1 |
greg |
2.1 |
#ifndef lint |
2 |
greg |
2.2 |
static const char RCSid[] = "$Id: interp2d.c,v 2.1 2013/02/09 00:55:40 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 |
|
|
/************************************************************* |
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 |
|
|
**************************************************************/ |
27 |
|
|
|
28 |
|
|
#include <stdio.h> |
29 |
|
|
#include <stdlib.h> |
30 |
|
|
#include "rtmath.h" |
31 |
|
|
#include "interp2d.h" |
32 |
|
|
|
33 |
|
|
#define DECODE_RAD(ip,er) ((ip)->rmin*(1. + .5*(er))) |
34 |
|
|
#define ENCODE_RAD(ip,r) ((int)(2.*(r)/(ip)->rmin) - 2) |
35 |
|
|
|
36 |
|
|
/* Sample order (private) */ |
37 |
|
|
typedef struct { |
38 |
|
|
int si; /* sample index */ |
39 |
|
|
float dm; /* distance measure in this direction */ |
40 |
|
|
} SAMPORD; |
41 |
|
|
|
42 |
greg |
2.2 |
/* Allocate a new set of interpolation samples (caller assigns spt[] array) */ |
43 |
greg |
2.1 |
INTERP2 * |
44 |
|
|
interp2_alloc(int nsamps) |
45 |
|
|
{ |
46 |
|
|
INTERP2 *nip; |
47 |
|
|
|
48 |
|
|
if (nsamps <= 1) |
49 |
|
|
return(NULL); |
50 |
|
|
|
51 |
|
|
nip = (INTERP2 *)malloc(sizeof(INTERP2) + sizeof(float)*2*(nsamps-1)); |
52 |
|
|
if (nip == NULL) |
53 |
|
|
return(NULL); |
54 |
|
|
|
55 |
|
|
nip->ns = nsamps; |
56 |
|
|
nip->rmin = .5; /* default radius minimum */ |
57 |
|
|
nip->smf = NI2DSMF; /* default smoothing factor */ |
58 |
|
|
nip->ra = NULL; |
59 |
|
|
/* caller must assign spt[] array */ |
60 |
|
|
return(nip); |
61 |
|
|
} |
62 |
|
|
|
63 |
greg |
2.2 |
/* Resize interpolation array (caller must assign any new values) */ |
64 |
|
|
INTERP2 * |
65 |
|
|
interp2_realloc(INTERP2 *ip, int nsamps) |
66 |
|
|
{ |
67 |
|
|
if (ip == NULL) |
68 |
|
|
return(interp2_alloc(nsamps)); |
69 |
|
|
if (nsamps <= 1) { |
70 |
|
|
interp2_free(ip); |
71 |
|
|
return(NULL); |
72 |
|
|
} |
73 |
|
|
if (nsamps == ip->ns); |
74 |
|
|
return(ip); |
75 |
|
|
if (ip->ra != NULL) { /* will need to recompute distribution */ |
76 |
|
|
free(ip->ra); |
77 |
|
|
ip->ra = NULL; |
78 |
|
|
} |
79 |
|
|
ip = (INTERP2 *)realloc(ip, sizeof(INTERP2)+sizeof(float)*2*(nsamps-1)); |
80 |
|
|
if (ip == NULL) |
81 |
|
|
return(NULL); |
82 |
|
|
ip->ns = nsamps; |
83 |
|
|
return(ip); |
84 |
|
|
} |
85 |
|
|
|
86 |
greg |
2.1 |
/* private call-back to sort position index */ |
87 |
|
|
static int |
88 |
|
|
cmp_spos(const void *p1, const void *p2) |
89 |
|
|
{ |
90 |
|
|
const SAMPORD *so1 = (const SAMPORD *)p1; |
91 |
|
|
const SAMPORD *so2 = (const SAMPORD *)p2; |
92 |
|
|
|
93 |
|
|
if (so1->dm > so2->dm) |
94 |
|
|
return 1; |
95 |
|
|
if (so1->dm < so2->dm) |
96 |
|
|
return -1; |
97 |
|
|
return 0; |
98 |
|
|
} |
99 |
|
|
|
100 |
greg |
2.2 |
/* private routine to order samples in a particular direction */ |
101 |
|
|
static void |
102 |
|
|
sort_samples(SAMPORD *sord, const INTERP2 *ip, double ang) |
103 |
|
|
{ |
104 |
|
|
const double cosd = cos(ang); |
105 |
|
|
const double sind = sin(ang); |
106 |
|
|
int i; |
107 |
|
|
|
108 |
|
|
for (i = ip->ns; i--; ) { |
109 |
|
|
sord[i].si = i; |
110 |
|
|
sord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
111 |
|
|
} |
112 |
|
|
qsort(sord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
113 |
|
|
} |
114 |
|
|
|
115 |
greg |
2.1 |
/* private routine to encode radius with range checks */ |
116 |
|
|
static int |
117 |
|
|
encode_radius(const INTERP2 *ip, double r) |
118 |
|
|
{ |
119 |
|
|
const int er = ENCODE_RAD(ip, r); |
120 |
|
|
|
121 |
|
|
if (er <= 0) |
122 |
|
|
return(0); |
123 |
|
|
if (er >= 0xffff) |
124 |
|
|
return(0xffff); |
125 |
|
|
return(er); |
126 |
|
|
} |
127 |
|
|
|
128 |
greg |
2.2 |
/* (Re)compute anisotropic basis function interpolant (normally automatic) */ |
129 |
|
|
int |
130 |
|
|
interp2_analyze(INTERP2 *ip) |
131 |
greg |
2.1 |
{ |
132 |
|
|
SAMPORD *sortord; |
133 |
greg |
2.2 |
int *rightrndx, *leftrndx, *endrndx; |
134 |
greg |
2.1 |
int bd; |
135 |
|
|
/* sanity checks */ |
136 |
|
|
if (ip == NULL || (ip->ns <= 1) | (ip->rmin <= 0)) |
137 |
|
|
return(0); |
138 |
|
|
/* need to allocate? */ |
139 |
|
|
if (ip->ra == NULL) { |
140 |
|
|
ip->ra = (unsigned short (*)[NI2DIR])malloc( |
141 |
|
|
sizeof(unsigned short)*NI2DIR*ip->ns); |
142 |
|
|
if (ip->ra == NULL) |
143 |
|
|
return(0); |
144 |
|
|
} |
145 |
|
|
/* get temporary arrays */ |
146 |
|
|
sortord = (SAMPORD *)malloc(sizeof(SAMPORD)*ip->ns); |
147 |
|
|
rightrndx = (int *)malloc(sizeof(int)*ip->ns); |
148 |
|
|
leftrndx = (int *)malloc(sizeof(int)*ip->ns); |
149 |
greg |
2.2 |
endrndx = (int *)malloc(sizeof(int)*ip->ns); |
150 |
|
|
if ((sortord == NULL) | (rightrndx == NULL) | |
151 |
|
|
(leftrndx == NULL) | (endrndx == NULL)) |
152 |
greg |
2.1 |
return(0); |
153 |
|
|
/* run through bidirections */ |
154 |
|
|
for (bd = 0; bd < NI2DIR/2; bd++) { |
155 |
|
|
const double ang = 2.*PI/NI2DIR*bd; |
156 |
greg |
2.2 |
int *sptr; |
157 |
greg |
2.1 |
int i; |
158 |
|
|
/* create right reverse index */ |
159 |
greg |
2.2 |
if (bd) { /* re-use from previous iteration? */ |
160 |
|
|
sptr = rightrndx; |
161 |
greg |
2.1 |
rightrndx = leftrndx; |
162 |
|
|
leftrndx = sptr; |
163 |
greg |
2.2 |
} else { /* else sort first half-plane */ |
164 |
|
|
sort_samples(sortord, ip, PI/2. - PI/NI2DIR); |
165 |
|
|
for (i = ip->ns; i--; ) |
166 |
greg |
2.1 |
rightrndx[sortord[i].si] = i; |
167 |
greg |
2.2 |
/* & store reverse order for later */ |
168 |
|
|
for (i = ip->ns; i--; ) |
169 |
|
|
endrndx[sortord[i].si] = ip->ns-1 - i; |
170 |
greg |
2.1 |
} |
171 |
|
|
/* create new left reverse index */ |
172 |
greg |
2.2 |
if (bd == NI2DIR/2 - 1) { /* use order from first iteration? */ |
173 |
|
|
sptr = leftrndx; |
174 |
|
|
leftrndx = endrndx; |
175 |
|
|
endrndx = sptr; |
176 |
|
|
} else { /* else compute new half-plane */ |
177 |
|
|
sort_samples(sortord, ip, ang + (PI/2. + PI/NI2DIR)); |
178 |
|
|
for (i = ip->ns; i--; ) |
179 |
|
|
leftrndx[sortord[i].si] = i; |
180 |
greg |
2.1 |
} |
181 |
|
|
/* sort grid values in this direction */ |
182 |
greg |
2.2 |
sort_samples(sortord, ip, ang); |
183 |
greg |
2.1 |
/* find nearest neighbors each side */ |
184 |
greg |
2.2 |
for (i = ip->ns; i--; ) { |
185 |
greg |
2.1 |
const int rpos = rightrndx[sortord[i].si]; |
186 |
|
|
const int lpos = leftrndx[sortord[i].si]; |
187 |
|
|
int j; |
188 |
|
|
/* preload with large radius */ |
189 |
|
|
ip->ra[i][bd] = ip->ra[i][bd+NI2DIR/2] = encode_radius(ip, |
190 |
|
|
.25*(sortord[ip->ns-1].dm - sortord[0].dm)); |
191 |
|
|
for (j = i; ++j < ip->ns; ) /* nearest above */ |
192 |
|
|
if (rightrndx[sortord[j].si] > rpos && |
193 |
|
|
leftrndx[sortord[j].si] < lpos) { |
194 |
|
|
ip->ra[i][bd] = encode_radius(ip, |
195 |
|
|
.5*(sortord[j].dm - sortord[i].dm)); |
196 |
|
|
break; |
197 |
|
|
} |
198 |
|
|
for (j = i; j-- > 0; ) /* nearest below */ |
199 |
|
|
if (rightrndx[sortord[j].si] < rpos && |
200 |
|
|
leftrndx[sortord[j].si] > lpos) { |
201 |
|
|
ip->ra[i][bd+NI2DIR/2] = encode_radius(ip, |
202 |
|
|
.5*(sortord[i].dm - sortord[j].dm)); |
203 |
|
|
break; |
204 |
|
|
} |
205 |
|
|
} |
206 |
|
|
} |
207 |
|
|
free(sortord); /* clean up */ |
208 |
|
|
free(rightrndx); |
209 |
|
|
free(leftrndx); |
210 |
greg |
2.2 |
free(endrndx); |
211 |
greg |
2.1 |
return(1); |
212 |
|
|
} |
213 |
|
|
|
214 |
|
|
/* private call returns log of raw weight for a particular sample */ |
215 |
|
|
static double |
216 |
|
|
get_ln_wt(const INTERP2 *ip, const int i, double x, double y) |
217 |
|
|
{ |
218 |
|
|
double dir, rd; |
219 |
|
|
int ri; |
220 |
|
|
/* get relative direction */ |
221 |
|
|
x -= ip->spt[i][0]; |
222 |
|
|
y -= ip->spt[i][1]; |
223 |
|
|
dir = atan2a(y, x); |
224 |
|
|
dir += 2.*PI*(dir < 0); |
225 |
|
|
/* linear radius interpolation */ |
226 |
|
|
rd = dir * (NI2DIR/2./PI); |
227 |
|
|
ri = (int)rd; |
228 |
|
|
rd -= (double)ri; |
229 |
|
|
rd = (1.-rd)*ip->ra[i][ri] + rd*ip->ra[i][(ri+1)%NI2DIR]; |
230 |
|
|
rd = ip->smf * DECODE_RAD(ip, rd); |
231 |
|
|
/* return log of Gaussian weight */ |
232 |
|
|
return( (x*x + y*y) / (-2.*rd*rd) ); |
233 |
|
|
} |
234 |
|
|
|
235 |
|
|
/* Assign full set of normalized weights to interpolate the given position */ |
236 |
|
|
int |
237 |
|
|
interp2_weights(float wtv[], INTERP2 *ip, double x, double y) |
238 |
|
|
{ |
239 |
|
|
double wnorm; |
240 |
|
|
int i; |
241 |
|
|
|
242 |
|
|
if ((wtv == NULL) | (ip == NULL)) |
243 |
|
|
return(0); |
244 |
|
|
/* need to compute interpolant? */ |
245 |
greg |
2.2 |
if (ip->ra == NULL && !interp2_analyze(ip)) |
246 |
greg |
2.1 |
return(0); |
247 |
|
|
|
248 |
|
|
wnorm = 0; /* compute raw weights */ |
249 |
|
|
for (i = ip->ns; i--; ) { |
250 |
|
|
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 */ |
256 |
|
|
wtv[i] = wt; |
257 |
|
|
wnorm += wt; |
258 |
|
|
} |
259 |
|
|
if (wnorm <= 0) /* too far from all our samples! */ |
260 |
|
|
return(0); |
261 |
|
|
wnorm = 1./wnorm; /* normalize weights */ |
262 |
|
|
for (i = ip->ns; i--; ) |
263 |
|
|
wtv[i] *= wnorm; |
264 |
|
|
return(ip->ns); /* all done */ |
265 |
|
|
} |
266 |
|
|
|
267 |
|
|
|
268 |
|
|
/* Get normalized weights and indexes for n best samples in descending order */ |
269 |
|
|
int |
270 |
|
|
interp2_topsamp(float wt[], int si[], const int n, INTERP2 *ip, double x, double y) |
271 |
|
|
{ |
272 |
|
|
int nn = 0; |
273 |
|
|
double wnorm; |
274 |
|
|
int i, j; |
275 |
|
|
|
276 |
|
|
if ((n <= 0) | (wt == NULL) | (si == NULL) | (ip == NULL)) |
277 |
|
|
return(0); |
278 |
|
|
/* need to compute interpolant? */ |
279 |
greg |
2.2 |
if (ip->ra == NULL && !interp2_analyze(ip)) |
280 |
greg |
2.1 |
return(0); |
281 |
|
|
/* identify top n weights */ |
282 |
|
|
for (i = ip->ns; i--; ) { |
283 |
|
|
const double lnwt = get_ln_wt(ip, i, x, y); |
284 |
|
|
for (j = nn; j > 0; j--) { |
285 |
|
|
if (wt[j-1] >= lnwt) |
286 |
|
|
break; |
287 |
|
|
if (j < n) { |
288 |
|
|
wt[j] = wt[j-1]; |
289 |
|
|
si[j] = si[j-1]; |
290 |
|
|
} |
291 |
|
|
} |
292 |
|
|
if (j < n) { /* add/insert sample */ |
293 |
|
|
wt[j] = lnwt; |
294 |
|
|
si[j] = i; |
295 |
|
|
nn += (nn < n); |
296 |
|
|
} |
297 |
|
|
} |
298 |
|
|
wnorm = 0; /* exponentiate and normalize */ |
299 |
|
|
for (j = nn; j--; ) { |
300 |
|
|
double dwt = exp(wt[j]); |
301 |
|
|
wt[j] = dwt; |
302 |
|
|
wnorm += dwt; |
303 |
|
|
} |
304 |
|
|
if (wnorm <= 0) |
305 |
|
|
return(0); |
306 |
|
|
wnorm = 1./wnorm; |
307 |
|
|
for (j = nn; j--; ) |
308 |
|
|
wt[j] *= wnorm; |
309 |
|
|
return(nn); /* return actual # samples */ |
310 |
|
|
} |
311 |
|
|
|
312 |
|
|
/* Free interpolant */ |
313 |
|
|
void |
314 |
|
|
interp2_free(INTERP2 *ip) |
315 |
|
|
{ |
316 |
|
|
if (ip == NULL) |
317 |
|
|
return; |
318 |
|
|
if (ip->ra != NULL) |
319 |
|
|
free(ip->ra); |
320 |
|
|
free(ip); |
321 |
|
|
} |