ns = ld[ 1 ].n, ne = umax_2( nr, ns ), nw = 2 * ns;
    p->size[ 0 ] = 1;
    p->size[ 1 ] = nr;
    p->size[ 2 ] = nr * ns;
    p->ld = ld;
    p->work = tmalloc( realType, 4 * ne + nw );
    p->ed.x[ 0 ] = p->work + nw;
    p->ed.x[ 1 ] = p->ed.x[ 0 ] + ne;
    p->ed.fd1[ 0 ] = p->ed.x[ 1 ] + ne;
    p->ed.fd1[ 1 ] = p->ed.fd1[ 0 ] + ne;
}

void opt_alloc_3	(	opt_data_3 *	p,
		lagrange_data *	ld
	)

Definition at line 1196 of file findpt.c.

References opt_data_3::ed, opt_data_3::fd, opt_edge_data_3::fd1, opt_edge_data_3::fd2, opt_face_data_3::fdn, opt_data_3::ld, lagrange_data::n, nr, opt_data_3::size, tmalloc, opt_data_3::work, opt_face_data_3::x, and opt_edge_data_3::x.

Referenced by findpt_setup_3(), moab::ElemUtil::hex_findpt(), moab::Element::SpectralHex::Init(), moab::SpectralHex::initFcn(), and moab::element_utility::Spectral_hex_map< moab::Matrix3 >::initialize_spectral_hex().

{
    const unsigned nr = ld[ 0 ].n, ns = ld[ 1 ].n, nt = ld[ 2 ].n, nf = umax_3( nr * ns, nr * nt, ns * nt ),
                   ne = umax_3( nr, ns, nt ), nw = 2 * ns * nt + 3 * ns;
    p->size[ 0 ] = 1;
    p->size[ 1 ] = nr;
    p->size[ 2 ] = nr * ns;
    p->size[ 3 ] = p->size[ 2 ] * nt;
    p->ld = ld;
    p->work = tmalloc( realType, 6 * nf + 9 * ne + nw );
    p->fd.x[ 0 ] = p->work + nw;
    p->fd.x[ 1 ] = p->fd.x[ 0 ] + nf;
    p->fd.x[ 2 ] = p->fd.x[ 1 ] + nf;
    p->fd.fdn[ 0 ] = p->fd.x[ 2 ] + nf;
    p->fd.fdn[ 1 ] = p->fd.fdn[ 0 ] + nf;
    p->fd.fdn[ 2 ] = p->fd.fdn[ 1 ] + nf;
    p->ed.x[ 0 ] = p->fd.fdn[ 2 ] + nf;
    p->ed.x[ 1 ] = p->ed.x[ 0 ] + ne;
    p->ed.x[ 2 ] = p->ed.x[ 1 ] + ne;
    p->ed.fd1[ 0 ] = p->ed.x[ 2 ] + ne;
    p->ed.fd1[ 1 ] = p->ed.fd1[ 0 ] + ne;
    p->ed.fd1[ 2 ] = p->ed.fd1[ 1 ] + ne;
    p->ed.fd2[ 0 ] = p->ed.fd1[ 2 ] + ne;
    p->ed.fd2[ 1 ] = p->ed.fd2[ 0 ] + ne;
    p->ed.fd2[ 2 ] = p->ed.fd2[ 1 ] + ne;
}

static void opt_area_intp_2

(

opt_data_2 *

p

)

[static]

Definition at line 1631 of file findpt.c.

References opt_data_2::elx, opt_data_2::jac, opt_data_2::ld, n, tensor_ig2(), opt_data_2::work, and opt_data_2::x.

Referenced by opt_area_set_intp_2().

{
    unsigned             d;
    const lagrange_data* ld = p->ld;

    for( d = 0; d < 2; ++d )
        p->x[ d ] = tensor_ig2( ld[ 0 ].J, ld[ 0 ].D, ld[ 0 ].n, ld[ 1 ].J, ld[ 1 ].D, ld[ 1 ].n, p->elx[ d ],
                                &p->jac[ d * 2 ], p->work );
}

static void opt_area_set_2	(	opt_data_2 *	p,
		const realType	r[2]
	)		[static]

Definition at line 1624 of file findpt.c.

References lagrange_1(), and opt_data_2::ld.

Referenced by opt_area_set_intp_2().

{
    lagrange_1( &p->ld[ 0 ], r[ 0 ] );
    lagrange_1( &p->ld[ 1 ], r[ 1 ] );
}

static void opt_area_set_intp_2	(	opt_data_2 *	p,
		const realType	r[2]
	)		[static]

Definition at line 1641 of file findpt.c.

References opt_area_intp_2(), and opt_area_set_2().

Referenced by opt_findpt_2().

{
    opt_area_set_2( p, r );
    opt_area_intp_2( p );
}

static unsigned opt_constr	(	unsigned	constraints,
		unsigned	d
	)		[static]

Definition at line 1160 of file findpt.c.

References opt_constr_wide.

Referenced by opt_edge_proj_2(), opt_edge_proj_3(), and opt_face_proj_3().

{
    return ( opt_constr_wide[ constraints ] >> ( d * 2 ) ) & 3;
}

static unsigned opt_constr_pack_2

(

const unsigned *

c

)

[static]

Definition at line 1180 of file findpt.c.

Referenced by opt_findpt_2().

{
    return c[ 1 ] * 3 + c[ 0 ];
}

static unsigned opt_constr_pack_3

(

const unsigned *

c

)

[static]

Definition at line 1185 of file findpt.c.

Referenced by opt_findpt_3().

{
    return ( c[ 2 ] * 3 + c[ 1 ] ) * 3 + c[ 0 ];
}

static void opt_constr_unpack_2	(	unsigned	constraints,
		unsigned *	c
	)		[static]

Definition at line 1165 of file findpt.c.

References opt_constr_wide.

Referenced by opt_findpt_2(), and opt_point_proj_2().

{
    const char cw = opt_constr_wide[ constraints ];
    c[ 0 ] = cw & 3;
    c[ 1 ] = cw >> 2;
}

static void opt_constr_unpack_3	(	unsigned	constraints,
		unsigned *	c
	)		[static]

Definition at line 1172 of file findpt.c.

References opt_constr_wide.

Referenced by opt_findpt_3(), and opt_point_proj_3().

{
    const char cw = opt_constr_wide[ constraints ];
    c[ 0 ] = cw & 3;
    c[ 1 ] = ( cw >> 2 ) & 3;
    c[ 2 ] = cw >> 4;
}

static void opt_edge_hess_2	(	opt_data_2 *	p,
		realType	hess[2]
	)		[static]

Definition at line 1703 of file findpt.c.

References lagrange_data::D2, opt_edge_data_2::de, opt_data_2::ed, lagrange_2u(), opt_data_2::ld, n, lagrange_data::n, tensor_i1(), and opt_edge_data_2::x.

Referenced by opt_findpt_2().

{
    unsigned        d;
    const unsigned  de = p->ed.de, n = p->ld[ de ].n;
    const realType* D2 = p->ld[ de ].D2;
    lagrange_2u( &p->ld[ de ] );
    for( d = 0; d < 2; ++d )
        hess[ d ] = tensor_i1( D2, n, p->ed.x[ d ] );
}

static void opt_edge_hess_3	(	opt_data_3 *	p,
		realType	hess[3]
	)		[static]

Definition at line 1398 of file findpt.c.

References lagrange_data::D2, opt_edge_data_3::de, opt_data_3::ed, lagrange_2u(), opt_data_3::ld, n, lagrange_data::n, tensor_i1(), and opt_edge_data_3::x.

Referenced by opt_findpt_3().

{
    unsigned        d;
    const unsigned  de = p->ed.de, n = p->ld[ de ].n;
    const realType* D2 = p->ld[ de ].D2;
    lagrange_2u( &p->ld[ de ] );
    for( d = 0; d < 3; ++d )
        hess[ d ] = tensor_i1( D2, n, p->ed.x[ d ] );
}

static void opt_edge_intp_2

(

opt_data_2 *

p

)

[static]

Definition at line 1685 of file findpt.c.

References lagrange_data::D, opt_edge_data_2::d1, opt_edge_data_2::de, opt_data_2::ed, opt_edge_data_2::fd1, lagrange_data::J, opt_data_2::jac, opt_data_2::ld, n, lagrange_data::n, tensor_i1(), tensor_ig1(), opt_edge_data_2::x, and opt_data_2::x.

Referenced by opt_edge_set_intp_2().

{
    unsigned        d;
    const unsigned  de = p->ed.de, d1 = p->ed.d1, n = p->ld[ de ].n;
    const realType *J = p->ld[ de ].J, *D = p->ld[ de ].D;
    for( d = 0; d < 2; ++d )
    {
        p->x[ d ] = tensor_ig1( J, D, n, p->ed.x[ d ], &p->jac[ d * 2 + de ] );
        p->jac[ d * 2 + d1 ] = tensor_i1( J, n, p->ed.fd1[ d ] );
    }
}

static void opt_edge_intp_3

(

opt_data_3 *

p

)

[static]

Definition at line 1378 of file findpt.c.

References lagrange_data::D, opt_edge_data_3::d1, opt_edge_data_3::d2, opt_edge_data_3::de, opt_data_3::ed, opt_edge_data_3::fd1, opt_edge_data_3::fd2, lagrange_data::J, opt_data_3::jac, opt_data_3::ld, n, lagrange_data::n, tensor_i1(), tensor_ig1(), opt_edge_data_3::x, and opt_data_3::x.

Referenced by opt_edge_set_intp_3().

{
    unsigned        d;
    const unsigned  de = p->ed.de, d1 = p->ed.d1, d2 = p->ed.d2, n = p->ld[ de ].n;
    const realType *J = p->ld[ de ].J, *D = p->ld[ de ].D;

    for( d = 0; d < 3; ++d )
    {
        p->x[ d ] = tensor_ig1( J, D, n, p->ed.x[ d ], &p->jac[ d * 3 + de ] );
        p->jac[ d * 3 + d1 ] = tensor_i1( J, n, p->ed.fd1[ d ] );
        p->jac[ d * 3 + d2 ] = tensor_i1( J, n, p->ed.fd2[ d ] );
    }
}

static void opt_edge_proj_2

(

opt_data_2 *

p

)

[static]

Definition at line 1647 of file findpt.c.

References opt_edge_data_2::constraints, opt_edge_data_2::d1, lagrange_data::D_z0, lagrange_data::D_zn, opt_edge_data_2::de, opt_data_2::ed, opt_data_2::elx, opt_edge_data_2::fd1, opt_data_2::ld, lagrange_data::n, opt_constr(), opt_data_2::size, and opt_edge_data_2::x.

Referenced by opt_edge_set_2().

{
    unsigned       d, off = 0;
    const unsigned de = p->ed.de, d1 = p->ed.d1, se = p->size[ de ], s1 = p->size[ d1 ], ne = p->ld[ de ].n,
                   n1 = p->ld[ d1 ].n;
    const realType* fD1;
    if( opt_constr( p->ed.constraints, d1 ) == 0 )
        fD1 = p->ld[ d1 ].D_z0;
    else
        fD1 = p->ld[ d1 ].D_zn, off = p->size[ d1 + 1 ] - p->size[ d1 ];
    for( d = 0; d < 2; ++d )
    {
        unsigned        i, j;
        const realType* in = p->elx[ d ] + off;
        for( i = 0; i < ne; ++i, in += se )
        {
            const realType* in1 = in - off;
            realType*       fd1 = &p->ed.fd1[ d ][ i ];
            p->ed.x[ d ][ i ] = *in;
            *fd1 = 0;
            for( j = 0; j < n1; ++j, in1 += s1 )
                *fd1 += *in1 * fD1[ j ];
        }
    }
}

static void opt_edge_proj_3

(

opt_data_3 *

p

)

[static]

Definition at line 1332 of file findpt.c.

References opt_edge_data_3::constraints, opt_edge_data_3::d1, opt_edge_data_3::d2, lagrange_data::D_z0, lagrange_data::D_zn, opt_edge_data_3::de, opt_data_3::ed, opt_data_3::elx, opt_edge_data_3::fd1, opt_edge_data_3::fd2, opt_data_3::ld, lagrange_data::n, opt_constr(), opt_data_3::size, and opt_edge_data_3::x.

Referenced by opt_edge_set_3().

{
    unsigned       d, off, off1 = 0, off2 = 0;
    const unsigned de = p->ed.de, d1 = p->ed.d1, d2 = p->ed.d2, se = p->size[ de ], s1 = p->size[ d1 ],
                   s2 = p->size[ d2 ], ne = p->ld[ de ].n, n1 = p->ld[ d1 ].n, n2 = p->ld[ d2 ].n;
    const realType *fD1, *fD2;
    if( opt_constr( p->ed.constraints, d1 ) == 0 )
        fD1 = p->ld[ d1 ].D_z0;
    else
        fD1 = p->ld[ d1 ].D_zn, off1 = p->size[ d1 + 1 ] - p->size[ d1 ];
    if( opt_constr( p->ed.constraints, d2 ) == 0 )
        fD2 = p->ld[ d2 ].D_z0;
    else
        fD2 = p->ld[ d2 ].D_zn, off2 = p->size[ d2 + 1 ] - p->size[ d2 ];
    off = off1 + off2;
    for( d = 0; d < 3; ++d )
    {
        unsigned        i, j;
        const realType* in = p->elx[ d ] + off;
        for( i = 0; i < ne; ++i, in += se )
        {
            const realType *in1 = in - off1, *in2 = in - off2;
            realType *      fd1 = &p->ed.fd1[ d ][ i ], *fd2 = &p->ed.fd2[ d ][ i ];
            p->ed.x[ d ][ i ] = *in;
            *fd1 = *fd2 = 0;
            for( j = 0; j < n1; ++j, in1 += s1 )
                *fd1 += *in1 * fD1[ j ];
            for( j = 0; j < n2; ++j, in2 += s2 )
                *fd2 += *in2 * fD2[ j ];
        }
    }
}

static void opt_edge_set_2	(	opt_data_2 *	p,
		const realType	r[2],
		unsigned	constr
	)		[static]

Definition at line 1673 of file findpt.c.

References opt_edge_data_2::constraints, opt_edge_data_2::d1, opt_edge_data_2::de, opt_data_2::ed, lagrange_1(), opt_data_2::ld, opt_constr_not, and opt_edge_proj_2().

Referenced by opt_edge_set_intp_2(), and opt_findpt_2().

{
    if( p->ed.constraints != constr )
    {
        p->ed.constraints = constr;
        p->ed.de = opt_constr_not[ constr ];
        p->ed.d1 = 1 - p->ed.de;
        opt_edge_proj_2( p );
    }
    lagrange_1( &p->ld[ p->ed.de ], r[ p->ed.de ] );
}

static void opt_edge_set_3	(	opt_data_3 *	p,
		const realType	r[3],
		unsigned	constr
	)		[static]

Definition at line 1365 of file findpt.c.

References opt_edge_data_3::constraints, opt_edge_data_3::d1, opt_edge_data_3::d2, opt_edge_data_3::de, opt_data_3::ed, lagrange_1(), opt_data_3::ld, opt_constr_not, opt_edge_proj_3(), opt_other1_3, and opt_other2_3.

Referenced by opt_edge_set_intp_3(), and opt_findpt_3().

{
    if( p->ed.constraints != constr )
    {
        p->ed.constraints = constr;
        p->ed.de = opt_constr_not[ constr ];
        p->ed.d1 = opt_other1_3[ p->ed.de ];
        p->ed.d2 = opt_other2_3[ p->ed.de ];
        opt_edge_proj_3( p );
    }
    lagrange_1( &p->ld[ p->ed.de ], r[ p->ed.de ] );
}

static void opt_edge_set_intp_2	(	opt_data_2 *	p,
		const realType	r[2],
		unsigned	constr
	)		[static]

Definition at line 1697 of file findpt.c.

References opt_edge_intp_2(), and opt_edge_set_2().

Referenced by opt_findpt_2().

{
    opt_edge_set_2( p, r, constr );
    opt_edge_intp_2( p );
}

static void opt_edge_set_intp_3	(	opt_data_3 *	p,
		const realType	r[3],
		unsigned	constr
	)		[static]

Definition at line 1392 of file findpt.c.

References opt_edge_intp_3(), and opt_edge_set_3().

Referenced by opt_findpt_3().

{
    opt_edge_set_3( p, r, constr );
    opt_edge_intp_3( p );
}

static void opt_face_hess_3	(	opt_data_3 *	p,
		realType	hess[9]
	)		[static]

Definition at line 1313 of file findpt.c.

References lagrange_data::D, opt_face_data_3::d1, lagrange_data::D2, opt_face_data_3::d2, opt_data_3::fd, lagrange_data::J, lagrange_2u(), opt_data_3::ld, lagrange_data::n, tensor_i2(), tensor_ig2(), opt_data_3::work, and opt_face_data_3::x.

Referenced by opt_findpt_3().

{
    unsigned        d;
    const unsigned  d1 = p->fd.d1, d2 = p->fd.d2, n1 = p->ld[ d1 ].n, n2 = p->ld[ d2 ].n;
    const realType *J1 = p->ld[ d1 ].J, *J2 = p->ld[ d2 ].J, *D1 = p->ld[ d1 ].D, *D2 = p->ld[ d2 ].D,
                   *S1 = p->ld[ d1 ].D2, *S2 = p->ld[ d2 ].D2;

    lagrange_2u( &p->ld[ d1 ] );
    lagrange_2u( &p->ld[ d2 ] );

    for( d = 0; d < 3; ++d )
    {
        (void)tensor_ig2( J1, S1, n1, J2, S2, n2, p->fd.x[ d ], hess + d * 3, p->work );
        hess[ d * 3 + 0 ] = tensor_i2( S1, n1, J2, n2, p->fd.x[ d ], p->work );
        hess[ d * 3 + 1 ] = tensor_i2( J1, n1, S2, n2, p->fd.x[ d ], p->work );
        hess[ d * 3 + 2 ] = tensor_i2( D1, n1, D2, n2, p->fd.x[ d ], p->work );
    }
}

static void opt_face_intp_3

(

opt_data_3 *

p

)

[static]

Definition at line 1291 of file findpt.c.

References lagrange_data::D, opt_face_data_3::d1, opt_face_data_3::d2, opt_face_data_3::dn, opt_data_3::fd, opt_face_data_3::fdn, lagrange_data::J, opt_data_3::jac, opt_data_3::ld, lagrange_data::n, tensor_i2(), tensor_ig2(), opt_data_3::work, opt_face_data_3::x, and opt_data_3::x.

Referenced by opt_face_set_intp_3().

{
    unsigned        d;
    const unsigned  dn = p->fd.dn, d1 = p->fd.d1, d2 = p->fd.d2, n1 = p->ld[ d1 ].n, n2 = p->ld[ d2 ].n;
    const realType *J1 = p->ld[ d1 ].J, *J2 = p->ld[ d2 ].J, *D1 = p->ld[ d1 ].D, *D2 = p->ld[ d2 ].D;

    for( d = 0; d < 3; ++d )
    {
        realType g[ 2 ];
        p->x[ d ] = tensor_ig2( J1, D1, n1, J2, D2, n2, p->fd.x[ d ], &g[ 0 ], p->work );
        p->jac[ d * 3 + d1 ] = g[ 0 ];
        p->jac[ d * 3 + d2 ] = g[ 1 ];
        p->jac[ d * 3 + dn ] = tensor_i2( J1, n1, J2, n2, p->fd.fdn[ d ], p->work );
    }
}

static void opt_face_proj_3

(

opt_data_3 *

p

)

[static]

Definition at line 1252 of file findpt.c.

References opt_face_data_3::constraints, opt_face_data_3::d1, opt_face_data_3::d2, lagrange_data::D_z0, lagrange_data::D_zn, opt_face_data_3::dn, opt_data_3::elx, opt_data_3::fd, opt_face_data_3::fdn, opt_data_3::ld, lagrange_data::n, opt_constr(), opt_data_3::size, and opt_face_data_3::x.

Referenced by opt_face_set_3().

{
    unsigned       d, off = 0;
    const unsigned dn = p->fd.dn, d1 = p->fd.d1, d2 = p->fd.d2, so = p->size[ d2 ] - p->size[ d1 + 1 ],
                   s1 = p->size[ d1 ], sn = p->size[ dn ], n1 = p->ld[ d1 ].n, n2 = p->ld[ d2 ].n, nn = p->ld[ dn ].n;
    const realType* D = p->ld[ dn ].D_z0;
    if( opt_constr( p->fd.constraints, dn ) == 2 ) off = p->size[ dn + 1 ] - p->size[ dn ], D = p->ld[ dn ].D_zn;
    for( d = 0; d < 3; ++d )
    {
        unsigned        i, j, k, arrindex = 0;
        const realType* in = p->elx[ d ] + off;
        for( j = n2; j; --j, in += so )
            for( i = n1; i; --i, ++arrindex, in += s1 )
            {
                const realType* ind = in - off;
                realType*       fdn = &p->fd.fdn[ d ][ arrindex ];
                p->fd.x[ d ][ arrindex ] = *in;
                *fdn = 0;
                for( k = 0; k < nn; ++k, ind += sn )
                    *fdn += *ind * D[ k ];
            }
    }
}

static void opt_face_set_3	(	opt_data_3 *	p,
		const realType	r[3],
		unsigned	constr
	)		[static]

Definition at line 1276 of file findpt.c.

References opt_face_data_3::constraints, opt_face_data_3::d1, opt_face_data_3::d2, opt_face_data_3::dn, opt_data_3::fd, lagrange_1(), opt_data_3::ld, opt_constr_dir_3, opt_face_proj_3(), opt_other1_3, and opt_other2_3.

Referenced by opt_face_set_intp_3(), and opt_findpt_3().

{
    if( p->fd.constraints != constr )
    {
        p->fd.constraints = constr;
        p->fd.dn = opt_constr_dir_3[ constr ];
        p->fd.d1 = opt_other1_3[ p->fd.dn ];
        p->fd.d2 = opt_other2_3[ p->fd.dn ];
        opt_face_proj_3( p );
    }
    lagrange_1( &p->ld[ p->fd.d1 ], r[ p->fd.d1 ] );
    lagrange_1( &p->ld[ p->fd.d2 ], r[ p->fd.d2 ] );
}

static void opt_face_set_intp_3	(	opt_data_3 *	p,
		const realType	r[3],
		unsigned	constr
	)		[static]

Definition at line 1307 of file findpt.c.

References opt_face_intp_3(), and opt_face_set_3().

Referenced by opt_findpt_3().

{
    opt_face_set_3( p, r, constr );
    opt_face_intp_3( p );
}

double opt_findpt_2	(	opt_data_2 *	p,
		const realType *const	elx[2],
		const realType	xstar[2],
		realType	r[2],
		unsigned *	constr
	)

Definition at line 1762 of file findpt.c.

References opt_edge_data_2::constraints, opt_point_data_2::constraints, opt_edge_data_2::d1, opt_edge_data_2::de, DIAGNOSTICS, opt_data_2::ed, opt_data_2::elx, opt_data_2::jac, mat_app_2c(), MOAB_POLY_EPS, opt_area_set_intp_2(), opt_constr_num_2, opt_constr_pack_2(), opt_constr_unpack_2(), opt_edge_hess_2(), opt_edge_set_2(), opt_edge_set_intp_2(), opt_no_constraints_2, opt_point_set_2(), opt_point_set_intp_2(), opt_data_2::pd, r1norm_2(), r2norm_2(), tinyla_solve_2(), and opt_data_2::x.

Referenced by findpt_guess_2(), findpt_pass_2(), moab::Element::SpectralQuad::ievaluate(), and moab::SpectralQuad::reverseEvalFcn().

{
    realType dr[ 2 ], resid[ 2 ], steep[ 2 ];

    unsigned c = *constr, ac, d, cc[ 2 ], step = 0;

    p->elx[ 0 ] = elx[ 0 ], p->elx[ 1 ] = elx[ 1 ];

    p->ed.constraints = opt_no_constraints_2;
    p->pd.constraints = opt_no_constraints_2;

#if DIAGNOSTICS
    printf( "opt_findpt: xstar = %g, %g\n", xstar[ 0 ], xstar[ 1 ] );
#endif

    do
    {
        ++step;
        if( step == 50 ) /*fail("%s: opt_findpt_2 did not converge\n",__FILE__);*/
            return 1.e+30;
#if DIAGNOSTICS
        printf( "  iteration %u\n", step );
        printf( "    %d constraint(s) active\n", (int)opt_constr_num_2[ c ] );
#endif
        /* update face/edge/point data if necessary,
           and evaluate x(r) as well as the jacobian */
        switch( opt_constr_num_2[ c ] )
        {
            case 0:
                opt_area_set_intp_2( p, r );
                break;
            case 1:
                opt_edge_set_intp_2( p, r, c );
                break;
            case 2:
                opt_point_set_intp_2( p, c );
                break;
        }
#if DIAGNOSTICS
        printf( "    r = %g, %g\n", r[ 0 ], r[ 1 ] );
        printf( "    x = %g, %g\n", p->x[ 0 ], p->x[ 1 ] );
#endif
        /* compute residual */
        for( d = 0; d < 2; ++d )
            resid[ d ] = xstar[ d ] - p->x[ d ];
#if DIAGNOSTICS
        printf( "    resid = %g, %g\n", resid[ 0 ], resid[ 1 ] );
        printf( "    2-norm = %g\n", r2norm_2( resid[ 0 ], resid[ 1 ] ) );
#endif
        /* check constraints against steepest descent direction */
        ac = c;
        if( opt_constr_num_2[ c ] )
        {
            opt_constr_unpack_2( c, cc );
            mat_app_2c( steep, p->jac, resid ); /* steepest descent = J^T r */
#if DIAGNOSTICS
            printf( "    steepest descent = %g, %g\n", steep[ 0 ], steep[ 1 ] );
#endif
            for( d = 0; d < 2; ++d )
                if( ( cc[ d ] == 0 && steep[ d ] > 0 ) || ( cc[ d ] == 2 && steep[ d ] < 0 ) ) cc[ d ] = 1;
            ac = opt_constr_pack_2( cc );
        }
        /* update face/edge/point data if necessary */
        if( ac != c )
        {
            c = ac;
#if DIAGNOSTICS
            printf( "    relaxed to %d constraints\n", (int)opt_constr_num_2[ c ] );
#endif
            switch( opt_constr_num_2[ c ] )
            {
                case 1:
                    opt_edge_set_2( p, r, c );
                    break;
                case 2:
                    opt_point_set_2( p, c );
                    break;
            }
        }
        /* compute Newton step */
        switch( opt_constr_num_2[ c ] )
        {
            case 0:
                tinyla_solve_2( dr, p->jac, resid );
                break;
            case 1: {
                const unsigned  de = p->ed.de, d1 = p->ed.d1;
                realType        fac, H[ 2 ];
                const realType* J = p->jac + de;
                opt_edge_hess_2( p, H );
                fac = J[ 0 ] * J[ 0 ] + J[ 2 ] * J[ 2 ] - ( resid[ 0 ] * H[ 0 ] + resid[ 1 ] * H[ 1 ] );
                dr[ de ] = steep[ de ] / fac;
                dr[ d1 ] = 0;
            }
            break;
            case 2:
                dr[ 0 ] = dr[ 1 ] = 0;
                break;
        }
#if DIAGNOSTICS
        printf( "    dr = %g, %g\n", dr[ 0 ], dr[ 1 ] );
#endif
        /* project new iteration onto [-1,1]^2 */
        opt_constr_unpack_2( c, cc );
        for( d = 0; d < 2; ++d )
        {
            if( cc[ d ] != 1 ) continue;
            r[ d ] += dr[ d ];
            if( r[ d ] <= -1 )
                dr[ d ] -= r[ d ] + 1, r[ d ] = -1, cc[ d ] = 0;
            else if( r[ d ] >= 1 )
                dr[ d ] -= r[ d ] - 1, r[ d ] = 1, cc[ d ] = 2;
        }
        c = opt_constr_pack_2( cc );
    } while( r1norm_2( dr[ 0 ], dr[ 1 ] ) > 2 * MOAB_POLY_EPS );
    *constr = c;
    return r2norm_2( resid[ 0 ], resid[ 1 ] );
}

double opt_findpt_3	(	opt_data_3 *	p,
		const realType *const	elx[3],
		const realType	xstar[3],
		realType	r[3],
		unsigned *	constr
	)

Definition at line 1457 of file findpt.c.

References opt_face_data_3::constraints, opt_edge_data_3::constraints, opt_point_data_3::constraints, opt_face_data_3::d1, opt_edge_data_3::d1, opt_face_data_3::d2, opt_edge_data_3::d2, opt_edge_data_3::de, DIAGNOSTICS, opt_face_data_3::dn, opt_data_3::ed, opt_data_3::elx, opt_data_3::fd, opt_data_3::jac, mat_app_3c(), MOAB_POLY_EPS, opt_constr_num_3, opt_constr_pack_3(), opt_constr_unpack_3(), opt_edge_hess_3(), opt_edge_set_3(), opt_edge_set_intp_3(), opt_face_hess_3(), opt_face_set_3(), opt_face_set_intp_3(), opt_no_constraints_3, opt_point_set_3(), opt_point_set_intp_3(), opt_vol_set_intp_3(), opt_data_3::pd, r1norm_3(), r2norm_3(), tinyla_solve_3(), tinyla_solve_sym_2(), and opt_data_3::x.

Referenced by findpt_guess_3(), findpt_pass_3(), moab::ElemUtil::hex_findpt(), and moab::Element::SpectralHex::ievaluate().

{
    realType dr[ 3 ], resid[ 3 ], steep[ 3 ];

    unsigned c = *constr, ac, d, cc[ 3 ], step = 0;

    p->elx[ 0 ] = elx[ 0 ], p->elx[ 1 ] = elx[ 1 ], p->elx[ 2 ] = elx[ 2 ];

    p->fd.constraints = opt_no_constraints_3;
    p->ed.constraints = opt_no_constraints_3;
    p->pd.constraints = opt_no_constraints_3;

#if DIAGNOSTICS
    printf( "opt_findpt: xstar = %g, %g, %g\n", xstar[ 0 ], xstar[ 1 ], xstar[ 2 ] );
#endif

    do
    {
        ++step;
        if( step == 50 ) /*fail("%s: opt_findpt_3 did not converge\n",__FILE__);*/
            return 1.e+30;
#if DIAGNOSTICS
        printf( "  iteration %u\n", step );
        printf( "    %d constraint(s) active\n", (int)opt_constr_num_3[ c ] );
#endif
        /* update face/edge/point data if necessary,
           and evaluate x(r) as well as the jacobian */
        switch( opt_constr_num_3[ c ] )
        {
            case 0:
                opt_vol_set_intp_3( p, r );
                break;
            case 1:
                opt_face_set_intp_3( p, r, c );
                break;
            case 2:
                opt_edge_set_intp_3( p, r, c );
                break;
            case 3:
                opt_point_set_intp_3( p, c );
                break;
        }
#if DIAGNOSTICS
        printf( "    r = %g, %g, %g\n", r[ 0 ], r[ 1 ], r[ 2 ] );
        printf( "    x = %g, %g, %g\n", p->x[ 0 ], p->x[ 1 ], p->x[ 2 ] );
#endif
        /* compute residual */
        for( d = 0; d < 3; ++d )
            resid[ d ] = xstar[ d ] - p->x[ d ];
#if DIAGNOSTICS
        printf( "    resid = %g, %g, %g\n", resid[ 0 ], resid[ 1 ], resid[ 2 ] );
        printf( "    2-norm = %g\n", r2norm_3( resid[ 0 ], resid[ 1 ], resid[ 2 ] ) );
#endif
        /* check constraints against steepest descent direction */
        ac = c;
        if( opt_constr_num_3[ c ] )
        {
            opt_constr_unpack_3( c, cc );
            mat_app_3c( steep, p->jac, resid ); /* steepest descent = J^T r */
#if DIAGNOSTICS
            printf( "    steepest descent = %g, %g, %g\n", steep[ 0 ], steep[ 1 ], steep[ 2 ] );
#endif
            for( d = 0; d < 3; ++d )
                if( ( cc[ d ] == 0 && steep[ d ] > 0 ) || ( cc[ d ] == 2 && steep[ d ] < 0 ) ) cc[ d ] = 1;
            ac = opt_constr_pack_3( cc );
        }
        /* update face/edge/point data if necessary */
        if( ac != c )
        {
            c = ac;
#if DIAGNOSTICS
            printf( "    relaxed to %d constraints\n", (int)opt_constr_num_3[ c ] );
#endif
            switch( opt_constr_num_3[ c ] )
            {
                case 1:
                    opt_face_set_3( p, r, c );
                    break;
                case 2:
                    opt_edge_set_3( p, r, c );
                    break;
                case 3:
                    opt_point_set_3( p, c );
                    break;
            }
        }
        /* compute Newton step */
        switch( opt_constr_num_3[ c ] )
        {
            case 0:
                tinyla_solve_3( dr, p->jac, resid );
                break;
            case 1: {
                const unsigned  dn = p->fd.dn, d1 = p->fd.d1, d2 = p->fd.d2;
                realType        A[ 4 ], H[ 9 ];
                const realType* J = p->jac;
                opt_face_hess_3( p, H );
                A[ 0 ] = J[ d1 ] * J[ d1 ] + J[ 3 + d1 ] * J[ 3 + d1 ] + J[ 6 + d1 ] * J[ 6 + d1 ];
                A[ 1 ] = J[ d2 ] * J[ d2 ] + J[ 3 + d2 ] * J[ 3 + d2 ] + J[ 6 + d2 ] * J[ 6 + d2 ];
                A[ 2 ] = J[ d1 ] * J[ d2 ] + J[ 3 + d1 ] * J[ 3 + d2 ] + J[ 6 + d1 ] * J[ 6 + d2 ];
                A[ 0 ] -= resid[ 0 ] * H[ 0 ] + resid[ 1 ] * H[ 3 ] + resid[ 2 ] * H[ 6 ];
                A[ 1 ] -= resid[ 0 ] * H[ 1 ] + resid[ 1 ] * H[ 4 ] + resid[ 2 ] * H[ 7 ];
                A[ 2 ] -= resid[ 0 ] * H[ 2 ] + resid[ 1 ] * H[ 5 ] + resid[ 2 ] * H[ 8 ];
                tinyla_solve_sym_2( &dr[ d1 ], &dr[ d2 ], A, steep[ d1 ], steep[ d2 ] );
                dr[ dn ] = 0;
            }
            break;
            case 2: {
                const unsigned  de = p->ed.de, d1 = p->ed.d1, d2 = p->ed.d2;
                realType        fac, H[ 3 ];
                const realType* J = p->jac + de;
                opt_edge_hess_3( p, H );
                fac = J[ 0 ] * J[ 0 ] + J[ 3 ] * J[ 3 ] + J[ 6 ] * J[ 6 ] -
                      ( resid[ 0 ] * H[ 0 ] + resid[ 1 ] * H[ 1 ] + resid[ 2 ] * H[ 2 ] );
                dr[ de ] = steep[ de ] / fac;
                dr[ d1 ] = 0, dr[ d2 ] = 0;
            }
            break;
            case 3:
                dr[ 0 ] = dr[ 1 ] = dr[ 2 ] = 0;
                break;
        }
#if DIAGNOSTICS
        printf( "    dr = %g, %g, %g\n", dr[ 0 ], dr[ 1 ], dr[ 2 ] );
#endif
        /* project new iteration onto [-1,1]^3 */
        opt_constr_unpack_3( c, cc );
        for( d = 0; d < 3; ++d )
        {
            if( cc[ d ] != 1 ) continue;
            r[ d ] += dr[ d ];
            if( r[ d ] <= -1 )
                dr[ d ] -= r[ d ] + 1, r[ d ] = -1, cc[ d ] = 0;
            else if( r[ d ] >= 1 )
                dr[ d ] -= r[ d ] - 1, r[ d ] = 1, cc[ d ] = 2;
        }
        c = opt_constr_pack_3( cc );
    } while( r1norm_3( dr[ 0 ], dr[ 1 ], dr[ 2 ] ) > 3 * MOAB_POLY_EPS );
    *constr = c;
#if 0
  printf("opt_findpt_3 converged in %u iterations\n", step);
#endif
    return r2norm_3( resid[ 0 ], resid[ 1 ], resid[ 2 ] );
}

void opt_free_2

(

opt_data_2 *

p

)

Definition at line 1619 of file findpt.c.

References opt_data_2::work.

Referenced by findpt_free_2(), and moab::Element::SpectralQuad::freedata().

{
    free( p->work );
}

void opt_free_3

(

opt_data_3 *

p

)

Definition at line 1223 of file findpt.c.

References opt_data_3::work.

Referenced by findpt_free_3(), moab::element_utility::Spectral_hex_map< moab::Matrix3 >::free_data(), moab::Element::SpectralHex::freedata(), and moab::ElemUtil::hex_findpt().

{
    free( p->work );
}

static void opt_point_intp_2

(

opt_data_2 *

p

)

[static]

Definition at line 1748 of file findpt.c.

References opt_point_data_2::jac, opt_data_2::jac, opt_data_2::pd, opt_point_data_2::x, and opt_data_2::x.

Referenced by opt_point_set_intp_2().

{
    memcpy( p->x, p->pd.x, 2 * sizeof( realType ) );
    memcpy( p->jac, p->pd.jac, 4 * sizeof( realType ) );
}

static void opt_point_intp_3

(

opt_data_3 *

p

)

[static]

Definition at line 1443 of file findpt.c.

References opt_point_data_3::jac, opt_data_3::jac, opt_data_3::pd, opt_point_data_3::x, and opt_data_3::x.

Referenced by opt_point_set_intp_3().

{
    memcpy( p->x, p->pd.x, 3 * sizeof( realType ) );
    memcpy( p->jac, p->pd.jac, 9 * sizeof( realType ) );
}

static void opt_point_proj_2

(

opt_data_2 *

p

)

[static]

Definition at line 1713 of file findpt.c.

References opt_point_data_2::constraints, lagrange_data::D_z0, lagrange_data::D_zn, opt_data_2::elx, opt_point_data_2::jac, opt_data_2::ld, lagrange_data::n, opt_constr_unpack_2(), opt_data_2::pd, opt_data_2::size, and opt_point_data_2::x.

Referenced by opt_point_set_2().

{
    unsigned        off[ 2 ], offt, d, c[ 2 ];
    const realType* fD[ 2 ];
    opt_constr_unpack_2( p->pd.constraints, c );
    for( d = 0; d < 2; ++d )
        if( c[ d ] == 0 )
            fD[ d ] = p->ld[ d ].D_z0, off[ d ] = 0;
        else
            fD[ d ] = p->ld[ d ].D_zn, off[ d ] = p->size[ d + 1 ] - p->size[ d ];
    offt = off[ 0 ] + off[ 1 ];
    for( d = 0; d < 4; ++d )
        p->pd.jac[ d ] = 0;
    for( d = 0; d < 2; ++d )
    {
        unsigned i, j;
        p->pd.x[ d ] = p->elx[ d ][ offt ];
        for( i = 0; i < 2; ++i )
        {
            const realType* in = p->elx[ d ] + offt - off[ i ];
            for( j = 0; j < p->ld[ i ].n; ++j, in += p->size[ i ] )
                p->pd.jac[ d * 2 + i ] += *in * fD[ i ][ j ];
        }
    }
}

static void opt_point_proj_3

(

opt_data_3 *

p

)

[static]

Definition at line 1408 of file findpt.c.

References opt_point_data_3::constraints, lagrange_data::D_z0, lagrange_data::D_zn, opt_data_3::elx, opt_point_data_3::jac, opt_data_3::ld, lagrange_data::n, opt_constr_unpack_3(), opt_data_3::pd, opt_data_3::size, and opt_point_data_3::x.

Referenced by opt_point_set_3().

{
    unsigned        off[ 3 ], offt, d, c[ 3 ];
    const realType* fD[ 3 ];
    opt_constr_unpack_3( p->pd.constraints, c );
    for( d = 0; d < 3; ++d )
        if( c[ d ] == 0 )
            fD[ d ] = p->ld[ d ].D_z0, off[ d ] = 0;
        else
            fD[ d ] = p->ld[ d ].D_zn, off[ d ] = p->size[ d + 1 ] - p->size[ d ];
    offt = off[ 0 ] + off[ 1 ] + off[ 2 ];
    for( d = 0; d < 9; ++d )
        p->pd.jac[ d ] = 0;
    for( d = 0; d < 3; ++d )
    {
        unsigned i, j;
        p->pd.x[ d ] = p->elx[ d ][ offt ];
        for( i = 0; i < 3; ++i )
        {
            const realType* in = p->elx[ d ] + offt - off[ i ];
            for( j = 0; j < p->ld[ i ].n; ++j, in += p->size[ i ] )
                p->pd.jac[ d * 3 + i ] += *in * fD[ i ][ j ];
        }
    }
}

static void opt_point_set_2	(	opt_data_2 *	p,
		unsigned	constr
	)		[static]

Definition at line 1739 of file findpt.c.

References opt_point_data_2::constraints, opt_point_proj_2(), and opt_data_2::pd.

Referenced by opt_findpt_2(), and opt_point_set_intp_2().

{
    if( p->pd.constraints != constr )
    {
        p->pd.constraints = constr;
        opt_point_proj_2( p );
    }
}

static void opt_point_set_3	(	opt_data_3 *	p,
		unsigned	constr
	)		[static]

Definition at line 1434 of file findpt.c.

References opt_point_data_3::constraints, opt_point_proj_3(), and opt_data_3::pd.

Referenced by opt_findpt_3(), and opt_point_set_intp_3().

{
    if( p->pd.constraints != constr )
    {
        p->pd.constraints = constr;
        opt_point_proj_3( p );
    }
}

static void opt_point_set_intp_2	(	opt_data_2 *	p,
		unsigned	constr
	)		[static]

Definition at line 1754 of file findpt.c.

References opt_point_intp_2(), and opt_point_set_2().

Referenced by opt_findpt_2().

{
    opt_point_set_2( p, constr );
    opt_point_intp_2( p );
}

static void opt_point_set_intp_3	(	opt_data_3 *	p,
		unsigned	constr
	)		[static]

Definition at line 1449 of file findpt.c.

References opt_point_intp_3(), and opt_point_set_3().

Referenced by opt_findpt_3().

{
    opt_point_set_3( p, constr );
    opt_point_intp_3( p );
}

static void opt_vol_intp_3

(

opt_data_3 *

p

)

[static]

Definition at line 1236 of file findpt.c.

References opt_data_3::elx, opt_data_3::jac, opt_data_3::ld, n, tensor_ig3(), opt_data_3::work, and opt_data_3::x.

Referenced by opt_vol_set_intp_3().

{
    unsigned             d;
    const lagrange_data* ld = p->ld;

    for( d = 0; d < 3; ++d )
        p->x[ d ] = tensor_ig3( ld[ 0 ].J, ld[ 0 ].D, ld[ 0 ].n, ld[ 1 ].J, ld[ 1 ].D, ld[ 1 ].n, ld[ 2 ].J, ld[ 2 ].D,
                                ld[ 2 ].n, p->elx[ d ], &p->jac[ d * 3 ], p->work );
}

static void opt_vol_set_3	(	opt_data_3 *	p,
		const realType	r[3]
	)		[static]

Definition at line 1228 of file findpt.c.

References lagrange_1(), and opt_data_3::ld.

Referenced by opt_vol_set_intp_3().

{
    lagrange_1( &p->ld[ 0 ], r[ 0 ] );
    lagrange_1( &p->ld[ 1 ], r[ 1 ] );
    lagrange_1( &p->ld[ 2 ], r[ 2 ] );
}

void opt_vol_set_intp_3	(	opt_data_3 *	p,
		const realType	r[3]
	)

Definition at line 1246 of file findpt.c.

References opt_vol_intp_3(), and opt_vol_set_3().

Referenced by moab::element_utility::Spectral_hex_map< moab::Matrix3 >::integrate_scalar_field(), moab::Element::SpectralHex::integrate_scalar_field(), moab::element_utility::Spectral_hex_map< moab::Matrix3 >::jacobian(), moab::Element::SpectralHex::jacobian(), and opt_findpt_3().

{
    opt_vol_set_3( p, r );
    opt_vol_intp_3( p );
}

static void tinyla_solve_2	(	realType	x[2],
		const realType	A[4],
		const realType	b[2]
	)		[static]

Definition at line 311 of file findpt.c.

References MBMesquite::inv(), mat_app_2r(), and mat_inv_2().

Referenced by opt_findpt_2().

{
    realType inv[ 4 ];
    mat_inv_2( A, inv );
    mat_app_2r( x, inv, b );
}

static void tinyla_solve_3	(	realType	x[3],
		const realType	A[9],
		const realType	b[3]
	)		[static]

Definition at line 318 of file findpt.c.

References MBMesquite::inv(), mat_app_3r(), and mat_inv_3().

Referenced by opt_findpt_3().

{
    realType inv[ 9 ];
    mat_inv_3( A, inv );
    mat_app_3r( x, inv, b );
}

static void tinyla_solve_sym_2	(	realType *	x0,
		realType *	x1,
		const realType	A[3],
		realType	b0,
		realType	b1
	)		[static]

Definition at line 329 of file findpt.c.

References b1.

Referenced by opt_findpt_3().

{
    const realType idet = 1 / ( A[ 0 ] * A[ 1 ] - A[ 2 ] * A[ 2 ] );
    *x0 = idet * ( A[ 1 ] * b0 - A[ 2 ] * b1 );
    *x1 = idet * ( A[ 0 ] * b1 - A[ 2 ] * b0 );
}

---

Variable Documentation

const char opt_constr_dir_3[27] [static]

Initial value:

 { -1, -1, -1, -1, 2,  -1, -1, -1, -1, -1, 1,  -1, 0, -1,
                                             0,  -1, 1,  -1, -1, -1, -1, -1, 2,  -1, -1, -1, -1 }

Definition at line 1147 of file findpt.c.

Referenced by opt_face_set_3().

const char opt_constr_not[27] [static]

Initial value:

 { -1, 0, -1, 1, -1, 1, -1, 0, -1, 2, -1, 2, -1, -1,
                                           -1, 2, -1, 2, -1, 0, -1, 1, -1, 1, -1, 0, -1 }

Definition at line 1151 of file findpt.c.

Referenced by opt_edge_set_2(), and opt_edge_set_3().

const char opt_constr_num_2[9] = { 2, 1, 2, 1, 0, 1, 2, 1, 2 } [static]

Definition at line 1141 of file findpt.c.

Referenced by opt_findpt_2().

const char opt_constr_num_3[27] [static]

Initial value:

 { 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 0,
                                             1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3 }

Definition at line 1142 of file findpt.c.

Referenced by opt_findpt_3().

const char opt_constr_wide[27] [static]

Initial value:

 { 0x00, 0x01, 0x02, 0x04, 0x05, 0x06, 0x08, 0x09, 0x0a,
                                            0x10, 0x11, 0x12, 0x14, 0x15, 0x16, 0x18, 0x19, 0x1a,
                                            0x20, 0x21, 0x22, 0x24, 0x25, 0x26, 0x28, 0x29, 0x2a }

Definition at line 1154 of file findpt.c.

Referenced by opt_constr(), opt_constr_unpack_2(), and opt_constr_unpack_3().

const unsigned opt_no_constraints_2 = 3 + 1

Definition at line 10 of file findpt.c.

Referenced by findpt_guess_2(), findpt_pass_2(), and opt_findpt_2().

const unsigned opt_no_constraints_3 = 9 + 3 + 1

Definition at line 11 of file findpt.c.

Referenced by findpt_guess_3(), findpt_pass_3(), moab::ElemUtil::hex_findpt(), moab::Element::SpectralHex::ievaluate(), moab::Element::SpectralQuad::ievaluate(), opt_findpt_3(), and moab::SpectralQuad::reverseEvalFcn().

const unsigned opt_other1_3[3] = { 1, 0, 0 } [static]

Definition at line 1158 of file findpt.c.

Referenced by opt_edge_set_3(), and opt_face_set_3().

const unsigned opt_other2_3[3] = { 2, 2, 1 } [static]

Definition at line 1158 of file findpt.c.

Referenced by opt_edge_set_3(), and opt_face_set_3().