1 |
#ifndef lint |
2 |
static const char RCSid[] = "$Id: interp2d.c,v 2.9 2013/02/12 18:41:39 greg Exp $"; |
3 |
#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 |
/*************************************************************** |
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 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_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 { |
40 |
int si; /* sample index */ |
41 |
float dm; /* distance measure in this direction */ |
42 |
} SAMPORD; |
43 |
|
44 |
/* Allocate a new set of interpolation samples (caller assigns spt[] array) */ |
45 |
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 |
nip->dmin = 1; /* default minimum diameter */ |
59 |
nip->smf = NI2DSMF; /* default smoothing factor */ |
60 |
nip->da = NULL; |
61 |
/* caller must assign spt[] array */ |
62 |
return(nip); |
63 |
} |
64 |
|
65 |
/* 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 |
if (nsamps == ip->ns) |
76 |
return(ip); |
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) |
83 |
return(NULL); |
84 |
ip->ns = 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) |
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 |
/* 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 = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
136 |
} |
137 |
qsort(sord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
138 |
} |
139 |
|
140 |
/* private routine to encode sample diameter with range checks */ |
141 |
static int |
142 |
encode_diameter(const INTERP2 *ip, double d) |
143 |
{ |
144 |
const int ed = ENCODE_DIA(ip, d); |
145 |
|
146 |
if (ed <= 0) |
147 |
return(0); |
148 |
if (ed >= 0xffff) |
149 |
return(0xffff); |
150 |
return(ed); |
151 |
} |
152 |
|
153 |
/* (Re)compute anisotropic basis function interpolant (normally automatic) */ |
154 |
int |
155 |
interp2_analyze(INTERP2 *ip) |
156 |
{ |
157 |
SAMPORD *sortord; |
158 |
int *rightrndx, *leftrndx, *endrndx; |
159 |
int i, bd; |
160 |
/* sanity checks */ |
161 |
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 |
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); |
200 |
leftrndx = (int *)malloc(sizeof(int)*ip->ns); |
201 |
endrndx = (int *)malloc(sizeof(int)*ip->ns); |
202 |
if ((sortord == NULL) | (rightrndx == NULL) | |
203 |
(leftrndx == NULL) | (endrndx == NULL)) |
204 |
return(0); |
205 |
/* run through bidirections */ |
206 |
for (bd = 0; bd < NI2DIR/2; bd++) { |
207 |
const double ang = 2.*PI/NI2DIR*bd; |
208 |
int *sptr; |
209 |
/* create right reverse index */ |
210 |
if (bd) { /* re-use from previous iteration? */ |
211 |
sptr = rightrndx; |
212 |
rightrndx = leftrndx; |
213 |
leftrndx = sptr; |
214 |
} else { /* else sort first half-plane */ |
215 |
sort_samples(sortord, ip, PI/2. - PI/NI2DIR); |
216 |
for (i = ip->ns; i--; ) |
217 |
rightrndx[sortord[i].si] = i; |
218 |
/* & store reverse order for later */ |
219 |
for (i = ip->ns; i--; ) |
220 |
endrndx[sortord[i].si] = ip->ns-1 - i; |
221 |
} |
222 |
/* create new left reverse index */ |
223 |
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 |
} |
232 |
/* sort grid values in this direction */ |
233 |
sort_samples(sortord, ip, ang); |
234 |
/* find nearest neighbors each side */ |
235 |
for (i = ip->ns; i--; ) { |
236 |
const int ii = sortord[i].si; |
237 |
int j; |
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] > 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] < 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 |
} |
257 |
} |
258 |
free(sortord); /* clean up */ |
259 |
free(rightrndx); |
260 |
free(leftrndx); |
261 |
free(endrndx); |
262 |
return(1); |
263 |
} |
264 |
|
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 |
int xfi, yfi; |
270 |
double dir, rd, r2, d2; |
271 |
int ri; |
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 |
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->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 */ |
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 |
double wt = interp2_wti(ip, i, x, y); |
323 |
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 |
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] >= wti) |
352 |
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 |
wt[j] = wti; |
360 |
si[j] = i; |
361 |
nn += (nn < n); |
362 |
} |
363 |
} |
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; |
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 |
if (ip->da != NULL) |
382 |
free(ip->da); |
383 |
free(ip); |
384 |
} |