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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 2.7 by greg, Tue Feb 12 17:47:58 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.
27 > ****************************************************************/
28  
29   #include <stdio.h>
30   #include <stdlib.h>
31   #include "rtmath.h"
32   #include "interp2d.h"
33  
34 < #define DECODE_RAD(ip,er)       ((ip)->rmin*(1. + .5*(er)))
35 < #define ENCODE_RAD(ip,r)        ((int)(2.*(r)/(ip)->rmin) - 2)
34 > #define DECODE_DIA(ip,ed)       ((ip)->dmin*(1. + .5*(ed)))
35 > #define ENCODE_DIA(ip,d)        ((int)(2.*(d)/(ip)->dmin) - 2)
36  
37   /* Sample order (private) */
38   typedef struct {
# Line 53 | Line 54 | interp2_alloc(int nsamps)
54                  return(NULL);
55  
56          nip->ns = nsamps;
57 <        nip->rmin = .5;         /* default radius minimum */
57 >        nip->dmin = 1;          /* default minimum diameter */
58          nip->smf = NI2DSMF;     /* default smoothing factor */
59 <        nip->ra = NULL;
59 >        nip->da = NULL;
60                                  /* caller must assign spt[] array */
61          return(nip);
62   }
# Line 72 | Line 73 | interp2_realloc(INTERP2 *ip, int nsamps)
73          }
74          if (nsamps == ip->ns);
75                  return(ip);
76 <        if (ip->ra != NULL) {   /* will need to recompute distribution */
77 <                free(ip->ra);
78 <                ip->ra = NULL;
76 >        if (ip->da != NULL) {   /* will need to recompute distribution */
77 >                free(ip->da);
78 >                ip->da = NULL;
79          }
80          ip = (INTERP2 *)realloc(ip, sizeof(INTERP2)+sizeof(float)*2*(nsamps-1));
81          if (ip == NULL)
# Line 83 | Line 84 | interp2_realloc(INTERP2 *ip, int nsamps)
84          return(ip);
85   }
86  
87 + /* Set minimum distance under which samples will start to merge */
88 + void
89 + interp2_spacing(INTERP2 *ip, double mind)
90 + {
91 +        if (mind <= 0)
92 +                return;
93 +        if ((.998*ip->dmin <= mind) & (mind <= 1.002*ip->dmin))
94 +                return;
95 +        if (ip->da != NULL) {   /* will need to recompute distribution */
96 +                free(ip->da);
97 +                ip->da = NULL;
98 +        }
99 +        ip->dmin = mind;
100 + }
101 +
102 + /* Modify smoothing parameter by the given factor */
103 + void
104 + interp2_smooth(INTERP2 *ip, double sf)
105 + {
106 +        if ((ip->smf *= sf) < NI2DSMF)
107 +                ip->smf = NI2DSMF;
108 + }
109 +
110   /* private call-back to sort position index */
111   static int
112   cmp_spos(const void *p1, const void *p2)
# Line 112 | Line 136 | sort_samples(SAMPORD *sord, const INTERP2 *ip, double
136          qsort(sord, ip->ns, sizeof(SAMPORD), &cmp_spos);
137   }
138  
139 < /* private routine to encode radius with range checks */
139 > /* private routine to encode sample diameter with range checks */
140   static int
141 < encode_radius(const INTERP2 *ip, double r)
141 > encode_diameter(const INTERP2 *ip, double d)
142   {
143 <        const int       er = ENCODE_RAD(ip, r);
143 >        const int       ed = ENCODE_DIA(ip, d);
144  
145 <        if (er <= 0)
145 >        if (ed <= 0)
146                  return(0);
147 <        if (er >= 0xffff)
147 >        if (ed >= 0xffff)
148                  return(0xffff);
149 <        return(er);
149 >        return(ed);
150   }
151  
152   /* (Re)compute anisotropic basis function interpolant (normally automatic) */
# Line 133 | Line 157 | interp2_analyze(INTERP2 *ip)
157          int     *rightrndx, *leftrndx, *endrndx;
158          int     bd;
159                                          /* sanity checks */
160 <        if (ip == NULL || (ip->ns <= 1) | (ip->rmin <= 0))
160 >        if (ip == NULL || (ip->ns <= 1) | (ip->dmin <= 0))
161                  return(0);
162                                          /* need to allocate? */
163 <        if (ip->ra == NULL) {
164 <                ip->ra = (unsigned short (*)[NI2DIR])malloc(
163 >        if (ip->da == NULL) {
164 >                ip->da = (unsigned short (*)[NI2DIR])malloc(
165                                  sizeof(unsigned short)*NI2DIR*ip->ns);
166 <                if (ip->ra == NULL)
166 >                if (ip->da == NULL)
167                          return(0);
168          }
169                                          /* get temporary arrays */
# Line 182 | Line 206 | interp2_analyze(INTERP2 *ip)
206              sort_samples(sortord, ip, ang);
207                                          /* find nearest neighbors each side */
208              for (i = ip->ns; i--; ) {
209 <                const int       rpos = rightrndx[sortord[i].si];
186 <                const int       lpos = leftrndx[sortord[i].si];
209 >                const int       ii = sortord[i].si;
210                  int             j;
211 <                                        /* preload with large radius */
212 <                ip->ra[i][bd] = ip->ra[i][bd+NI2DIR/2] = encode_radius(ip,
213 <                            .25*(sortord[ip->ns-1].dm - sortord[0].dm));
211 >                                        /* preload with large radii */
212 >                ip->da[ii][bd] = ip->da[ii][bd+NI2DIR/2] = encode_diameter(ip,
213 >                            .5*(sortord[ip->ns-1].dm - sortord[0].dm));
214                  for (j = i; ++j < ip->ns; )     /* nearest above */
215 <                    if (rightrndx[sortord[j].si] > rpos &&
216 <                                    leftrndx[sortord[j].si] < lpos) {
217 <                        ip->ra[i][bd] = encode_radius(ip,
218 <                                        .5*(sortord[j].dm - sortord[i].dm));
215 >                    if (rightrndx[sortord[j].si] > rightrndx[ii] &&
216 >                                    leftrndx[sortord[j].si] < leftrndx[ii]) {
217 >                        ip->da[ii][bd] = encode_diameter(ip,
218 >                                                sortord[j].dm - sortord[i].dm);
219                          break;
220                      }
221                  for (j = i; j-- > 0; )          /* nearest below */
222 <                    if (rightrndx[sortord[j].si] < rpos &&
223 <                                    leftrndx[sortord[j].si] > lpos) {
224 <                        ip->ra[i][bd+NI2DIR/2] = encode_radius(ip,
225 <                                        .5*(sortord[i].dm - sortord[j].dm));
222 >                    if (rightrndx[sortord[j].si] < rightrndx[ii] &&
223 >                                    leftrndx[sortord[j].si] > leftrndx[ii]) {
224 >                        ip->da[ii][bd+NI2DIR/2] = encode_diameter(ip,
225 >                                                sortord[i].dm - sortord[j].dm);
226                          break;
227                      }
228              }
# Line 211 | Line 234 | interp2_analyze(INTERP2 *ip)
234          return(1);
235   }
236  
237 < /* private call returns log of raw weight for a particular sample */
237 > /* private call returns raw weight for a particular sample */
238   static double
239 < get_ln_wt(const INTERP2 *ip, const int i, double x, double y)
239 > get_wt(const INTERP2 *ip, const int i, double x, double y)
240   {
241 <        double  dir, rd;
241 >        double  dir, rd, r2, d2;
242          int     ri;
243                                  /* get relative direction */
244          x -= ip->spt[i][0];
# Line 226 | Line 249 | get_ln_wt(const INTERP2 *ip, const int i, double x, do
249          rd = dir * (NI2DIR/2./PI);
250          ri = (int)rd;
251          rd -= (double)ri;
252 <        rd = (1.-rd)*ip->ra[i][ri] + rd*ip->ra[i][(ri+1)%NI2DIR];
253 <        rd = ip->smf * DECODE_RAD(ip, rd);
254 <                                /* return log of Gaussian weight */
255 <        return( (x*x + y*y) / (-2.*rd*rd) );
252 >        rd = (1.-rd)*ip->da[i][ri] + rd*ip->da[i][(ri+1)%NI2DIR];
253 >        rd = ip->smf * DECODE_DIA(ip, rd);
254 >        r2 = 2.*rd*rd;
255 >        d2 = x*x + y*y;
256 >        if (d2 > 21.*r2)        /* result would be < 1e-9 */
257 >                return(.0);
258 >                                /* Gaussian times harmonic weighting */
259 >        return( exp(-d2/r2) * ip->dmin/(ip->dmin + sqrt(d2)) );
260   }
261  
262   /* Assign full set of normalized weights to interpolate the given position */
# Line 242 | Line 269 | interp2_weights(float wtv[], INTERP2 *ip, double x, do
269          if ((wtv == NULL) | (ip == NULL))
270                  return(0);
271                                          /* need to compute interpolant? */
272 <        if (ip->ra == NULL && !interp2_analyze(ip))
272 >        if (ip->da == NULL && !interp2_analyze(ip))
273                  return(0);
274  
275          wnorm = 0;                      /* compute raw weights */
276          for (i = ip->ns; i--; ) {
277 <                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 */
277 >                double  wt = get_wt(ip, i, x, y);
278                  wtv[i] = wt;
279                  wnorm += wt;
280          }
# Line 276 | Line 298 | interp2_topsamp(float wt[], int si[], const int n, INT
298          if ((n <= 0) | (wt == NULL) | (si == NULL) | (ip == NULL))
299                  return(0);
300                                          /* need to compute interpolant? */
301 <        if (ip->ra == NULL && !interp2_analyze(ip))
301 >        if (ip->da == NULL && !interp2_analyze(ip))
302                  return(0);
303                                          /* identify top n weights */
304          for (i = ip->ns; i--; ) {
305 <                const double    lnwt = get_ln_wt(ip, i, x, y);
305 >                const double    wti = get_wt(ip, i, x, y);
306                  for (j = nn; j > 0; j--) {
307 <                        if (wt[j-1] >= lnwt)
307 >                        if (wt[j-1] >= wti)
308                                  break;
309                          if (j < n) {
310                                  wt[j] = wt[j-1];
# Line 290 | Line 312 | interp2_topsamp(float wt[], int si[], const int n, INT
312                          }
313                  }
314                  if (j < n) {            /* add/insert sample */
315 <                        wt[j] = lnwt;
315 >                        wt[j] = wti;
316                          si[j] = i;
317                          nn += (nn < n);
318                  }
319          }
320 <        wnorm = 0;                      /* exponentiate and normalize */
321 <        for (j = nn; j--; ) {
322 <                double  dwt = exp(wt[j]);
301 <                wt[j] = dwt;
302 <                wnorm += dwt;
303 <        }
320 >        wnorm = 0;                      /* normalize sample weights */
321 >        for (j = nn; j--; )
322 >                wnorm += wt[j];
323          if (wnorm <= 0)
324                  return(0);
325          wnorm = 1./wnorm;
# Line 315 | Line 334 | interp2_free(INTERP2 *ip)
334   {
335          if (ip == NULL)
336                  return;
337 <        if (ip->ra != NULL)
338 <                free(ip->ra);
337 >        if (ip->da != NULL)
338 >                free(ip->da);
339          free(ip);
340   }

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