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#ifndef lint
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static const char RCSid[] = "$Id: interp2d.c,v 2.7 2013/02/12 17:47:58 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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#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 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.
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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_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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/* 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 (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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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->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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/* 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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/* 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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/* 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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/* 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 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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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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/* 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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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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/* (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 bd;
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/* sanity checks */
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if (ip == NULL || (ip->ns <= 1) | (ip->dmin <= 0))
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return(0);
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/* need to allocate? */
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if (ip->da == NULL) {
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ip->da = (unsigned short (*)[NI2DIR])malloc(
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sizeof(unsigned short)*NI2DIR*ip->ns);
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if (ip->da == 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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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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int i;
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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][bd] = ip->da[ii][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][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][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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/* private call returns raw weight for a particular sample */
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static double
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get_wt(const 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][ri] + rd*ip->da[i][(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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/* 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->da == NULL && !interp2_analyze(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_wt(ip, i, x, y);
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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->da == NULL && !interp2_analyze(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 wti = get_wt(ip, i, x, y);
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for (j = nn; j > 0; j--) {
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if (wt[j-1] >= wti)
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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] = wti;
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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; /* normalize sample weights */
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for (j = nn; j--; )
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wnorm += wt[j];
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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->da != NULL)
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free(ip->da);
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free(ip);
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}
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