src/common/interp2d.c

#ifndef lint
static const char RCSid[] = "$Id: interp2d.c,v 2.9 2013/02/12 18:41:39 greg Exp $";
#endif
/*
 * General interpolation method for unstructured values on 2-D plane.
 *
 *      G.Ward Feb 2013
 */

#include "copyright.h"

/***************************************************************
 * This is a general method for 2-D interpolation similar to
 * radial basis functions but allowing for a good deal of local
 * anisotropy in the point distribution.  Each sample point
 * is examined to determine the closest neighboring samples in
 * each of NI2DIR surrounding directions.  To speed this
 * calculation, we sort the data into half-planes and apply
 * simple tests to see which neighbor is closest in each
 * angular slice.  Once we have our approximate neighborhood
 * for a sample, we can use it in a modified Gaussian weighting
 * with allowing local anisotropy.  Harmonic weighting is added
 * to reduce the influence of distant neighbors.  This yields a
 * smooth interpolation regardless of how the sample points are
 * initially distributed.  Evaluation is accelerated by use of
 * a fast approximation to the atan2(y,x) function and an array
 * of flags indicating where weights are (nearly) zero.
 ****************************************************************/

#include <stdio.h>
#include <stdlib.h>
#include "rtmath.h"
#include "interp2d.h"

#define DECODE_DIA(ip,ed)       ((ip)->dmin*(1. + .5*(ed)))
#define ENCODE_DIA(ip,d)        ((int)(2.*(d)/(ip)->dmin) - 2)

/* Sample order (private) */
typedef struct {
        int     si;             /* sample index */
        float   dm;             /* distance measure in this direction */
} SAMPORD;

/* Allocate a new set of interpolation samples (caller assigns spt[] array) */
INTERP2 *
interp2_alloc(int nsamps)
{
        INTERP2         *nip;

        if (nsamps <= 1)
                return(NULL);

        nip = (INTERP2 *)malloc(sizeof(INTERP2) + sizeof(float)*2*(nsamps-1));
        if (nip == NULL)
                return(NULL);

        nip->ns = nsamps;
        nip->dmin = 1;          /* default minimum diameter */
        nip->smf = NI2DSMF;     /* default smoothing factor */
        nip->da = NULL;
                                /* caller must assign spt[] array */
        return(nip);
}

/* Resize interpolation array (caller must assign any new values) */
INTERP2 *
interp2_realloc(INTERP2 *ip, int nsamps)
{
        if (ip == NULL)
                return(interp2_alloc(nsamps));
        if (nsamps <= 1) {
                interp2_free(ip);
                return(NULL);
        }
        if (nsamps == ip->ns)
                return(ip);
        if (ip->da != NULL) {   /* will need to recompute distribution */
                free(ip->da);
                ip->da = NULL;
        }
        ip = (INTERP2 *)realloc(ip, sizeof(INTERP2)+sizeof(float)*2*(nsamps-1));
        if (ip == NULL)
                return(NULL);
        ip->ns = nsamps;
        return(ip);
}

/* Set minimum distance under which samples will start to merge */
void
interp2_spacing(INTERP2 *ip, double mind)
{
        if (mind <= 0)
                return;
        if ((.998*ip->dmin <= mind) & (mind <= 1.002*ip->dmin))
                return;
        if (ip->da != NULL) {   /* will need to recompute distribution */
                free(ip->da);
                ip->da = NULL;
        }
        ip->dmin = mind;
}

/* Modify smoothing parameter by the given factor */
void
interp2_smooth(INTERP2 *ip, double sf)
{
        if ((ip->smf *= sf) < NI2DSMF)
                ip->smf = NI2DSMF;
}

/* private call-back to sort position index */
static int
cmp_spos(const void *p1, const void *p2)
{
        const SAMPORD   *so1 = (const SAMPORD *)p1;
        const SAMPORD   *so2 = (const SAMPORD *)p2;

        if (so1->dm > so2->dm)
                return 1;
        if (so1->dm < so2->dm)
                return -1;
        return 0;
}

/* private routine to order samples in a particular direction */
static void
sort_samples(SAMPORD *sord, const INTERP2 *ip, double ang)
{
        const double    cosd = cos(ang);
        const double    sind = sin(ang);
        int             i;

        for (i = ip->ns; i--; ) {
                sord[i].si = i;
                sord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1];
        }
        qsort(sord, ip->ns, sizeof(SAMPORD), &cmp_spos);
}

/* private routine to encode sample diameter with range checks */
static int
encode_diameter(const INTERP2 *ip, double d)
{
        const int       ed = ENCODE_DIA(ip, d);

        if (ed <= 0)
                return(0);
        if (ed >= 0xffff)
                return(0xffff);
        return(ed);
}

/* (Re)compute anisotropic basis function interpolant (normally automatic) */
int
interp2_analyze(INTERP2 *ip)
{
        SAMPORD *sortord;
        int     *rightrndx, *leftrndx, *endrndx;
        int     i, bd;
                                        /* sanity checks */
        if (ip == NULL)
                return(0);
        if (ip->da != NULL) {           /* free previous data if any */
                free(ip->da);
                ip->da = NULL;
        }
        if ((ip->ns <= 1) | (ip->dmin <= 0))
                return(0);
                                        /* compute sample domain */
        ip->smin[0] = ip->smin[1] = FHUGE;
        ip->smul[0] = ip->smul[1] = -FHUGE;
        for (i = ip->ns; i--; ) {
                if (ip->spt[i][0] < ip->smin[0])
                        ip->smin[0] = ip->spt[i][0];
                if (ip->spt[i][0] > ip->smul[0])
                        ip->smul[0] = ip->spt[i][0];
                if (ip->spt[i][1] < ip->smin[1])
                        ip->smin[1] = ip->spt[i][1];
                if (ip->spt[i][1] > ip->smul[1])
                        ip->smul[1] = ip->spt[i][1];
        }
        ip->smul[0] -= ip->smin[0];
        ip->smul[1] -= ip->smin[1];
        ip->grid2 = (ip->smul[0]*ip->smul[0] + ip->smul[1]*ip->smul[1]) *
                        (4./NI2DIM/NI2DIM);
        if (ip->grid2 <= FTINY*ip->dmin*ip->dmin)
                return(0);
        if (ip->smul[0] > FTINY)
                ip->smul[0] = NI2DIM / ip->smul[0];
        if (ip->smul[1] > FTINY)
                ip->smul[1] = NI2DIM / ip->smul[1];
                                        /* allocate analysis data */
        ip->da = (struct interp2_samp *)calloc( ip->ns,
                                        sizeof(struct interp2_samp) );
        if (ip->da == NULL)
                return(0);
                                        /* get temporary arrays */
        sortord = (SAMPORD *)malloc(sizeof(SAMPORD)*ip->ns);
        rightrndx = (int *)malloc(sizeof(int)*ip->ns);
        leftrndx = (int *)malloc(sizeof(int)*ip->ns);
        endrndx = (int *)malloc(sizeof(int)*ip->ns);
        if ((sortord == NULL) | (rightrndx == NULL) |
                        (leftrndx == NULL) | (endrndx == NULL))
                return(0);
                                        /* run through bidirections */
        for (bd = 0; bd < NI2DIR/2; bd++) {
            const double        ang = 2.*PI/NI2DIR*bd;
            int                 *sptr;
                                        /* create right reverse index */
            if (bd) {                   /* re-use from previous iteration? */
                sptr = rightrndx;
                rightrndx = leftrndx;
                leftrndx = sptr;
            } else {                    /* else sort first half-plane */
                sort_samples(sortord, ip, PI/2. - PI/NI2DIR);
                for (i = ip->ns; i--; )
                    rightrndx[sortord[i].si] = i;
                                        /* & store reverse order for later */
                for (i = ip->ns; i--; )
                    endrndx[sortord[i].si] = ip->ns-1 - i;
            }
                                        /* create new left reverse index */
            if (bd == NI2DIR/2 - 1) {   /* use order from first iteration? */
                sptr = leftrndx;
                leftrndx = endrndx;
                endrndx = sptr;
            } else {                    /* else compute new half-plane */
                sort_samples(sortord, ip, ang + (PI/2. + PI/NI2DIR));
                for (i = ip->ns; i--; )
                    leftrndx[sortord[i].si] = i;
            }
                                        /* sort grid values in this direction */
            sort_samples(sortord, ip, ang);
                                        /* find nearest neighbors each side */
            for (i = ip->ns; i--; ) {
                const int       ii = sortord[i].si;
                int             j;
                                        /* preload with large radii */
                ip->da[ii].dia[bd] =
                ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip,
                                .5*(sortord[ip->ns-1].dm - sortord[0].dm));
                for (j = i; ++j < ip->ns; )     /* nearest above */
                    if (rightrndx[sortord[j].si] > rightrndx[ii] &&
                                    leftrndx[sortord[j].si] < leftrndx[ii]) {
                        ip->da[ii].dia[bd] = encode_diameter(ip,
                                                sortord[j].dm - sortord[i].dm);
                        break;
                    }
                for (j = i; j-- > 0; )          /* nearest below */
                    if (rightrndx[sortord[j].si] < rightrndx[ii] &&
                                    leftrndx[sortord[j].si] > leftrndx[ii]) {
                        ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip,
                                                sortord[i].dm - sortord[j].dm);
                        break;
                    }
            }
        }
        free(sortord);                  /* clean up */
        free(rightrndx);
        free(leftrndx);
        free(endrndx);
        return(1);
}

/* Compute unnormalized weight for a position relative to a sample */
double
interp2_wti(INTERP2 *ip, const int i, double x, double y)
{
        int     xfi, yfi;
        double  dir, rd, r2, d2;
        int     ri;
                                /* need to compute interpolant? */
        if (ip->da == NULL && !interp2_analyze(ip))
                return(0);
                                /* get grid position */
        xfi = (x - ip->smin[0]) * ip->smul[0];
        if (xfi >= NI2DIM)
                xfi = NI2DIM-1;
        else
                xfi *= (xfi >= 0);
        yfi = (y - ip->smin[1]) * ip->smul[1];
        if (yfi >= NI2DIM)
                yfi = NI2DIM-1;
        else
                yfi *= (yfi >= 0);
        x -= ip->spt[i][0];     /* check distance */
        y -= ip->spt[i][1];
        d2 = x*x + y*y;
                                /* zero weight this zone? */
        if (d2 > ip->grid2 && ip->da[i].blkflg[yfi] & 1<<xfi)
                return(.0);

        dir = atan2a(y, x);     /* get relative direction */
        dir += 2.*PI*(dir < 0);
                                /* linear radius interpolation */
        rd = dir * (NI2DIR/2./PI);
        ri = (int)rd;
        rd -= (double)ri;
        rd = (1.-rd)*ip->da[i].dia[ri] + rd*ip->da[i].dia[(ri+1)%NI2DIR];
        rd = ip->smf * DECODE_DIA(ip, rd);
        r2 = 2.*rd*rd;
        if (d2 > 21.*r2) {      /* result would be < 1e-9 */
                ip->da[i].blkflg[yfi] |= 1<<xfi;
                return(.0);
        }
                                /* Gaussian times harmonic weighting */
        return( exp(-d2/r2) * ip->dmin/(ip->dmin + sqrt(d2)) );
}

/* Assign full set of normalized weights to interpolate the given position */
int
interp2_weights(float wtv[], INTERP2 *ip, double x, double y)
{
        double  wnorm;
        int     i;

        if ((wtv == NULL) | (ip == NULL))
                return(0);

        wnorm = 0;                      /* compute raw weights */
        for (i = ip->ns; i--; ) {
                double  wt = interp2_wti(ip, i, x, y);
                wtv[i] = wt;
                wnorm += wt;
        }
        if (wnorm <= 0)                 /* too far from all our samples! */
                return(0);
        wnorm = 1./wnorm;               /* normalize weights */
        for (i = ip->ns; i--; )
                wtv[i] *= wnorm;
        return(ip->ns);                 /* all done */
}


/* Get normalized weights and indexes for n best samples in descending order */
int
interp2_topsamp(float wt[], int si[], const int n, INTERP2 *ip, double x, double y)
{
        int     nn = 0;
        double  wnorm;
        int     i, j;

        if ((n <= 0) | (wt == NULL) | (si == NULL) | (ip == NULL))
                return(0);
                                        /* identify top n weights */
        for (i = ip->ns; i--; ) {
                const double    wti = interp2_wti(ip, i, x, y);
                if (wti <= 1e-9)
                        continue;
                for (j = nn; j > 0; j--) {
                        if (wt[j-1] >= wti)
                                break;
                        if (j < n) {
                                wt[j] = wt[j-1];
                                si[j] = si[j-1];
                        }
                }
                if (j < n) {            /* add/insert sample */
                        wt[j] = wti;
                        si[j] = i;
                        nn += (nn < n);
                }
        }
        wnorm = 0;                      /* normalize sample weights */
        for (j = nn; j--; )
                wnorm += wt[j];
        if (wnorm <= 0)
                return(0);
        wnorm = 1./wnorm;
        for (j = nn; j--; )
                wt[j] *= wnorm;
        return(nn);                     /* return actual # samples */
}

/* Free interpolant */
void
interp2_free(INTERP2 *ip)
{
        if (ip == NULL)
                return;
        if (ip->da != NULL)
                free(ip->da);
        free(ip);
}
Revision:	2.10
Committed:	Thu Feb 14 19:57:10 2013 UTC (11 years, 2 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.9:	+74 -32 lines
Log Message:	Doubled calculation speed and exposed raw weight computation
#	User	Rev	Content
1	greg	2.1	#ifndef lint
2	greg	2.10	static const char RCSid[] = "$Id: interp2d.c,v 2.9 2013/02/12 18:41:39 greg Exp $";
3	greg	2.1	#endif
4			/*
5			* General interpolation method for unstructured values on 2-D plane.
6			*
7			* G.Ward Feb 2013
8			*/
9
10			#include "copyright.h"
11
12	greg	2.4	/***************************************************************
13	greg	2.1	* This is a general method for 2-D interpolation similar to
14			* radial basis functions but allowing for a good deal of local
15			* anisotropy in the point distribution. Each sample point
16			* is examined to determine the closest neighboring samples in
17			* each of NI2DIR surrounding directions. To speed this
18	greg	2.4	* calculation, we sort the data into half-planes and apply
19			* simple tests to see which neighbor is closest in each
20	greg	2.7	* angular slice. Once we have our approximate neighborhood
21	greg	2.3	* for a sample, we can use it in a modified Gaussian weighting
22	greg	2.4	* with allowing local anisotropy. Harmonic weighting is added
23	greg	2.3	* to reduce the influence of distant neighbors. This yields a
24			* smooth interpolation regardless of how the sample points are
25	greg	2.4	* initially distributed. Evaluation is accelerated by use of
26	greg	2.10	* a fast approximation to the atan2(y,x) function and an array
27			* of flags indicating where weights are (nearly) zero.
28	greg	2.4	****************************************************************/
29	greg	2.1
30			#include <stdio.h>
31			#include <stdlib.h>
32			#include "rtmath.h"
33			#include "interp2d.h"
34
35	greg	2.4	#define DECODE_DIA(ip,ed) ((ip)->dmin(1. + .5(ed)))
36			#define ENCODE_DIA(ip,d) ((int)(2.*(d)/(ip)->dmin) - 2)
37	greg	2.1
38			/* Sample order (private) */
39			typedef struct {
40			int si; /* sample index */
41			float dm; /* distance measure in this direction */
42			} SAMPORD;
43
44	greg	2.2	/* Allocate a new set of interpolation samples (caller assigns spt[] array) */
45	greg	2.1	INTERP2 *
46			interp2_alloc(int nsamps)
47			{
48			INTERP2 *nip;
49
50			if (nsamps <= 1)
51			return(NULL);
52
53			nip = (INTERP2 )malloc(sizeof(INTERP2) + sizeof(float)2*(nsamps-1));
54			if (nip == NULL)
55			return(NULL);
56
57			nip->ns = nsamps;
58	greg	2.4	nip->dmin = 1; /* default minimum diameter */
59	greg	2.1	nip->smf = NI2DSMF; /* default smoothing factor */
60	greg	2.4	nip->da = NULL;
61	greg	2.1	/* caller must assign spt[] array */
62			return(nip);
63			}
64
65	greg	2.2	/* Resize interpolation array (caller must assign any new values) */
66			INTERP2 *
67			interp2_realloc(INTERP2 *ip, int nsamps)
68			{
69			if (ip == NULL)
70			return(interp2_alloc(nsamps));
71			if (nsamps <= 1) {
72			interp2_free(ip);
73			return(NULL);
74			}
75	greg	2.8	if (nsamps == ip->ns)
76	greg	2.2	return(ip);
77	greg	2.4	if (ip->da != NULL) { /* will need to recompute distribution */
78			free(ip->da);
79			ip->da = NULL;
80	greg	2.2	}
81			ip = (INTERP2 )realloc(ip, sizeof(INTERP2)+sizeof(float)2*(nsamps-1));
82			if (ip == NULL)
83			return(NULL);
84			ip->ns = nsamps;
85			return(ip);
86			}
87
88	greg	2.5	/* Set minimum distance under which samples will start to merge */
89			void
90			interp2_spacing(INTERP2 *ip, double mind)
91			{
92			if (mind <= 0)
93			return;
94	greg	2.7	if ((.998ip->dmin <= mind) & (mind <= 1.002ip->dmin))
95	greg	2.5	return;
96			if (ip->da != NULL) { /* will need to recompute distribution */
97			free(ip->da);
98			ip->da = NULL;
99			}
100			ip->dmin = mind;
101			}
102
103			/* Modify smoothing parameter by the given factor */
104			void
105			interp2_smooth(INTERP2 *ip, double sf)
106			{
107			if ((ip->smf *= sf) < NI2DSMF)
108			ip->smf = NI2DSMF;
109			}
110
111	greg	2.1	/* private call-back to sort position index */
112			static int
113			cmp_spos(const void p1, const void p2)
114			{
115			const SAMPORD so1 = (const SAMPORD )p1;
116			const SAMPORD so2 = (const SAMPORD )p2;
117
118			if (so1->dm > so2->dm)
119			return 1;
120			if (so1->dm < so2->dm)
121			return -1;
122			return 0;
123			}
124
125	greg	2.2	/* private routine to order samples in a particular direction */
126			static void
127			sort_samples(SAMPORD sord, const INTERP2 ip, double ang)
128			{
129			const double cosd = cos(ang);
130			const double sind = sin(ang);
131			int i;
132
133			for (i = ip->ns; i--; ) {
134			sord[i].si = i;
135			sord[i].dm = cosdip->spt[i][0] + sindip->spt[i][1];
136			}
137			qsort(sord, ip->ns, sizeof(SAMPORD), &cmp_spos);
138			}
139
140	greg	2.4	/* private routine to encode sample diameter with range checks */
141	greg	2.1	static int
142	greg	2.4	encode_diameter(const INTERP2 *ip, double d)
143	greg	2.1	{
144	greg	2.4	const int ed = ENCODE_DIA(ip, d);
145	greg	2.1
146	greg	2.4	if (ed <= 0)
147	greg	2.1	return(0);
148	greg	2.4	if (ed >= 0xffff)
149	greg	2.1	return(0xffff);
150	greg	2.4	return(ed);
151	greg	2.1	}
152
153	greg	2.2	/* (Re)compute anisotropic basis function interpolant (normally automatic) */
154			int
155			interp2_analyze(INTERP2 *ip)
156	greg	2.1	{
157			SAMPORD *sortord;
158	greg	2.2	int rightrndx, leftrndx, *endrndx;
159	greg	2.10	int i, bd;
160	greg	2.1	/* sanity checks */
161	greg	2.10	if (ip == NULL)
162			return(0);
163			if (ip->da != NULL) { /* free previous data if any */
164			free(ip->da);
165			ip->da = NULL;
166			}
167			if ((ip->ns <= 1) \| (ip->dmin <= 0))
168	greg	2.1	return(0);
169	greg	2.10	/* compute sample domain */
170			ip->smin[0] = ip->smin[1] = FHUGE;
171			ip->smul[0] = ip->smul[1] = -FHUGE;
172			for (i = ip->ns; i--; ) {
173			if (ip->spt[i][0] < ip->smin[0])
174			ip->smin[0] = ip->spt[i][0];
175			if (ip->spt[i][0] > ip->smul[0])
176			ip->smul[0] = ip->spt[i][0];
177			if (ip->spt[i][1] < ip->smin[1])
178			ip->smin[1] = ip->spt[i][1];
179			if (ip->spt[i][1] > ip->smul[1])
180			ip->smul[1] = ip->spt[i][1];
181	greg	2.1	}
182	greg	2.10	ip->smul[0] -= ip->smin[0];
183			ip->smul[1] -= ip->smin[1];
184			ip->grid2 = (ip->smul[0]ip->smul[0] + ip->smul[1]ip->smul[1]) *
185			(4./NI2DIM/NI2DIM);
186			if (ip->grid2 <= FTINYip->dminip->dmin)
187			return(0);
188			if (ip->smul[0] > FTINY)
189			ip->smul[0] = NI2DIM / ip->smul[0];
190			if (ip->smul[1] > FTINY)
191			ip->smul[1] = NI2DIM / ip->smul[1];
192			/* allocate analysis data */
193			ip->da = (struct interp2_samp *)calloc( ip->ns,
194			sizeof(struct interp2_samp) );
195			if (ip->da == NULL)
196			return(0);
197	greg	2.1	/* get temporary arrays */
198			sortord = (SAMPORD )malloc(sizeof(SAMPORD)ip->ns);
199			rightrndx = (int )malloc(sizeof(int)ip->ns);
200			leftrndx = (int )malloc(sizeof(int)ip->ns);
201	greg	2.2	endrndx = (int )malloc(sizeof(int)ip->ns);
202			if ((sortord == NULL) \| (rightrndx == NULL) \|
203			(leftrndx == NULL) \| (endrndx == NULL))
204	greg	2.1	return(0);
205			/* run through bidirections */
206			for (bd = 0; bd < NI2DIR/2; bd++) {
207			const double ang = 2.PI/NI2DIRbd;
208	greg	2.2	int *sptr;
209	greg	2.1	/* create right reverse index */
210	greg	2.2	if (bd) { /* re-use from previous iteration? */
211			sptr = rightrndx;
212	greg	2.1	rightrndx = leftrndx;
213			leftrndx = sptr;
214	greg	2.2	} else { /* else sort first half-plane */
215			sort_samples(sortord, ip, PI/2. - PI/NI2DIR);
216			for (i = ip->ns; i--; )
217	greg	2.1	rightrndx[sortord[i].si] = i;
218	greg	2.2	/* & store reverse order for later */
219			for (i = ip->ns; i--; )
220			endrndx[sortord[i].si] = ip->ns-1 - i;
221	greg	2.1	}
222			/* create new left reverse index */
223	greg	2.2	if (bd == NI2DIR/2 - 1) { /* use order from first iteration? */
224			sptr = leftrndx;
225			leftrndx = endrndx;
226			endrndx = sptr;
227			} else { /* else compute new half-plane */
228			sort_samples(sortord, ip, ang + (PI/2. + PI/NI2DIR));
229			for (i = ip->ns; i--; )
230			leftrndx[sortord[i].si] = i;
231	greg	2.1	}
232			/* sort grid values in this direction */
233	greg	2.2	sort_samples(sortord, ip, ang);
234	greg	2.1	/* find nearest neighbors each side */
235	greg	2.2	for (i = ip->ns; i--; ) {
236	greg	2.3	const int ii = sortord[i].si;
237	greg	2.1	int j;
238	greg	2.3	/* preload with large radii */
239	greg	2.10	ip->da[ii].dia[bd] =
240			ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip,
241			.5*(sortord[ip->ns-1].dm - sortord[0].dm));
242	greg	2.1	for (j = i; ++j < ip->ns; ) /* nearest above */
243	greg	2.3	if (rightrndx[sortord[j].si] > rightrndx[ii] &&
244			leftrndx[sortord[j].si] < leftrndx[ii]) {
245	greg	2.10	ip->da[ii].dia[bd] = encode_diameter(ip,
246	greg	2.4	sortord[j].dm - sortord[i].dm);
247	greg	2.1	break;
248			}
249			for (j = i; j-- > 0; ) /* nearest below */
250	greg	2.3	if (rightrndx[sortord[j].si] < rightrndx[ii] &&
251			leftrndx[sortord[j].si] > leftrndx[ii]) {
252	greg	2.10	ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip,
253	greg	2.4	sortord[i].dm - sortord[j].dm);
254	greg	2.1	break;
255			}
256			}
257			}
258			free(sortord); /* clean up */
259			free(rightrndx);
260			free(leftrndx);
261	greg	2.2	free(endrndx);
262	greg	2.1	return(1);
263			}
264
265	greg	2.10	/* Compute unnormalized weight for a position relative to a sample */
266			double
267			interp2_wti(INTERP2 *ip, const int i, double x, double y)
268	greg	2.1	{
269	greg	2.10	int xfi, yfi;
270	greg	2.6	double dir, rd, r2, d2;
271	greg	2.1	int ri;
272	greg	2.10	/* need to compute interpolant? */
273			if (ip->da == NULL && !interp2_analyze(ip))
274			return(0);
275			/* get grid position */
276			xfi = (x - ip->smin[0]) * ip->smul[0];
277			if (xfi >= NI2DIM)
278			xfi = NI2DIM-1;
279			else
280			xfi *= (xfi >= 0);
281			yfi = (y - ip->smin[1]) * ip->smul[1];
282			if (yfi >= NI2DIM)
283			yfi = NI2DIM-1;
284			else
285			yfi *= (yfi >= 0);
286			x -= ip->spt[i][0]; /* check distance */
287	greg	2.1	y -= ip->spt[i][1];
288	greg	2.10	d2 = xx + yy;
289			/* zero weight this zone? */
290			if (d2 > ip->grid2 && ip->da[i].blkflg[yfi] & 1<<xfi)
291			return(.0);
292
293			dir = atan2a(y, x); /* get relative direction */
294	greg	2.1	dir += 2.PI(dir < 0);
295			/* linear radius interpolation */
296			rd = dir * (NI2DIR/2./PI);
297			ri = (int)rd;
298			rd -= (double)ri;
299	greg	2.10	rd = (1.-rd)ip->da[i].dia[ri] + rdip->da[i].dia[(ri+1)%NI2DIR];
300	greg	2.4	rd = ip->smf * DECODE_DIA(ip, rd);
301	greg	2.6	r2 = 2.rdrd;
302	greg	2.10	if (d2 > 21.r2) { / result would be < 1e-9 */
303			ip->da[i].blkflg[yfi] \|= 1<<xfi;
304	greg	2.6	return(.0);
305	greg	2.10	}
306	greg	2.3	/* Gaussian times harmonic weighting */
307	greg	2.6	return( exp(-d2/r2) * ip->dmin/(ip->dmin + sqrt(d2)) );
308	greg	2.1	}
309
310			/* Assign full set of normalized weights to interpolate the given position */
311			int
312			interp2_weights(float wtv[], INTERP2 *ip, double x, double y)
313			{
314			double wnorm;
315			int i;
316
317			if ((wtv == NULL) \| (ip == NULL))
318			return(0);
319
320			wnorm = 0; /* compute raw weights */
321			for (i = ip->ns; i--; ) {
322	greg	2.10	double wt = interp2_wti(ip, i, x, y);
323	greg	2.1	wtv[i] = wt;
324			wnorm += wt;
325			}
326			if (wnorm <= 0) /* too far from all our samples! */
327			return(0);
328			wnorm = 1./wnorm; /* normalize weights */
329			for (i = ip->ns; i--; )
330			wtv[i] *= wnorm;
331			return(ip->ns); /* all done */
332			}
333
334
335			/* Get normalized weights and indexes for n best samples in descending order */
336			int
337			interp2_topsamp(float wt[], int si[], const int n, INTERP2 *ip, double x, double y)
338			{
339			int nn = 0;
340			double wnorm;
341			int i, j;
342
343			if ((n <= 0) \| (wt == NULL) \| (si == NULL) \| (ip == NULL))
344			return(0);
345			/* identify top n weights */
346			for (i = ip->ns; i--; ) {
347	greg	2.10	const double wti = interp2_wti(ip, i, x, y);
348	greg	2.9	if (wti <= 1e-9)
349			continue;
350	greg	2.1	for (j = nn; j > 0; j--) {
351	greg	2.3	if (wt[j-1] >= wti)
352	greg	2.1	break;
353			if (j < n) {
354			wt[j] = wt[j-1];
355			si[j] = si[j-1];
356			}
357			}
358			if (j < n) { /* add/insert sample */
359	greg	2.3	wt[j] = wti;
360	greg	2.1	si[j] = i;
361			nn += (nn < n);
362			}
363			}
364	greg	2.3	wnorm = 0; /* normalize sample weights */
365			for (j = nn; j--; )
366			wnorm += wt[j];
367	greg	2.1	if (wnorm <= 0)
368			return(0);
369			wnorm = 1./wnorm;
370			for (j = nn; j--; )
371			wt[j] *= wnorm;
372			return(nn); /* return actual # samples */
373			}
374
375			/* Free interpolant */
376			void
377			interp2_free(INTERP2 *ip)
378			{
379			if (ip == NULL)
380			return;
381	greg	2.4	if (ip->da != NULL)
382			free(ip->da);
383	greg	2.1	free(ip);
384			}