| 1 |
#ifndef lint |
| 2 |
static const char RCSid[] = "$Id$"; |
| 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 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 |
/* Allocate a new set of interpolation samples */ |
| 43 |
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 |
/* private call-back to sort position index */ |
| 64 |
static int |
| 65 |
cmp_spos(const void *p1, const void *p2) |
| 66 |
{ |
| 67 |
const SAMPORD *so1 = (const SAMPORD *)p1; |
| 68 |
const SAMPORD *so2 = (const SAMPORD *)p2; |
| 69 |
|
| 70 |
if (so1->dm > so2->dm) |
| 71 |
return 1; |
| 72 |
if (so1->dm < so2->dm) |
| 73 |
return -1; |
| 74 |
return 0; |
| 75 |
} |
| 76 |
|
| 77 |
/* private routine to encode radius with range checks */ |
| 78 |
static int |
| 79 |
encode_radius(const INTERP2 *ip, double r) |
| 80 |
{ |
| 81 |
const int er = ENCODE_RAD(ip, r); |
| 82 |
|
| 83 |
if (er <= 0) |
| 84 |
return(0); |
| 85 |
if (er >= 0xffff) |
| 86 |
return(0xffff); |
| 87 |
return(er); |
| 88 |
} |
| 89 |
|
| 90 |
/* Compute anisotropic Gaussian basis function interpolant */ |
| 91 |
static int |
| 92 |
interp2_compute(INTERP2 *ip) |
| 93 |
{ |
| 94 |
SAMPORD *sortord; |
| 95 |
int *rightrndx, *leftrndx; |
| 96 |
int bd; |
| 97 |
/* sanity checks */ |
| 98 |
if (ip == NULL || (ip->ns <= 1) | (ip->rmin <= 0)) |
| 99 |
return(0); |
| 100 |
/* need to allocate? */ |
| 101 |
if (ip->ra == NULL) { |
| 102 |
ip->ra = (unsigned short (*)[NI2DIR])malloc( |
| 103 |
sizeof(unsigned short)*NI2DIR*ip->ns); |
| 104 |
if (ip->ra == NULL) |
| 105 |
return(0); |
| 106 |
} |
| 107 |
/* get temporary arrays */ |
| 108 |
sortord = (SAMPORD *)malloc(sizeof(SAMPORD)*ip->ns); |
| 109 |
rightrndx = (int *)malloc(sizeof(int)*ip->ns); |
| 110 |
leftrndx = (int *)malloc(sizeof(int)*ip->ns); |
| 111 |
if ((sortord == NULL) | (rightrndx == NULL) | (leftrndx == NULL)) |
| 112 |
return(0); |
| 113 |
/* run through bidirections */ |
| 114 |
for (bd = 0; bd < NI2DIR/2; bd++) { |
| 115 |
const double ang = 2.*PI/NI2DIR*bd; |
| 116 |
double cosd, sind; |
| 117 |
int i; |
| 118 |
/* create right reverse index */ |
| 119 |
if (bd) { /* re-use from prev. iteration? */ |
| 120 |
int *sptr = rightrndx; |
| 121 |
rightrndx = leftrndx; |
| 122 |
leftrndx = sptr; |
| 123 |
} else { /* else compute it */ |
| 124 |
cosd = cos(ang + (PI/2. - PI/NI2DIR)); |
| 125 |
sind = sin(ang + (PI/2. - PI/NI2DIR)); |
| 126 |
for (i = 0; i < ip->ns; i++) { |
| 127 |
sortord[i].si = i; |
| 128 |
sortord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
| 129 |
} |
| 130 |
qsort(sortord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
| 131 |
for (i = 0; i < ip->ns; i++) |
| 132 |
rightrndx[sortord[i].si] = i; |
| 133 |
} |
| 134 |
/* create new left reverse index */ |
| 135 |
cosd = cos(ang + (PI/2. + PI/NI2DIR)); |
| 136 |
sind = sin(ang + (PI/2. + PI/NI2DIR)); |
| 137 |
for (i = 0; i < ip->ns; i++) { |
| 138 |
sortord[i].si = i; |
| 139 |
sortord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
| 140 |
} |
| 141 |
qsort(sortord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
| 142 |
for (i = 0; i < ip->ns; i++) |
| 143 |
leftrndx[sortord[i].si] = i; |
| 144 |
/* sort grid values in this direction */ |
| 145 |
cosd = cos(ang); |
| 146 |
sind = sin(ang); |
| 147 |
for (i = 0; i < ip->ns; i++) { |
| 148 |
sortord[i].si = i; |
| 149 |
sortord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
| 150 |
} |
| 151 |
qsort(sortord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
| 152 |
/* find nearest neighbors each side */ |
| 153 |
for (i = 0; i < ip->ns; i++) { |
| 154 |
const int rpos = rightrndx[sortord[i].si]; |
| 155 |
const int lpos = leftrndx[sortord[i].si]; |
| 156 |
int j; |
| 157 |
/* preload with large radius */ |
| 158 |
ip->ra[i][bd] = ip->ra[i][bd+NI2DIR/2] = encode_radius(ip, |
| 159 |
.25*(sortord[ip->ns-1].dm - sortord[0].dm)); |
| 160 |
for (j = i; ++j < ip->ns; ) /* nearest above */ |
| 161 |
if (rightrndx[sortord[j].si] > rpos && |
| 162 |
leftrndx[sortord[j].si] < lpos) { |
| 163 |
ip->ra[i][bd] = encode_radius(ip, |
| 164 |
.5*(sortord[j].dm - sortord[i].dm)); |
| 165 |
break; |
| 166 |
} |
| 167 |
for (j = i; j-- > 0; ) /* nearest below */ |
| 168 |
if (rightrndx[sortord[j].si] < rpos && |
| 169 |
leftrndx[sortord[j].si] > lpos) { |
| 170 |
ip->ra[i][bd+NI2DIR/2] = encode_radius(ip, |
| 171 |
.5*(sortord[i].dm - sortord[j].dm)); |
| 172 |
break; |
| 173 |
} |
| 174 |
} |
| 175 |
} |
| 176 |
free(sortord); /* clean up */ |
| 177 |
free(rightrndx); |
| 178 |
free(leftrndx); |
| 179 |
return(1); |
| 180 |
} |
| 181 |
|
| 182 |
/* private call returns log of raw weight for a particular sample */ |
| 183 |
static double |
| 184 |
get_ln_wt(const INTERP2 *ip, const int i, double x, double y) |
| 185 |
{ |
| 186 |
double dir, rd; |
| 187 |
int ri; |
| 188 |
/* get relative direction */ |
| 189 |
x -= ip->spt[i][0]; |
| 190 |
y -= ip->spt[i][1]; |
| 191 |
dir = atan2a(y, x); |
| 192 |
dir += 2.*PI*(dir < 0); |
| 193 |
/* linear radius interpolation */ |
| 194 |
rd = dir * (NI2DIR/2./PI); |
| 195 |
ri = (int)rd; |
| 196 |
rd -= (double)ri; |
| 197 |
rd = (1.-rd)*ip->ra[i][ri] + rd*ip->ra[i][(ri+1)%NI2DIR]; |
| 198 |
rd = ip->smf * DECODE_RAD(ip, rd); |
| 199 |
/* return log of Gaussian weight */ |
| 200 |
return( (x*x + y*y) / (-2.*rd*rd) ); |
| 201 |
} |
| 202 |
|
| 203 |
/* Assign full set of normalized weights to interpolate the given position */ |
| 204 |
int |
| 205 |
interp2_weights(float wtv[], INTERP2 *ip, double x, double y) |
| 206 |
{ |
| 207 |
double wnorm; |
| 208 |
int i; |
| 209 |
|
| 210 |
if ((wtv == NULL) | (ip == NULL)) |
| 211 |
return(0); |
| 212 |
/* need to compute interpolant? */ |
| 213 |
if (ip->ra == NULL && !interp2_compute(ip)) |
| 214 |
return(0); |
| 215 |
|
| 216 |
wnorm = 0; /* compute raw weights */ |
| 217 |
for (i = ip->ns; i--; ) { |
| 218 |
double wt = get_ln_wt(ip, i, x, y); |
| 219 |
if (wt < -21.) { |
| 220 |
wtv[i] = 0; /* ignore weights < 1e-9 */ |
| 221 |
continue; |
| 222 |
} |
| 223 |
wt = exp(wt); /* Gaussian weight */ |
| 224 |
wtv[i] = wt; |
| 225 |
wnorm += wt; |
| 226 |
} |
| 227 |
if (wnorm <= 0) /* too far from all our samples! */ |
| 228 |
return(0); |
| 229 |
wnorm = 1./wnorm; /* normalize weights */ |
| 230 |
for (i = ip->ns; i--; ) |
| 231 |
wtv[i] *= wnorm; |
| 232 |
return(ip->ns); /* all done */ |
| 233 |
} |
| 234 |
|
| 235 |
|
| 236 |
/* Get normalized weights and indexes for n best samples in descending order */ |
| 237 |
int |
| 238 |
interp2_topsamp(float wt[], int si[], const int n, INTERP2 *ip, double x, double y) |
| 239 |
{ |
| 240 |
int nn = 0; |
| 241 |
double wnorm; |
| 242 |
int i, j; |
| 243 |
|
| 244 |
if ((n <= 0) | (wt == NULL) | (si == NULL) | (ip == NULL)) |
| 245 |
return(0); |
| 246 |
/* need to compute interpolant? */ |
| 247 |
if (ip->ra == NULL && !interp2_compute(ip)) |
| 248 |
return(0); |
| 249 |
/* identify top n weights */ |
| 250 |
for (i = ip->ns; i--; ) { |
| 251 |
const double lnwt = get_ln_wt(ip, i, x, y); |
| 252 |
for (j = nn; j > 0; j--) { |
| 253 |
if (wt[j-1] >= lnwt) |
| 254 |
break; |
| 255 |
if (j < n) { |
| 256 |
wt[j] = wt[j-1]; |
| 257 |
si[j] = si[j-1]; |
| 258 |
} |
| 259 |
} |
| 260 |
if (j < n) { /* add/insert sample */ |
| 261 |
wt[j] = lnwt; |
| 262 |
si[j] = i; |
| 263 |
nn += (nn < n); |
| 264 |
} |
| 265 |
} |
| 266 |
wnorm = 0; /* exponentiate and normalize */ |
| 267 |
for (j = nn; j--; ) { |
| 268 |
double dwt = exp(wt[j]); |
| 269 |
wt[j] = dwt; |
| 270 |
wnorm += dwt; |
| 271 |
} |
| 272 |
if (wnorm <= 0) |
| 273 |
return(0); |
| 274 |
wnorm = 1./wnorm; |
| 275 |
for (j = nn; j--; ) |
| 276 |
wt[j] *= wnorm; |
| 277 |
return(nn); /* return actual # samples */ |
| 278 |
} |
| 279 |
|
| 280 |
/* Free interpolant */ |
| 281 |
void |
| 282 |
interp2_free(INTERP2 *ip) |
| 283 |
{ |
| 284 |
if (ip == NULL) |
| 285 |
return; |
| 286 |
if (ip->ra != NULL) |
| 287 |
free(ip->ra); |
| 288 |
free(ip); |
| 289 |
} |
