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#ifndef lint |
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static const char RCSid[] = "$Id: interp2d.c,v 2.10 2013/02/14 19:57:10 greg Exp $"; |
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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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|
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#include "copyright.h" |
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|
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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 half-planes and apply |
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* simple tests to see which neighbor is closest in each |
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* angular slice. Once we have our approximate neighborhood |
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* for a sample, we can use it in a modified Gaussian weighting |
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* with allowing local anisotropy. Harmonic weighting is added |
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* to reduce the influence of distant neighbors. This yields a |
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* smooth interpolation regardless of how the sample points are |
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* initially distributed. Evaluation is accelerated by use of |
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* a fast approximation to the atan2(y,x) function and an array |
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* of flags indicating where weights are (nearly) zero. |
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****************************************************************/ |
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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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|
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#define DECODE_DIA(ip,ed) ((ip)->dmin*(1. + .5*(ed))) |
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#define ENCODE_DIA(ip,d) ((int)(2.*(d)/(ip)->dmin) - 2) |
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|
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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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|
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/* Allocate a new set of interpolation samples (caller assigns spt[] array) */ |
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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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|
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if (nsamps <= 1) |
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return(NULL); |
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|
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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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|
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nip->ns = nsamps; |
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nip->dmin = 1; /* default minimum diameter */ |
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nip->smf = NI2DSMF; /* default smoothing factor */ |
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nip->da = NULL; |
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/* caller must assign spt[] array */ |
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return(nip); |
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} |
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|
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/* Resize interpolation array (caller must assign any new values) */ |
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INTERP2 * |
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interp2_realloc(INTERP2 *ip, int nsamps) |
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{ |
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if (ip == NULL) |
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return(interp2_alloc(nsamps)); |
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if (nsamps <= 1) { |
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interp2_free(ip); |
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return(NULL); |
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} |
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if (nsamps == ip->ns) |
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return(ip); |
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if (ip->da != NULL) { /* will need to recompute distribution */ |
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free(ip->da); |
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ip->da = NULL; |
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} |
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ip = (INTERP2 *)realloc(ip, sizeof(INTERP2)+sizeof(float)*2*(nsamps-1)); |
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if (ip == NULL) |
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return(NULL); |
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ip->ns = nsamps; |
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return(ip); |
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} |
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|
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/* Set minimum distance under which samples will start to merge */ |
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void |
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interp2_spacing(INTERP2 *ip, double mind) |
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{ |
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if (mind <= 0) |
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return; |
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if ((.998*ip->dmin <= mind) & (mind <= 1.002*ip->dmin)) |
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return; |
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if (ip->da != NULL) { /* will need to recompute distribution */ |
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free(ip->da); |
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ip->da = NULL; |
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} |
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ip->dmin = mind; |
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} |
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|
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/* Modify smoothing parameter by the given factor */ |
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void |
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interp2_smooth(INTERP2 *ip, double sf) |
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{ |
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if ((ip->smf *= sf) < NI2DSMF) |
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ip->smf = NI2DSMF; |
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} |
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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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|
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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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|
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/* private routine to order samples in a particular direction */ |
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static void |
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sort_samples(SAMPORD *sord, const INTERP2 *ip, double ang) |
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{ |
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const double cosd = cos(ang); |
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const double sind = sin(ang); |
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int i; |
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|
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for (i = ip->ns; i--; ) { |
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sord[i].si = i; |
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sord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
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} |
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qsort(sord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
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} |
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|
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/* private routine to encode sample diameter with range checks */ |
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static int |
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encode_diameter(const INTERP2 *ip, double d) |
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{ |
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const int ed = ENCODE_DIA(ip, d); |
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|
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if (ed <= 0) |
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return(0); |
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if (ed >= 0xffff) |
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return(0xffff); |
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return(ed); |
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} |
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|
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/* (Re)compute anisotropic basis function interpolant (normally automatic) */ |
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int |
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interp2_analyze(INTERP2 *ip) |
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{ |
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SAMPORD *sortord; |
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int *rightrndx, *leftrndx, *endrndx; |
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int i, bd; |
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/* sanity checks */ |
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if (ip == NULL) |
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return(0); |
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if (ip->da != NULL) { /* free previous data if any */ |
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free(ip->da); |
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ip->da = NULL; |
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} |
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if ((ip->ns <= 1) | (ip->dmin <= 0)) |
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return(0); |
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/* compute sample domain */ |
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ip->smin[0] = ip->smin[1] = FHUGE; |
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ip->smax[0] = ip->smax[1] = -FHUGE; |
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for (i = ip->ns; i--; ) { |
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if (ip->spt[i][0] < ip->smin[0]) |
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ip->smin[0] = ip->spt[i][0]; |
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if (ip->spt[i][0] > ip->smax[0]) |
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ip->smax[0] = ip->spt[i][0]; |
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if (ip->spt[i][1] < ip->smin[1]) |
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ip->smin[1] = ip->spt[i][1]; |
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if (ip->spt[i][1] > ip->smax[1]) |
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ip->smax[1] = ip->spt[i][1]; |
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} |
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ip->grid2 = ((ip->smax[0]-ip->smin[0])*(ip->smax[0]-ip->smin[0]) + |
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(ip->smax[1]-ip->smin[1])*(ip->smax[1]-ip->smin[1])) * |
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(1./NI2DIM/NI2DIM); |
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if (ip->grid2 <= FTINY*ip->dmin*ip->dmin) |
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return(0); |
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/* allocate analysis data */ |
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ip->da = (struct interp2_samp *)calloc( ip->ns, |
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sizeof(struct interp2_samp) ); |
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if (ip->da == NULL) |
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return(0); |
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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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endrndx = (int *)malloc(sizeof(int)*ip->ns); |
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if ((sortord == NULL) | (rightrndx == NULL) | |
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(leftrndx == NULL) | (endrndx == 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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int *sptr; |
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/* create right reverse index */ |
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if (bd) { /* re-use from previous iteration? */ |
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sptr = rightrndx; |
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rightrndx = leftrndx; |
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leftrndx = sptr; |
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} else { /* else sort first half-plane */ |
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sort_samples(sortord, ip, PI/2. - PI/NI2DIR); |
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for (i = ip->ns; i--; ) |
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rightrndx[sortord[i].si] = i; |
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/* & store reverse order for later */ |
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for (i = ip->ns; i--; ) |
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endrndx[sortord[i].si] = ip->ns-1 - i; |
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} |
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/* create new left reverse index */ |
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if (bd == NI2DIR/2 - 1) { /* use order from first iteration? */ |
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sptr = leftrndx; |
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leftrndx = endrndx; |
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endrndx = sptr; |
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} else { /* else compute new half-plane */ |
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sort_samples(sortord, ip, ang + (PI/2. + PI/NI2DIR)); |
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for (i = ip->ns; i--; ) |
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leftrndx[sortord[i].si] = i; |
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} |
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/* sort grid values in this direction */ |
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sort_samples(sortord, ip, ang); |
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/* find nearest neighbors each side */ |
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for (i = ip->ns; i--; ) { |
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const int ii = sortord[i].si; |
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int j; |
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/* preload with large radii */ |
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ip->da[ii].dia[bd] = |
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ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip, |
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.5*(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] > rightrndx[ii] && |
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leftrndx[sortord[j].si] < leftrndx[ii]) { |
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ip->da[ii].dia[bd] = encode_diameter(ip, |
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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] < rightrndx[ii] && |
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leftrndx[sortord[j].si] > leftrndx[ii]) { |
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ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip, |
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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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free(endrndx); |
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return(1); |
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} |
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|
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/* Compute unnormalized weight for a position relative to a sample */ |
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double |
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interp2_wti(INTERP2 *ip, const int i, double x, double y) |
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{ |
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double dir, rd, r2, d2; |
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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->da[i].dia[ri] + rd*ip->da[i].dia[(ri+1)%NI2DIR]; |
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rd = ip->smf * DECODE_DIA(ip, rd); |
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r2 = 2.*rd*rd; |
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d2 = x*x + y*y; |
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if (d2 > 21.*r2) /* result would be < 1e-9 */ |
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return(.0); |
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/* Gaussian times harmonic weighting */ |
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return( exp(-d2/r2) * ip->dmin/(ip->dmin + sqrt(d2)) ); |
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} |
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|
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/* private call to get grid flag index */ |
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static int |
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interp2_flagpos(int fgi[2], INTERP2 *ip, double x, double y) |
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{ |
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int ingrid = 1; |
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|
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if (ip == NULL) /* paranoia */ |
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return(-1); |
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/* need to compute interpolant? */ |
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if (ip->da == NULL && !interp2_analyze(ip)) |
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return(-1); |
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/* get grid position */ |
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fgi[0] = (x - ip->smin[0]) * NI2DIM / (ip->smax[0] - ip->smin[0]); |
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if (fgi[0] >= NI2DIM) { |
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fgi[0] = NI2DIM-1; |
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ingrid = 0; |
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} else if (fgi[0] < 0) { |
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fgi[0] = 0; |
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ingrid = 0; |
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} |
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fgi[1] = (y - ip->smin[1]) * NI2DIM / (ip->smax[1] - ip->smin[1]); |
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if (fgi[1] >= NI2DIM) { |
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fgi[1] = NI2DIM-1; |
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ingrid = 0; |
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} else if (fgi[1] < 0) { |
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fgi[1] = 0; |
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ingrid = 0; |
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} |
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return(ingrid); |
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} |
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|
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/* private call to set black flag if not too close to the given sample */ |
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static void |
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setblk(INTERP2 *ip, const int i, const int gi[2]) |
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{ |
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double dx = (gi[0]+.5)*(1./NI2DIM)*(ip->smax[0] - ip->smin[0]) + |
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ip->smin[0] - ip->spt[i][0]; |
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double dy = (gi[1]+.5)*(1./NI2DIM)*(ip->smax[1] - ip->smin[1]) + |
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ip->smin[1] - ip->spt[i][1]; |
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|
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if (dx*dx + dy*dy > 2.*ip->grid2) |
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ip->da[i].blkflg[gi[1]] |= 1<<gi[0]; |
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} |
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|
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#define chkblk(ip,i,gi) ((ip)->da[i].blkflg[(gi)[1]]>>(gi)[0] & 1) |
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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 fgi[2]; |
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int ingrid; |
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int i; |
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|
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if (wtv == NULL) |
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return(0); |
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/* get flag position */ |
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if ((ingrid = interp2_flagpos(fgi, ip, x, y)) < 0) |
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return(0); |
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|
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wnorm = 0; /* compute raw weights */ |
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for (i = ip->ns; i--; ) |
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if (chkblk(ip, i, fgi)) { |
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wtv[i] = 0; |
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} else { |
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double wt = interp2_wti(ip, i, x, y); |
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wtv[i] = wt; |
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wnorm += wt; |
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if (wt <= 1e-9 && ingrid) |
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setblk(ip, i, fgi); |
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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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|
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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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{ |
| 370 |
int nn = 0; |
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int fgi[2]; |
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int ingrid; |
| 373 |
double wnorm; |
| 374 |
int i, j; |
| 375 |
|
| 376 |
if ((n <= 0) | (wt == NULL) | (si == NULL)) |
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return(0); |
| 378 |
/* get flag position */ |
| 379 |
if ((ingrid = interp2_flagpos(fgi, ip, x, y)) < 0) |
| 380 |
return(0); |
| 381 |
/* identify top n weights */ |
| 382 |
for (i = ip->ns; i--; ) |
| 383 |
if (!chkblk(ip, i, fgi)) { |
| 384 |
const double wti = interp2_wti(ip, i, x, y); |
| 385 |
if (wti <= 1e-9) { |
| 386 |
if (ingrid) |
| 387 |
setblk(ip, i, fgi); |
| 388 |
continue; |
| 389 |
} |
| 390 |
for (j = nn; j > 0; j--) { |
| 391 |
if (wt[j-1] >= wti) |
| 392 |
break; |
| 393 |
if (j < n) { |
| 394 |
wt[j] = wt[j-1]; |
| 395 |
si[j] = si[j-1]; |
| 396 |
} |
| 397 |
} |
| 398 |
if (j < n) { /* add/insert sample */ |
| 399 |
wt[j] = wti; |
| 400 |
si[j] = i; |
| 401 |
nn += (nn < n); |
| 402 |
} |
| 403 |
} |
| 404 |
wnorm = 0; /* normalize sample weights */ |
| 405 |
for (j = nn; j--; ) |
| 406 |
wnorm += wt[j]; |
| 407 |
if (wnorm <= 0) |
| 408 |
return(0); |
| 409 |
wnorm = 1./wnorm; |
| 410 |
for (j = nn; j--; ) |
| 411 |
wt[j] *= wnorm; |
| 412 |
return(nn); /* return actual # samples */ |
| 413 |
} |
| 414 |
|
| 415 |
/* Free interpolant */ |
| 416 |
void |
| 417 |
interp2_free(INTERP2 *ip) |
| 418 |
{ |
| 419 |
if (ip == NULL) |
| 420 |
return; |
| 421 |
if (ip->da != NULL) |
| 422 |
free(ip->da); |
| 423 |
free(ip); |
| 424 |
} |
