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greg |
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#ifndef lint |
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static const char RCSid[] = "$Id$"; |
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#endif |
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/* |
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* General interpolation method for unstructured values on 2-D plane. |
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* |
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* G.Ward Feb 2013 |
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*/ |
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#include "copyright.h" |
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/************************************************************* |
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* This is a general method for 2-D interpolation similar to |
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* radial basis functions but allowing for a good deal of local |
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* anisotropy in the point distribution. Each sample point |
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* is examined to determine the closest neighboring samples in |
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* each of NI2DIR surrounding directions. To speed this |
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* calculation, we sort the data into 3 half-planes and |
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* perform simple tests to see which neighbor is closest in |
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* a each direction. Once we have our approximate neighborhood |
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* for a sample, we can use it in a Gaussian weighting scheme |
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* with anisotropic surround. This gives us a fairly smooth |
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* interpolation however the sample points may be initially |
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* distributed. Evaluation is accelerated by use of a fast |
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* approximation to the atan2(y,x) function. |
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**************************************************************/ |
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#include <stdio.h> |
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#include <stdlib.h> |
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#include "rtmath.h" |
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#include "interp2d.h" |
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#define DECODE_RAD(ip,er) ((ip)->rmin*(1. + .5*(er))) |
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#define ENCODE_RAD(ip,r) ((int)(2.*(r)/(ip)->rmin) - 2) |
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/* Sample order (private) */ |
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typedef struct { |
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int si; /* sample index */ |
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float dm; /* distance measure in this direction */ |
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} SAMPORD; |
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/* Allocate a new set of interpolation samples */ |
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INTERP2 * |
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interp2_alloc(int nsamps) |
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{ |
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INTERP2 *nip; |
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if (nsamps <= 1) |
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return(NULL); |
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nip = (INTERP2 *)malloc(sizeof(INTERP2) + sizeof(float)*2*(nsamps-1)); |
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if (nip == NULL) |
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return(NULL); |
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nip->ns = nsamps; |
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nip->rmin = .5; /* default radius minimum */ |
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nip->smf = NI2DSMF; /* default smoothing factor */ |
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nip->ra = NULL; |
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/* caller must assign spt[] array */ |
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return(nip); |
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} |
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/* private call-back to sort position index */ |
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static int |
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cmp_spos(const void *p1, const void *p2) |
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{ |
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const SAMPORD *so1 = (const SAMPORD *)p1; |
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const SAMPORD *so2 = (const SAMPORD *)p2; |
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if (so1->dm > so2->dm) |
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return 1; |
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if (so1->dm < so2->dm) |
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return -1; |
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return 0; |
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} |
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/* private routine to encode radius with range checks */ |
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static int |
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encode_radius(const INTERP2 *ip, double r) |
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{ |
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const int er = ENCODE_RAD(ip, r); |
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if (er <= 0) |
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return(0); |
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if (er >= 0xffff) |
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return(0xffff); |
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return(er); |
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} |
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/* Compute anisotropic Gaussian basis function interpolant */ |
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static int |
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interp2_compute(INTERP2 *ip) |
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{ |
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SAMPORD *sortord; |
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int *rightrndx, *leftrndx; |
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int bd; |
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/* sanity checks */ |
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if (ip == NULL || (ip->ns <= 1) | (ip->rmin <= 0)) |
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return(0); |
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/* need to allocate? */ |
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if (ip->ra == NULL) { |
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ip->ra = (unsigned short (*)[NI2DIR])malloc( |
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sizeof(unsigned short)*NI2DIR*ip->ns); |
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if (ip->ra == NULL) |
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return(0); |
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} |
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/* get temporary arrays */ |
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sortord = (SAMPORD *)malloc(sizeof(SAMPORD)*ip->ns); |
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rightrndx = (int *)malloc(sizeof(int)*ip->ns); |
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leftrndx = (int *)malloc(sizeof(int)*ip->ns); |
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if ((sortord == NULL) | (rightrndx == NULL) | (leftrndx == NULL)) |
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return(0); |
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/* run through bidirections */ |
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for (bd = 0; bd < NI2DIR/2; bd++) { |
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const double ang = 2.*PI/NI2DIR*bd; |
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double cosd, sind; |
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int i; |
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/* create right reverse index */ |
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if (bd) { /* re-use from prev. iteration? */ |
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int *sptr = rightrndx; |
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rightrndx = leftrndx; |
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leftrndx = sptr; |
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} else { /* else compute it */ |
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cosd = cos(ang + (PI/2. - PI/NI2DIR)); |
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sind = sin(ang + (PI/2. - PI/NI2DIR)); |
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for (i = 0; i < ip->ns; i++) { |
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sortord[i].si = i; |
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sortord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
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} |
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qsort(sortord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
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for (i = 0; i < ip->ns; i++) |
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rightrndx[sortord[i].si] = i; |
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} |
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/* create new left reverse index */ |
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cosd = cos(ang + (PI/2. + PI/NI2DIR)); |
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sind = sin(ang + (PI/2. + PI/NI2DIR)); |
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for (i = 0; i < ip->ns; i++) { |
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sortord[i].si = i; |
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sortord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
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} |
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qsort(sortord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
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for (i = 0; i < ip->ns; i++) |
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leftrndx[sortord[i].si] = i; |
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/* sort grid values in this direction */ |
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cosd = cos(ang); |
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sind = sin(ang); |
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for (i = 0; i < ip->ns; i++) { |
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sortord[i].si = i; |
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sortord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
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} |
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qsort(sortord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
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/* find nearest neighbors each side */ |
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for (i = 0; i < ip->ns; i++) { |
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const int rpos = rightrndx[sortord[i].si]; |
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const int lpos = leftrndx[sortord[i].si]; |
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int j; |
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/* preload with large radius */ |
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ip->ra[i][bd] = ip->ra[i][bd+NI2DIR/2] = encode_radius(ip, |
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.25*(sortord[ip->ns-1].dm - sortord[0].dm)); |
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for (j = i; ++j < ip->ns; ) /* nearest above */ |
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if (rightrndx[sortord[j].si] > rpos && |
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leftrndx[sortord[j].si] < lpos) { |
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ip->ra[i][bd] = encode_radius(ip, |
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.5*(sortord[j].dm - sortord[i].dm)); |
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break; |
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} |
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for (j = i; j-- > 0; ) /* nearest below */ |
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if (rightrndx[sortord[j].si] < rpos && |
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leftrndx[sortord[j].si] > lpos) { |
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ip->ra[i][bd+NI2DIR/2] = encode_radius(ip, |
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.5*(sortord[i].dm - sortord[j].dm)); |
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break; |
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} |
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} |
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} |
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free(sortord); /* clean up */ |
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free(rightrndx); |
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free(leftrndx); |
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return(1); |
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} |
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/* private call returns log of raw weight for a particular sample */ |
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static double |
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get_ln_wt(const INTERP2 *ip, const int i, double x, double y) |
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{ |
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double dir, rd; |
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int ri; |
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/* get relative direction */ |
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x -= ip->spt[i][0]; |
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y -= ip->spt[i][1]; |
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dir = atan2a(y, x); |
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dir += 2.*PI*(dir < 0); |
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/* linear radius interpolation */ |
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rd = dir * (NI2DIR/2./PI); |
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ri = (int)rd; |
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rd -= (double)ri; |
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rd = (1.-rd)*ip->ra[i][ri] + rd*ip->ra[i][(ri+1)%NI2DIR]; |
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rd = ip->smf * DECODE_RAD(ip, rd); |
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/* return log of Gaussian weight */ |
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return( (x*x + y*y) / (-2.*rd*rd) ); |
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} |
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/* Assign full set of normalized weights to interpolate the given position */ |
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int |
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interp2_weights(float wtv[], INTERP2 *ip, double x, double y) |
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{ |
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double wnorm; |
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int i; |
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if ((wtv == NULL) | (ip == NULL)) |
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return(0); |
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/* need to compute interpolant? */ |
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if (ip->ra == NULL && !interp2_compute(ip)) |
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return(0); |
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wnorm = 0; /* compute raw weights */ |
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for (i = ip->ns; i--; ) { |
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double wt = get_ln_wt(ip, i, x, y); |
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if (wt < -21.) { |
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wtv[i] = 0; /* ignore weights < 1e-9 */ |
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continue; |
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} |
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wt = exp(wt); /* Gaussian weight */ |
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wtv[i] = wt; |
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wnorm += wt; |
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} |
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if (wnorm <= 0) /* too far from all our samples! */ |
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return(0); |
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wnorm = 1./wnorm; /* normalize weights */ |
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for (i = ip->ns; i--; ) |
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wtv[i] *= wnorm; |
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return(ip->ns); /* all done */ |
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} |
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/* Get normalized weights and indexes for n best samples in descending order */ |
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int |
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interp2_topsamp(float wt[], int si[], const int n, INTERP2 *ip, double x, double y) |
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{ |
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int nn = 0; |
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double wnorm; |
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int i, j; |
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if ((n <= 0) | (wt == NULL) | (si == NULL) | (ip == NULL)) |
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return(0); |
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/* need to compute interpolant? */ |
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if (ip->ra == NULL && !interp2_compute(ip)) |
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return(0); |
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/* identify top n weights */ |
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for (i = ip->ns; i--; ) { |
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const double lnwt = get_ln_wt(ip, i, x, y); |
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for (j = nn; j > 0; j--) { |
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if (wt[j-1] >= lnwt) |
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break; |
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if (j < n) { |
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wt[j] = wt[j-1]; |
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si[j] = si[j-1]; |
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} |
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} |
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if (j < n) { /* add/insert sample */ |
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wt[j] = lnwt; |
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si[j] = i; |
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nn += (nn < n); |
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} |
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} |
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wnorm = 0; /* exponentiate and normalize */ |
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for (j = nn; j--; ) { |
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double dwt = exp(wt[j]); |
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wt[j] = dwt; |
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wnorm += dwt; |
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} |
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if (wnorm <= 0) |
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return(0); |
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wnorm = 1./wnorm; |
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for (j = nn; j--; ) |
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wt[j] *= wnorm; |
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return(nn); /* return actual # samples */ |
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} |
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/* Free interpolant */ |
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void |
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interp2_free(INTERP2 *ip) |
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{ |
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if (ip == NULL) |
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return; |
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if (ip->ra != NULL) |
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free(ip->ra); |
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free(ip); |
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} |
