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root/radiance/ray/src/common/interp2d.c
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Comparing ray/src/common/interp2d.c (file contents):
Revision 2.2 by greg, Sat Feb 9 17:39:21 2013 UTC vs.
Revision 2.10 by greg, Thu Feb 14 19:57:10 2013 UTC

# Line 9 | Line 9 | static const char RCSid[] = "$Id$";
9  
10   #include "copyright.h"
11  
12 < /*************************************************************
12 > /***************************************************************
13   * 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 < * calculation, we sort the data into 3 half-planes and
19 < * perform simple tests to see which neighbor is closest in
20 < * a each direction.  Once we have our approximate neighborhood
21 < * for a sample, we can use it in a Gaussian weighting scheme
22 < * with anisotropic surround.  This gives us a fairly smooth
23 < * interpolation however the sample points may be initially
24 < * distributed.  Evaluation is accelerated by use of a fast
25 < * approximation to the atan2(y,x) function.
26 < **************************************************************/
18 > * calculation, we sort the data into half-planes and apply
19 > * simple tests to see which neighbor is closest in each
20 > * angular slice.  Once we have our approximate neighborhood
21 > * for a sample, we can use it in a modified Gaussian weighting
22 > * with allowing local anisotropy.  Harmonic weighting is added
23 > * to reduce the influence of distant neighbors.  This yields a
24 > * smooth interpolation regardless of how the sample points are
25 > * initially distributed.  Evaluation is accelerated by use of
26 > * a fast approximation to the atan2(y,x) function and an array
27 > * of flags indicating where weights are (nearly) zero.
28 > ****************************************************************/
29  
30   #include <stdio.h>
31   #include <stdlib.h>
32   #include "rtmath.h"
33   #include "interp2d.h"
34  
35 < #define DECODE_RAD(ip,er)       ((ip)->rmin*(1. + .5*(er)))
36 < #define ENCODE_RAD(ip,r)        ((int)(2.*(r)/(ip)->rmin) - 2)
35 > #define DECODE_DIA(ip,ed)       ((ip)->dmin*(1. + .5*(ed)))
36 > #define ENCODE_DIA(ip,d)        ((int)(2.*(d)/(ip)->dmin) - 2)
37  
38   /* Sample order (private) */
39   typedef struct {
# Line 53 | Line 55 | interp2_alloc(int nsamps)
55                  return(NULL);
56  
57          nip->ns = nsamps;
58 <        nip->rmin = .5;         /* default radius minimum */
58 >        nip->dmin = 1;          /* default minimum diameter */
59          nip->smf = NI2DSMF;     /* default smoothing factor */
60 <        nip->ra = NULL;
60 >        nip->da = NULL;
61                                  /* caller must assign spt[] array */
62          return(nip);
63   }
# Line 70 | Line 72 | interp2_realloc(INTERP2 *ip, int nsamps)
72                  interp2_free(ip);
73                  return(NULL);
74          }
75 <        if (nsamps == ip->ns);
75 >        if (nsamps == ip->ns)
76                  return(ip);
77 <        if (ip->ra != NULL) {   /* will need to recompute distribution */
78 <                free(ip->ra);
79 <                ip->ra = NULL;
77 >        if (ip->da != NULL) {   /* will need to recompute distribution */
78 >                free(ip->da);
79 >                ip->da = NULL;
80          }
81          ip = (INTERP2 *)realloc(ip, sizeof(INTERP2)+sizeof(float)*2*(nsamps-1));
82          if (ip == NULL)
# Line 83 | Line 85 | interp2_realloc(INTERP2 *ip, int nsamps)
85          return(ip);
86   }
87  
88 + /* 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 +        if ((.998*ip->dmin <= mind) & (mind <= 1.002*ip->dmin))
95 +                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   /* private call-back to sort position index */
112   static int
113   cmp_spos(const void *p1, const void *p2)
# Line 112 | Line 137 | sort_samples(SAMPORD *sord, const INTERP2 *ip, double
137          qsort(sord, ip->ns, sizeof(SAMPORD), &cmp_spos);
138   }
139  
140 < /* private routine to encode radius with range checks */
140 > /* private routine to encode sample diameter with range checks */
141   static int
142 < encode_radius(const INTERP2 *ip, double r)
142 > encode_diameter(const INTERP2 *ip, double d)
143   {
144 <        const int       er = ENCODE_RAD(ip, r);
144 >        const int       ed = ENCODE_DIA(ip, d);
145  
146 <        if (er <= 0)
146 >        if (ed <= 0)
147                  return(0);
148 <        if (er >= 0xffff)
148 >        if (ed >= 0xffff)
149                  return(0xffff);
150 <        return(er);
150 >        return(ed);
151   }
152  
153   /* (Re)compute anisotropic basis function interpolant (normally automatic) */
# Line 131 | Line 156 | interp2_analyze(INTERP2 *ip)
156   {
157          SAMPORD *sortord;
158          int     *rightrndx, *leftrndx, *endrndx;
159 <        int     bd;
159 >        int     i, bd;
160                                          /* sanity checks */
161 <        if (ip == NULL || (ip->ns <= 1) | (ip->rmin <= 0))
161 >        if (ip == NULL)
162                  return(0);
163 <                                        /* need to allocate? */
164 <        if (ip->ra == NULL) {
165 <                ip->ra = (unsigned short (*)[NI2DIR])malloc(
141 <                                sizeof(unsigned short)*NI2DIR*ip->ns);
142 <                if (ip->ra == NULL)
143 <                        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 +                return(0);
169 +                                        /* 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 +        }
182 +        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 <= FTINY*ip->dmin*ip->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                                          /* get temporary arrays */
198          sortord = (SAMPORD *)malloc(sizeof(SAMPORD)*ip->ns);
199          rightrndx = (int *)malloc(sizeof(int)*ip->ns);
# Line 154 | Line 206 | interp2_analyze(INTERP2 *ip)
206          for (bd = 0; bd < NI2DIR/2; bd++) {
207              const double        ang = 2.*PI/NI2DIR*bd;
208              int                 *sptr;
157 –            int                 i;
209                                          /* create right reverse index */
210              if (bd) {                   /* re-use from previous iteration? */
211                  sptr = rightrndx;
# Line 182 | Line 233 | interp2_analyze(INTERP2 *ip)
233              sort_samples(sortord, ip, ang);
234                                          /* find nearest neighbors each side */
235              for (i = ip->ns; i--; ) {
236 <                const int       rpos = rightrndx[sortord[i].si];
186 <                const int       lpos = leftrndx[sortord[i].si];
236 >                const int       ii = sortord[i].si;
237                  int             j;
238 <                                        /* preload with large radius */
239 <                ip->ra[i][bd] = ip->ra[i][bd+NI2DIR/2] = encode_radius(ip,
240 <                            .25*(sortord[ip->ns-1].dm - sortord[0].dm));
238 >                                        /* preload with large radii */
239 >                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                  for (j = i; ++j < ip->ns; )     /* nearest above */
243 <                    if (rightrndx[sortord[j].si] > rpos &&
244 <                                    leftrndx[sortord[j].si] < lpos) {
245 <                        ip->ra[i][bd] = encode_radius(ip,
246 <                                        .5*(sortord[j].dm - sortord[i].dm));
243 >                    if (rightrndx[sortord[j].si] > rightrndx[ii] &&
244 >                                    leftrndx[sortord[j].si] < leftrndx[ii]) {
245 >                        ip->da[ii].dia[bd] = encode_diameter(ip,
246 >                                                sortord[j].dm - sortord[i].dm);
247                          break;
248                      }
249                  for (j = i; j-- > 0; )          /* nearest below */
250 <                    if (rightrndx[sortord[j].si] < rpos &&
251 <                                    leftrndx[sortord[j].si] > lpos) {
252 <                        ip->ra[i][bd+NI2DIR/2] = encode_radius(ip,
253 <                                        .5*(sortord[i].dm - sortord[j].dm));
250 >                    if (rightrndx[sortord[j].si] < rightrndx[ii] &&
251 >                                    leftrndx[sortord[j].si] > leftrndx[ii]) {
252 >                        ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip,
253 >                                                sortord[i].dm - sortord[j].dm);
254                          break;
255                      }
256              }
# Line 211 | Line 262 | interp2_analyze(INTERP2 *ip)
262          return(1);
263   }
264  
265 < /* private call returns log of raw weight for a particular sample */
266 < static double
267 < get_ln_wt(const INTERP2 *ip, const int i, double x, double y)
265 > /* 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   {
269 <        double  dir, rd;
269 >        int     xfi, yfi;
270 >        double  dir, rd, r2, d2;
271          int     ri;
272 <                                /* get relative direction */
273 <        x -= ip->spt[i][0];
272 >                                /* 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          y -= ip->spt[i][1];
288 <        dir = atan2a(y, x);
288 >        d2 = x*x + y*y;
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          dir += 2.*PI*(dir < 0);
295                                  /* linear radius interpolation */
296          rd = dir * (NI2DIR/2./PI);
297          ri = (int)rd;
298          rd -= (double)ri;
299 <        rd = (1.-rd)*ip->ra[i][ri] + rd*ip->ra[i][(ri+1)%NI2DIR];
300 <        rd = ip->smf * DECODE_RAD(ip, rd);
301 <                                /* return log of Gaussian weight */
302 <        return( (x*x + y*y) / (-2.*rd*rd) );
299 >        rd = (1.-rd)*ip->da[i].dia[ri] + rd*ip->da[i].dia[(ri+1)%NI2DIR];
300 >        rd = ip->smf * DECODE_DIA(ip, rd);
301 >        r2 = 2.*rd*rd;
302 >        if (d2 > 21.*r2) {      /* result would be < 1e-9 */
303 >                ip->da[i].blkflg[yfi] |= 1<<xfi;
304 >                return(.0);
305 >        }
306 >                                /* Gaussian times harmonic weighting */
307 >        return( exp(-d2/r2) * ip->dmin/(ip->dmin + sqrt(d2)) );
308   }
309  
310   /* Assign full set of normalized weights to interpolate the given position */
# Line 241 | Line 316 | interp2_weights(float wtv[], INTERP2 *ip, double x, do
316  
317          if ((wtv == NULL) | (ip == NULL))
318                  return(0);
244 –                                        /* need to compute interpolant? */
245 –        if (ip->ra == NULL && !interp2_analyze(ip))
246 –                return(0);
319  
320          wnorm = 0;                      /* compute raw weights */
321          for (i = ip->ns; i--; ) {
322 <                double  wt = get_ln_wt(ip, i, x, y);
251 <                if (wt < -21.) {
252 <                        wtv[i] = 0;     /* ignore weights < 1e-9 */
253 <                        continue;
254 <                }
255 <                wt = exp(wt);           /* Gaussian weight */
322 >                double  wt = interp2_wti(ip, i, x, y);
323                  wtv[i] = wt;
324                  wnorm += wt;
325          }
# Line 275 | Line 342 | interp2_topsamp(float wt[], int si[], const int n, INT
342  
343          if ((n <= 0) | (wt == NULL) | (si == NULL) | (ip == NULL))
344                  return(0);
278 –                                        /* need to compute interpolant? */
279 –        if (ip->ra == NULL && !interp2_analyze(ip))
280 –                return(0);
345                                          /* identify top n weights */
346          for (i = ip->ns; i--; ) {
347 <                const double    lnwt = get_ln_wt(ip, i, x, y);
347 >                const double    wti = interp2_wti(ip, i, x, y);
348 >                if (wti <= 1e-9)
349 >                        continue;
350                  for (j = nn; j > 0; j--) {
351 <                        if (wt[j-1] >= lnwt)
351 >                        if (wt[j-1] >= wti)
352                                  break;
353                          if (j < n) {
354                                  wt[j] = wt[j-1];
# Line 290 | Line 356 | interp2_topsamp(float wt[], int si[], const int n, INT
356                          }
357                  }
358                  if (j < n) {            /* add/insert sample */
359 <                        wt[j] = lnwt;
359 >                        wt[j] = wti;
360                          si[j] = i;
361                          nn += (nn < n);
362                  }
363          }
364 <        wnorm = 0;                      /* exponentiate and normalize */
365 <        for (j = nn; j--; ) {
366 <                double  dwt = exp(wt[j]);
301 <                wt[j] = dwt;
302 <                wnorm += dwt;
303 <        }
364 >        wnorm = 0;                      /* normalize sample weights */
365 >        for (j = nn; j--; )
366 >                wnorm += wt[j];
367          if (wnorm <= 0)
368                  return(0);
369          wnorm = 1./wnorm;
# Line 315 | Line 378 | interp2_free(INTERP2 *ip)
378   {
379          if (ip == NULL)
380                  return;
381 <        if (ip->ra != NULL)
382 <                free(ip->ra);
381 >        if (ip->da != NULL)
382 >                free(ip->da);
383          free(ip);
384   }

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