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 |
< |
* direction. Once we have our approximate neighborhood |
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. |
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> |
72 |
|
interp2_free(ip); |
73 |
|
return(NULL); |
74 |
|
} |
75 |
< |
if (nsamps == ip->ns); |
75 |
> |
if (nsamps == ip->ns) |
76 |
|
return(ip); |
77 |
|
if (ip->da != NULL) { /* will need to recompute distribution */ |
78 |
|
free(ip->da); |
91 |
|
{ |
92 |
|
if (mind <= 0) |
93 |
|
return; |
94 |
< |
if ((.998*ip->dmin <= mind) && (mind <= 1.002*ip->dmin)) |
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); |
150 |
|
return(ed); |
151 |
|
} |
152 |
|
|
153 |
+ |
/* Compute unnormalized weight for a position relative to a sample */ |
154 |
+ |
double |
155 |
+ |
interp2_wti(INTERP2 *ip, const int i, double x, double y) |
156 |
+ |
{ |
157 |
+ |
double dir, rd, r2, d2; |
158 |
+ |
int ri; |
159 |
+ |
/* get relative direction */ |
160 |
+ |
x -= ip->spt[i][0]; |
161 |
+ |
y -= ip->spt[i][1]; |
162 |
+ |
dir = atan2a(y, x); |
163 |
+ |
dir += 2.*PI*(dir < 0); |
164 |
+ |
/* linear radius interpolation */ |
165 |
+ |
rd = dir * (NI2DIR/2./PI); |
166 |
+ |
ri = (int)rd; |
167 |
+ |
rd -= (double)ri; |
168 |
+ |
rd = (1.-rd)*ip->da[i].dia[ri] + rd*ip->da[i].dia[(ri+1)%NI2DIR]; |
169 |
+ |
rd = ip->smf * DECODE_DIA(ip, rd); |
170 |
+ |
r2 = 2.*rd*rd; |
171 |
+ |
d2 = x*x + y*y; |
172 |
+ |
if (d2 > 21.*r2) /* result would be < 1e-9 */ |
173 |
+ |
return(.0); |
174 |
+ |
/* Gaussian times harmonic weighting */ |
175 |
+ |
return( exp(-d2/r2) * ip->dmin/(ip->dmin + sqrt(d2)) ); |
176 |
+ |
} |
177 |
+ |
|
178 |
+ |
/* private call to get grid flag index */ |
179 |
+ |
static int |
180 |
+ |
interp2_flagpos(int fgi[2], INTERP2 *ip, double x, double y) |
181 |
+ |
{ |
182 |
+ |
int inbounds = 0; |
183 |
+ |
|
184 |
+ |
if (ip == NULL) /* paranoia */ |
185 |
+ |
return(-1); |
186 |
+ |
/* need to compute interpolant? */ |
187 |
+ |
if (ip->da == NULL && !interp2_analyze(ip)) |
188 |
+ |
return(-1); |
189 |
+ |
/* get x & y grid positions */ |
190 |
+ |
fgi[0] = (x - ip->smin[0]) * NI2DIM / (ip->smax[0] - ip->smin[0]); |
191 |
+ |
|
192 |
+ |
if (fgi[0] >= NI2DIM) |
193 |
+ |
fgi[0] = NI2DIM-1; |
194 |
+ |
else if (fgi[0] < 0) |
195 |
+ |
fgi[0] = 0; |
196 |
+ |
else |
197 |
+ |
++inbounds; |
198 |
+ |
|
199 |
+ |
fgi[1] = (y - ip->smin[1]) * NI2DIM / (ip->smax[1] - ip->smin[1]); |
200 |
+ |
|
201 |
+ |
if (fgi[1] >= NI2DIM) |
202 |
+ |
fgi[1] = NI2DIM-1; |
203 |
+ |
else if (fgi[1] < 0) |
204 |
+ |
fgi[1] = 0; |
205 |
+ |
else |
206 |
+ |
++inbounds; |
207 |
+ |
|
208 |
+ |
return(inbounds == 2); |
209 |
+ |
} |
210 |
+ |
|
211 |
+ |
#define setflg(fl,xi,yi) ((fl)[yi] |= 1<<(xi)) |
212 |
+ |
|
213 |
+ |
#define chkflg(fl,xi,yi) ((fl)[yi]>>(xi) & 1) |
214 |
+ |
|
215 |
+ |
/* private flood function to determine sample influence */ |
216 |
+ |
static void |
217 |
+ |
influence_flood(INTERP2 *ip, const int i, unsigned short visited[NI2DIM], |
218 |
+ |
int xfi, int yfi) |
219 |
+ |
{ |
220 |
+ |
double gx = (xfi+.5)*(1./NI2DIM)*(ip->smax[0] - ip->smin[0]) + |
221 |
+ |
ip->smin[0]; |
222 |
+ |
double gy = (yfi+.5)*(1./NI2DIM)*(ip->smax[1] - ip->smin[1]) + |
223 |
+ |
ip->smin[1]; |
224 |
+ |
double dx = gx - ip->spt[i][0]; |
225 |
+ |
double dy = gy - ip->spt[i][1]; |
226 |
+ |
|
227 |
+ |
setflg(visited, xfi, yfi); |
228 |
+ |
|
229 |
+ |
if (dx*dx + dy*dy > 2.*ip->grid2 && interp2_wti(ip, i, gx, gy) <= 1e-7) |
230 |
+ |
return; |
231 |
+ |
|
232 |
+ |
setflg(ip->da[i].infl, xfi, yfi); |
233 |
+ |
|
234 |
+ |
if (xfi > 0 && !chkflg(visited, xfi-1, yfi)) |
235 |
+ |
influence_flood(ip, i, visited, xfi-1, yfi); |
236 |
+ |
|
237 |
+ |
if (yfi > 0 && !chkflg(visited, xfi, yfi-1)) |
238 |
+ |
influence_flood(ip, i, visited, xfi, yfi-1); |
239 |
+ |
|
240 |
+ |
if (xfi < NI2DIM-1 && !chkflg(visited, xfi+1, yfi)) |
241 |
+ |
influence_flood(ip, i, visited, xfi+1, yfi); |
242 |
+ |
|
243 |
+ |
if (yfi < NI2DIM-1 && !chkflg(visited, xfi, yfi+1)) |
244 |
+ |
influence_flood(ip, i, visited, xfi, yfi+1); |
245 |
+ |
} |
246 |
+ |
|
247 |
|
/* (Re)compute anisotropic basis function interpolant (normally automatic) */ |
248 |
|
int |
249 |
|
interp2_analyze(INTERP2 *ip) |
250 |
|
{ |
251 |
|
SAMPORD *sortord; |
252 |
|
int *rightrndx, *leftrndx, *endrndx; |
253 |
< |
int bd; |
253 |
> |
int i, j, bd; |
254 |
|
/* sanity checks */ |
255 |
< |
if (ip == NULL || (ip->ns <= 1) | (ip->dmin <= 0)) |
255 |
> |
if (ip == NULL) |
256 |
|
return(0); |
257 |
< |
/* need to allocate? */ |
258 |
< |
if (ip->da == NULL) { |
259 |
< |
ip->da = (unsigned short (*)[NI2DIR])malloc( |
165 |
< |
sizeof(unsigned short)*NI2DIR*ip->ns); |
166 |
< |
if (ip->da == NULL) |
167 |
< |
return(0); |
257 |
> |
if (ip->da != NULL) { /* free previous data if any */ |
258 |
> |
free(ip->da); |
259 |
> |
ip->da = NULL; |
260 |
|
} |
261 |
< |
/* get temporary arrays */ |
261 |
> |
if ((ip->ns <= 1) | (ip->dmin <= 0)) |
262 |
> |
return(0); |
263 |
> |
/* compute sample domain */ |
264 |
> |
ip->smin[0] = ip->smin[1] = FHUGE; |
265 |
> |
ip->smax[0] = ip->smax[1] = -FHUGE; |
266 |
> |
for (i = ip->ns; i--; ) { |
267 |
> |
if (ip->spt[i][0] < ip->smin[0]) ip->smin[0] = ip->spt[i][0]; |
268 |
> |
if (ip->spt[i][0] > ip->smax[0]) ip->smax[0] = ip->spt[i][0]; |
269 |
> |
if (ip->spt[i][1] < ip->smin[1]) ip->smin[1] = ip->spt[i][1]; |
270 |
> |
if (ip->spt[i][1] > ip->smax[1]) ip->smax[1] = ip->spt[i][1]; |
271 |
> |
} |
272 |
> |
ip->grid2 = ((ip->smax[0]-ip->smin[0])*(ip->smax[0]-ip->smin[0]) + |
273 |
> |
(ip->smax[1]-ip->smin[1])*(ip->smax[1]-ip->smin[1])) * |
274 |
> |
(1./NI2DIM/NI2DIM); |
275 |
> |
if (ip->grid2 <= FTINY*ip->dmin*ip->dmin) |
276 |
> |
return(0); |
277 |
> |
/* allocate analysis data */ |
278 |
> |
ip->da = (struct interp2_samp *)calloc( ip->ns, |
279 |
> |
sizeof(struct interp2_samp) ); |
280 |
> |
if (ip->da == NULL) |
281 |
> |
return(0); |
282 |
> |
/* allocate temporary arrays */ |
283 |
|
sortord = (SAMPORD *)malloc(sizeof(SAMPORD)*ip->ns); |
284 |
|
rightrndx = (int *)malloc(sizeof(int)*ip->ns); |
285 |
|
leftrndx = (int *)malloc(sizeof(int)*ip->ns); |
291 |
|
for (bd = 0; bd < NI2DIR/2; bd++) { |
292 |
|
const double ang = 2.*PI/NI2DIR*bd; |
293 |
|
int *sptr; |
181 |
– |
int i; |
294 |
|
/* create right reverse index */ |
295 |
|
if (bd) { /* re-use from previous iteration? */ |
296 |
|
sptr = rightrndx; |
319 |
|
/* find nearest neighbors each side */ |
320 |
|
for (i = ip->ns; i--; ) { |
321 |
|
const int ii = sortord[i].si; |
210 |
– |
int j; |
322 |
|
/* preload with large radii */ |
323 |
< |
ip->da[ii][bd] = ip->da[ii][bd+NI2DIR/2] = encode_diameter(ip, |
324 |
< |
.5*(sortord[ip->ns-1].dm - sortord[0].dm)); |
323 |
> |
ip->da[ii].dia[bd] = |
324 |
> |
ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip, |
325 |
> |
.5*(sortord[ip->ns-1].dm - sortord[0].dm)); |
326 |
|
for (j = i; ++j < ip->ns; ) /* nearest above */ |
327 |
|
if (rightrndx[sortord[j].si] > rightrndx[ii] && |
328 |
|
leftrndx[sortord[j].si] < leftrndx[ii]) { |
329 |
< |
ip->da[ii][bd] = encode_diameter(ip, |
329 |
> |
ip->da[ii].dia[bd] = encode_diameter(ip, |
330 |
|
sortord[j].dm - sortord[i].dm); |
331 |
|
break; |
332 |
|
} |
333 |
|
for (j = i; j-- > 0; ) /* nearest below */ |
334 |
|
if (rightrndx[sortord[j].si] < rightrndx[ii] && |
335 |
|
leftrndx[sortord[j].si] > leftrndx[ii]) { |
336 |
< |
ip->da[ii][bd+NI2DIR/2] = encode_diameter(ip, |
336 |
> |
ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip, |
337 |
|
sortord[i].dm - sortord[j].dm); |
338 |
|
break; |
339 |
|
} |
340 |
|
} |
341 |
|
} |
342 |
< |
free(sortord); /* clean up */ |
342 |
> |
free(sortord); /* release temp arrays */ |
343 |
|
free(rightrndx); |
344 |
|
free(leftrndx); |
345 |
|
free(endrndx); |
346 |
< |
return(1); |
347 |
< |
} |
346 |
> |
/* fill influence maps */ |
347 |
> |
for (i = ip->ns; i--; ) { |
348 |
> |
unsigned short visited[NI2DIM]; |
349 |
> |
int fgi[2]; |
350 |
|
|
351 |
< |
/* private call returns raw weight for a particular sample */ |
352 |
< |
static double |
353 |
< |
get_wt(const INTERP2 *ip, const int i, double x, double y) |
354 |
< |
{ |
355 |
< |
double dir, rd, d2; |
242 |
< |
int ri; |
243 |
< |
/* get relative direction */ |
244 |
< |
x -= ip->spt[i][0]; |
245 |
< |
y -= ip->spt[i][1]; |
246 |
< |
dir = atan2a(y, x); |
247 |
< |
dir += 2.*PI*(dir < 0); |
248 |
< |
/* linear radius interpolation */ |
249 |
< |
rd = dir * (NI2DIR/2./PI); |
250 |
< |
ri = (int)rd; |
251 |
< |
rd -= (double)ri; |
252 |
< |
rd = (1.-rd)*ip->da[i][ri] + rd*ip->da[i][(ri+1)%NI2DIR]; |
253 |
< |
rd = ip->smf * DECODE_DIA(ip, rd); |
254 |
< |
d2 = x*x + y*y; |
255 |
< |
/* Gaussian times harmonic weighting */ |
256 |
< |
return( exp(d2/(-2.*rd*rd)) * ip->dmin/(ip->dmin + sqrt(d2)) ); |
351 |
> |
for (j = NI2DIM; j--; ) visited[j] = 0; |
352 |
> |
interp2_flagpos(fgi, ip, ip->spt[i][0], ip->spt[i][1]); |
353 |
> |
influence_flood(ip, i, visited, fgi[0], fgi[1]); |
354 |
> |
} |
355 |
> |
return(1); /* all done */ |
356 |
|
} |
357 |
|
|
358 |
|
/* Assign full set of normalized weights to interpolate the given position */ |
360 |
|
interp2_weights(float wtv[], INTERP2 *ip, double x, double y) |
361 |
|
{ |
362 |
|
double wnorm; |
363 |
+ |
int fgi[2]; |
364 |
|
int i; |
365 |
|
|
366 |
< |
if ((wtv == NULL) | (ip == NULL)) |
366 |
> |
if (wtv == NULL) |
367 |
|
return(0); |
368 |
< |
/* need to compute interpolant? */ |
369 |
< |
if (ip->da == NULL && !interp2_analyze(ip)) |
368 |
> |
/* get flag position */ |
369 |
> |
if (interp2_flagpos(fgi, ip, x, y) < 0) |
370 |
|
return(0); |
371 |
|
|
372 |
|
wnorm = 0; /* compute raw weights */ |
373 |
< |
for (i = ip->ns; i--; ) { |
374 |
< |
double wt = get_wt(ip, i, x, y); |
373 |
> |
for (i = ip->ns; i--; ) |
374 |
> |
if (chkflg(ip->da[i].infl, fgi[0], fgi[1])) { |
375 |
> |
double wt = interp2_wti(ip, i, x, y); |
376 |
|
wtv[i] = wt; |
377 |
|
wnorm += wt; |
378 |
< |
} |
378 |
> |
} else |
379 |
> |
wtv[i] = 0; |
380 |
|
if (wnorm <= 0) /* too far from all our samples! */ |
381 |
|
return(0); |
382 |
|
wnorm = 1./wnorm; /* normalize weights */ |
391 |
|
interp2_topsamp(float wt[], int si[], const int n, INTERP2 *ip, double x, double y) |
392 |
|
{ |
393 |
|
int nn = 0; |
394 |
+ |
int fgi[2]; |
395 |
|
double wnorm; |
396 |
|
int i, j; |
397 |
|
|
398 |
< |
if ((n <= 0) | (wt == NULL) | (si == NULL) | (ip == NULL)) |
398 |
> |
if ((n <= 0) | (wt == NULL) | (si == NULL)) |
399 |
|
return(0); |
400 |
< |
/* need to compute interpolant? */ |
401 |
< |
if (ip->da == NULL && !interp2_analyze(ip)) |
400 |
> |
/* get flag position */ |
401 |
> |
if (interp2_flagpos(fgi, ip, x, y) < 0) |
402 |
|
return(0); |
403 |
|
/* identify top n weights */ |
404 |
< |
for (i = ip->ns; i--; ) { |
405 |
< |
const double wti = get_wt(ip, i, x, y); |
404 |
> |
for (i = ip->ns; i--; ) |
405 |
> |
if (chkflg(ip->da[i].infl, fgi[0], fgi[1])) { |
406 |
> |
const double wti = interp2_wti(ip, i, x, y); |
407 |
|
for (j = nn; j > 0; j--) { |
408 |
|
if (wt[j-1] >= wti) |
409 |
|
break; |
417 |
|
si[j] = i; |
418 |
|
nn += (nn < n); |
419 |
|
} |
420 |
< |
} |
420 |
> |
} |
421 |
|
wnorm = 0; /* normalize sample weights */ |
422 |
|
for (j = nn; j--; ) |
423 |
|
wnorm += wt[j]; |