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#include "copyright.h" |
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|
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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 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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* 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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* direction. 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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|
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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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#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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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 */ |
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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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return(NULL); |
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|
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nip->ns = nsamps; |
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nip->rmin = .5; /* default radius minimum */ |
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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->ra = NULL; |
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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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/* 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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return 0; |
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} |
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|
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/* private routine to encode radius with range checks */ |
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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_radius(const INTERP2 *ip, double r) |
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encode_diameter(const INTERP2 *ip, double d) |
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{ |
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const int er = ENCODE_RAD(ip, r); |
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const int ed = ENCODE_DIA(ip, d); |
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|
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if (er <= 0) |
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if (ed <= 0) |
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return(0); |
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if (er >= 0xffff) |
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if (ed >= 0xffff) |
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return(0xffff); |
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return(er); |
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return(ed); |
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} |
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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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/* (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; |
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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->rmin <= 0)) |
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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->ra == NULL) { |
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ip->ra = (unsigned short (*)[NI2DIR])malloc( |
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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->ra == NULL) |
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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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if ((sortord == NULL) | (rightrndx == NULL) | (leftrndx == NULL)) |
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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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double cosd, sind; |
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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 prev. iteration? */ |
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int *sptr = rightrndx; |
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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 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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} 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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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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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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/* 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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> |
/* 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 = 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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> |
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 radius */ |
189 |
< |
ip->ra[i][bd] = ip->ra[i][bd+NI2DIR/2] = encode_radius(ip, |
190 |
< |
.25*(sortord[ip->ns-1].dm - sortord[0].dm)); |
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> |
/* preload with large radii */ |
189 |
> |
ip->da[ii][bd] = ip->da[ii][bd+NI2DIR/2] = encode_diameter(ip, |
190 |
> |
.5*(sortord[ip->ns-1].dm - sortord[0].dm)); |
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|
for (j = i; ++j < ip->ns; ) /* nearest above */ |
192 |
< |
if (rightrndx[sortord[j].si] > rpos && |
193 |
< |
leftrndx[sortord[j].si] < lpos) { |
194 |
< |
ip->ra[i][bd] = encode_radius(ip, |
195 |
< |
.5*(sortord[j].dm - sortord[i].dm)); |
192 |
> |
if (rightrndx[sortord[j].si] > rightrndx[ii] && |
193 |
> |
leftrndx[sortord[j].si] < leftrndx[ii]) { |
194 |
> |
ip->da[ii][bd] = encode_diameter(ip, |
195 |
> |
sortord[j].dm - sortord[i].dm); |
196 |
|
break; |
197 |
|
} |
198 |
|
for (j = i; j-- > 0; ) /* nearest below */ |
199 |
< |
if (rightrndx[sortord[j].si] < rpos && |
200 |
< |
leftrndx[sortord[j].si] > lpos) { |
201 |
< |
ip->ra[i][bd+NI2DIR/2] = encode_radius(ip, |
202 |
< |
.5*(sortord[i].dm - sortord[j].dm)); |
199 |
> |
if (rightrndx[sortord[j].si] < rightrndx[ii] && |
200 |
> |
leftrndx[sortord[j].si] > leftrndx[ii]) { |
201 |
> |
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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free(sortord); /* clean up */ |
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free(rightrndx); |
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free(leftrndx); |
210 |
+ |
free(endrndx); |
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return(1); |
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} |
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|
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< |
/* private call returns log of raw weight for a particular sample */ |
214 |
> |
/* private call returns raw weight for a particular sample */ |
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|
static double |
216 |
< |
get_ln_wt(const INTERP2 *ip, const int i, double x, double y) |
216 |
> |
get_wt(const INTERP2 *ip, const int i, double x, double y) |
217 |
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{ |
218 |
< |
double dir, rd; |
218 |
> |
double dir, rd, d2; |
219 |
|
int ri; |
220 |
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/* get relative direction */ |
221 |
|
x -= ip->spt[i][0]; |
226 |
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rd = dir * (NI2DIR/2./PI); |
227 |
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ri = (int)rd; |
228 |
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rd -= (double)ri; |
229 |
< |
rd = (1.-rd)*ip->ra[i][ri] + rd*ip->ra[i][(ri+1)%NI2DIR]; |
230 |
< |
rd = ip->smf * DECODE_RAD(ip, rd); |
231 |
< |
/* return log of Gaussian weight */ |
232 |
< |
return( (x*x + y*y) / (-2.*rd*rd) ); |
229 |
> |
rd = (1.-rd)*ip->da[i][ri] + rd*ip->da[i][(ri+1)%NI2DIR]; |
230 |
> |
rd = ip->smf * DECODE_DIA(ip, rd); |
231 |
> |
d2 = x*x + y*y; |
232 |
> |
/* Gaussian times harmonic weighting */ |
233 |
> |
return( exp(d2/(-2.*rd*rd)) * ip->dmin/(ip->dmin + sqrt(d2)) ); |
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} |
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|
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/* Assign full set of normalized weights to interpolate the given position */ |
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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)) |
246 |
> |
if (ip->da == NULL && !interp2_analyze(ip)) |
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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--; ) { |
251 |
< |
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 */ |
251 |
> |
double wt = get_wt(ip, i, x, y); |
252 |
|
wtv[i] = wt; |
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wnorm += wt; |
254 |
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} |
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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? */ |
275 |
< |
if (ip->ra == NULL && !interp2_compute(ip)) |
275 |
> |
if (ip->da == NULL && !interp2_analyze(ip)) |
276 |
|
return(0); |
277 |
|
/* identify top n weights */ |
278 |
|
for (i = ip->ns; i--; ) { |
279 |
< |
const double lnwt = get_ln_wt(ip, i, x, y); |
279 |
> |
const double wti = get_wt(ip, i, x, y); |
280 |
|
for (j = nn; j > 0; j--) { |
281 |
< |
if (wt[j-1] >= lnwt) |
281 |
> |
if (wt[j-1] >= wti) |
282 |
|
break; |
283 |
|
if (j < n) { |
284 |
|
wt[j] = wt[j-1]; |
286 |
|
} |
287 |
|
} |
288 |
|
if (j < n) { /* add/insert sample */ |
289 |
< |
wt[j] = lnwt; |
289 |
> |
wt[j] = wti; |
290 |
|
si[j] = i; |
291 |
|
nn += (nn < n); |
292 |
|
} |
293 |
|
} |
294 |
< |
wnorm = 0; /* exponentiate and normalize */ |
295 |
< |
for (j = nn; j--; ) { |
296 |
< |
double dwt = exp(wt[j]); |
269 |
< |
wt[j] = dwt; |
270 |
< |
wnorm += dwt; |
271 |
< |
} |
294 |
> |
wnorm = 0; /* normalize sample weights */ |
295 |
> |
for (j = nn; j--; ) |
296 |
> |
wnorm += wt[j]; |
297 |
|
if (wnorm <= 0) |
298 |
|
return(0); |
299 |
|
wnorm = 1./wnorm; |
308 |
|
{ |
309 |
|
if (ip == NULL) |
310 |
|
return; |
311 |
< |
if (ip->ra != NULL) |
312 |
< |
free(ip->ra); |
311 |
> |
if (ip->da != NULL) |
312 |
> |
free(ip->da); |
313 |
|
free(ip); |
314 |
|
} |