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greg |
2.1 |
#ifndef lint |
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greg |
2.11 |
static const char RCSid[] = "$Id: interp2d.c,v 2.10 2013/02/14 19:57:10 greg Exp $"; |
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greg |
2.1 |
#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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greg |
2.4 |
/*************************************************************** |
13 |
greg |
2.1 |
* 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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greg |
2.4 |
* 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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greg |
2.7 |
* angular slice. Once we have our approximate neighborhood |
21 |
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2.3 |
* for a sample, we can use it in a modified Gaussian weighting |
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greg |
2.4 |
* with allowing local anisotropy. Harmonic weighting is added |
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greg |
2.3 |
* 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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greg |
2.4 |
* initially distributed. Evaluation is accelerated by use of |
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2.10 |
* 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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2.4 |
****************************************************************/ |
29 |
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2.1 |
|
30 |
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#include <stdio.h> |
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#include <stdlib.h> |
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#include "rtmath.h" |
33 |
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#include "interp2d.h" |
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35 |
greg |
2.4 |
#define DECODE_DIA(ip,ed) ((ip)->dmin*(1. + .5*(ed))) |
36 |
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#define ENCODE_DIA(ip,d) ((int)(2.*(d)/(ip)->dmin) - 2) |
37 |
greg |
2.1 |
|
38 |
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/* Sample order (private) */ |
39 |
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typedef struct { |
40 |
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int si; /* sample index */ |
41 |
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float dm; /* distance measure in this direction */ |
42 |
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} SAMPORD; |
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|
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greg |
2.2 |
/* Allocate a new set of interpolation samples (caller assigns spt[] array) */ |
45 |
greg |
2.1 |
INTERP2 * |
46 |
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interp2_alloc(int nsamps) |
47 |
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{ |
48 |
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INTERP2 *nip; |
49 |
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50 |
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if (nsamps <= 1) |
51 |
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return(NULL); |
52 |
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53 |
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nip = (INTERP2 *)malloc(sizeof(INTERP2) + sizeof(float)*2*(nsamps-1)); |
54 |
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if (nip == NULL) |
55 |
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return(NULL); |
56 |
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nip->ns = nsamps; |
58 |
greg |
2.4 |
nip->dmin = 1; /* default minimum diameter */ |
59 |
greg |
2.1 |
nip->smf = NI2DSMF; /* default smoothing factor */ |
60 |
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2.4 |
nip->da = NULL; |
61 |
greg |
2.1 |
/* caller must assign spt[] array */ |
62 |
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return(nip); |
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} |
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greg |
2.2 |
/* Resize interpolation array (caller must assign any new values) */ |
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INTERP2 * |
67 |
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interp2_realloc(INTERP2 *ip, int nsamps) |
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{ |
69 |
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if (ip == NULL) |
70 |
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return(interp2_alloc(nsamps)); |
71 |
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if (nsamps <= 1) { |
72 |
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interp2_free(ip); |
73 |
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return(NULL); |
74 |
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} |
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greg |
2.8 |
if (nsamps == ip->ns) |
76 |
greg |
2.2 |
return(ip); |
77 |
greg |
2.4 |
if (ip->da != NULL) { /* will need to recompute distribution */ |
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free(ip->da); |
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ip->da = NULL; |
80 |
greg |
2.2 |
} |
81 |
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ip = (INTERP2 *)realloc(ip, sizeof(INTERP2)+sizeof(float)*2*(nsamps-1)); |
82 |
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if (ip == NULL) |
83 |
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return(NULL); |
84 |
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ip->ns = nsamps; |
85 |
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return(ip); |
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} |
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greg |
2.5 |
/* Set minimum distance under which samples will start to merge */ |
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void |
90 |
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interp2_spacing(INTERP2 *ip, double mind) |
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{ |
92 |
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if (mind <= 0) |
93 |
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return; |
94 |
greg |
2.7 |
if ((.998*ip->dmin <= mind) & (mind <= 1.002*ip->dmin)) |
95 |
greg |
2.5 |
return; |
96 |
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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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} |
100 |
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ip->dmin = mind; |
101 |
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} |
102 |
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103 |
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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) |
106 |
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{ |
107 |
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if ((ip->smf *= sf) < NI2DSMF) |
108 |
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ip->smf = NI2DSMF; |
109 |
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} |
110 |
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111 |
greg |
2.1 |
/* private call-back to sort position index */ |
112 |
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static int |
113 |
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cmp_spos(const void *p1, const void *p2) |
114 |
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{ |
115 |
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const SAMPORD *so1 = (const SAMPORD *)p1; |
116 |
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const SAMPORD *so2 = (const SAMPORD *)p2; |
117 |
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118 |
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if (so1->dm > so2->dm) |
119 |
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return 1; |
120 |
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if (so1->dm < so2->dm) |
121 |
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return -1; |
122 |
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return 0; |
123 |
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} |
124 |
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125 |
greg |
2.2 |
/* private routine to order samples in a particular direction */ |
126 |
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static void |
127 |
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sort_samples(SAMPORD *sord, const INTERP2 *ip, double ang) |
128 |
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{ |
129 |
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const double cosd = cos(ang); |
130 |
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const double sind = sin(ang); |
131 |
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int i; |
132 |
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133 |
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for (i = ip->ns; i--; ) { |
134 |
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sord[i].si = i; |
135 |
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sord[i].dm = cosd*ip->spt[i][0] + sind*ip->spt[i][1]; |
136 |
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} |
137 |
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qsort(sord, ip->ns, sizeof(SAMPORD), &cmp_spos); |
138 |
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} |
139 |
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140 |
greg |
2.4 |
/* private routine to encode sample diameter with range checks */ |
141 |
greg |
2.1 |
static int |
142 |
greg |
2.4 |
encode_diameter(const INTERP2 *ip, double d) |
143 |
greg |
2.1 |
{ |
144 |
greg |
2.4 |
const int ed = ENCODE_DIA(ip, d); |
145 |
greg |
2.1 |
|
146 |
greg |
2.4 |
if (ed <= 0) |
147 |
greg |
2.1 |
return(0); |
148 |
greg |
2.4 |
if (ed >= 0xffff) |
149 |
greg |
2.1 |
return(0xffff); |
150 |
greg |
2.4 |
return(ed); |
151 |
greg |
2.1 |
} |
152 |
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153 |
greg |
2.2 |
/* (Re)compute anisotropic basis function interpolant (normally automatic) */ |
154 |
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int |
155 |
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interp2_analyze(INTERP2 *ip) |
156 |
greg |
2.1 |
{ |
157 |
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SAMPORD *sortord; |
158 |
greg |
2.2 |
int *rightrndx, *leftrndx, *endrndx; |
159 |
greg |
2.10 |
int i, bd; |
160 |
greg |
2.1 |
/* sanity checks */ |
161 |
greg |
2.10 |
if (ip == NULL) |
162 |
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return(0); |
163 |
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if (ip->da != NULL) { /* free previous data if any */ |
164 |
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free(ip->da); |
165 |
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ip->da = NULL; |
166 |
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} |
167 |
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if ((ip->ns <= 1) | (ip->dmin <= 0)) |
168 |
greg |
2.1 |
return(0); |
169 |
greg |
2.10 |
/* compute sample domain */ |
170 |
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ip->smin[0] = ip->smin[1] = FHUGE; |
171 |
greg |
2.11 |
ip->smax[0] = ip->smax[1] = -FHUGE; |
172 |
greg |
2.10 |
for (i = ip->ns; i--; ) { |
173 |
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if (ip->spt[i][0] < ip->smin[0]) |
174 |
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ip->smin[0] = ip->spt[i][0]; |
175 |
greg |
2.11 |
if (ip->spt[i][0] > ip->smax[0]) |
176 |
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ip->smax[0] = ip->spt[i][0]; |
177 |
greg |
2.10 |
if (ip->spt[i][1] < ip->smin[1]) |
178 |
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ip->smin[1] = ip->spt[i][1]; |
179 |
greg |
2.11 |
if (ip->spt[i][1] > ip->smax[1]) |
180 |
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ip->smax[1] = ip->spt[i][1]; |
181 |
greg |
2.1 |
} |
182 |
greg |
2.11 |
ip->grid2 = ((ip->smax[0]-ip->smin[0])*(ip->smax[0]-ip->smin[0]) + |
183 |
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(ip->smax[1]-ip->smin[1])*(ip->smax[1]-ip->smin[1])) * |
184 |
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(1./NI2DIM/NI2DIM); |
185 |
greg |
2.10 |
if (ip->grid2 <= FTINY*ip->dmin*ip->dmin) |
186 |
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return(0); |
187 |
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/* allocate analysis data */ |
188 |
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ip->da = (struct interp2_samp *)calloc( ip->ns, |
189 |
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sizeof(struct interp2_samp) ); |
190 |
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if (ip->da == NULL) |
191 |
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return(0); |
192 |
greg |
2.1 |
/* get temporary arrays */ |
193 |
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sortord = (SAMPORD *)malloc(sizeof(SAMPORD)*ip->ns); |
194 |
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rightrndx = (int *)malloc(sizeof(int)*ip->ns); |
195 |
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leftrndx = (int *)malloc(sizeof(int)*ip->ns); |
196 |
greg |
2.2 |
endrndx = (int *)malloc(sizeof(int)*ip->ns); |
197 |
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if ((sortord == NULL) | (rightrndx == NULL) | |
198 |
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(leftrndx == NULL) | (endrndx == NULL)) |
199 |
greg |
2.1 |
return(0); |
200 |
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/* run through bidirections */ |
201 |
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for (bd = 0; bd < NI2DIR/2; bd++) { |
202 |
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const double ang = 2.*PI/NI2DIR*bd; |
203 |
greg |
2.2 |
int *sptr; |
204 |
greg |
2.1 |
/* create right reverse index */ |
205 |
greg |
2.2 |
if (bd) { /* re-use from previous iteration? */ |
206 |
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sptr = rightrndx; |
207 |
greg |
2.1 |
rightrndx = leftrndx; |
208 |
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leftrndx = sptr; |
209 |
greg |
2.2 |
} else { /* else sort first half-plane */ |
210 |
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sort_samples(sortord, ip, PI/2. - PI/NI2DIR); |
211 |
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for (i = ip->ns; i--; ) |
212 |
greg |
2.1 |
rightrndx[sortord[i].si] = i; |
213 |
greg |
2.2 |
/* & store reverse order for later */ |
214 |
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for (i = ip->ns; i--; ) |
215 |
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endrndx[sortord[i].si] = ip->ns-1 - i; |
216 |
greg |
2.1 |
} |
217 |
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/* create new left reverse index */ |
218 |
greg |
2.2 |
if (bd == NI2DIR/2 - 1) { /* use order from first iteration? */ |
219 |
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sptr = leftrndx; |
220 |
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leftrndx = endrndx; |
221 |
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endrndx = sptr; |
222 |
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} else { /* else compute new half-plane */ |
223 |
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sort_samples(sortord, ip, ang + (PI/2. + PI/NI2DIR)); |
224 |
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for (i = ip->ns; i--; ) |
225 |
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leftrndx[sortord[i].si] = i; |
226 |
greg |
2.1 |
} |
227 |
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/* sort grid values in this direction */ |
228 |
greg |
2.2 |
sort_samples(sortord, ip, ang); |
229 |
greg |
2.1 |
/* find nearest neighbors each side */ |
230 |
greg |
2.2 |
for (i = ip->ns; i--; ) { |
231 |
greg |
2.3 |
const int ii = sortord[i].si; |
232 |
greg |
2.1 |
int j; |
233 |
greg |
2.3 |
/* preload with large radii */ |
234 |
greg |
2.10 |
ip->da[ii].dia[bd] = |
235 |
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ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip, |
236 |
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.5*(sortord[ip->ns-1].dm - sortord[0].dm)); |
237 |
greg |
2.1 |
for (j = i; ++j < ip->ns; ) /* nearest above */ |
238 |
greg |
2.3 |
if (rightrndx[sortord[j].si] > rightrndx[ii] && |
239 |
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leftrndx[sortord[j].si] < leftrndx[ii]) { |
240 |
greg |
2.10 |
ip->da[ii].dia[bd] = encode_diameter(ip, |
241 |
greg |
2.4 |
sortord[j].dm - sortord[i].dm); |
242 |
greg |
2.1 |
break; |
243 |
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} |
244 |
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for (j = i; j-- > 0; ) /* nearest below */ |
245 |
greg |
2.3 |
if (rightrndx[sortord[j].si] < rightrndx[ii] && |
246 |
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leftrndx[sortord[j].si] > leftrndx[ii]) { |
247 |
greg |
2.10 |
ip->da[ii].dia[bd+NI2DIR/2] = encode_diameter(ip, |
248 |
greg |
2.4 |
sortord[i].dm - sortord[j].dm); |
249 |
greg |
2.1 |
break; |
250 |
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} |
251 |
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} |
252 |
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} |
253 |
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free(sortord); /* clean up */ |
254 |
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free(rightrndx); |
255 |
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free(leftrndx); |
256 |
greg |
2.2 |
free(endrndx); |
257 |
greg |
2.1 |
return(1); |
258 |
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} |
259 |
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|
260 |
greg |
2.10 |
/* Compute unnormalized weight for a position relative to a sample */ |
261 |
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double |
262 |
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interp2_wti(INTERP2 *ip, const int i, double x, double y) |
263 |
greg |
2.1 |
{ |
264 |
greg |
2.11 |
double dir, rd, r2, d2; |
265 |
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int ri; |
266 |
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/* get relative direction */ |
267 |
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x -= ip->spt[i][0]; |
268 |
greg |
2.1 |
y -= ip->spt[i][1]; |
269 |
greg |
2.11 |
dir = atan2a(y, x); |
270 |
greg |
2.1 |
dir += 2.*PI*(dir < 0); |
271 |
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/* linear radius interpolation */ |
272 |
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rd = dir * (NI2DIR/2./PI); |
273 |
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ri = (int)rd; |
274 |
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rd -= (double)ri; |
275 |
greg |
2.10 |
rd = (1.-rd)*ip->da[i].dia[ri] + rd*ip->da[i].dia[(ri+1)%NI2DIR]; |
276 |
greg |
2.4 |
rd = ip->smf * DECODE_DIA(ip, rd); |
277 |
greg |
2.6 |
r2 = 2.*rd*rd; |
278 |
greg |
2.11 |
d2 = x*x + y*y; |
279 |
|
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if (d2 > 21.*r2) /* result would be < 1e-9 */ |
280 |
greg |
2.6 |
return(.0); |
281 |
greg |
2.3 |
/* Gaussian times harmonic weighting */ |
282 |
greg |
2.6 |
return( exp(-d2/r2) * ip->dmin/(ip->dmin + sqrt(d2)) ); |
283 |
greg |
2.1 |
} |
284 |
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|
285 |
greg |
2.11 |
/* private call to get grid flag index */ |
286 |
|
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static int |
287 |
|
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interp2_flagpos(int fgi[2], INTERP2 *ip, double x, double y) |
288 |
|
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{ |
289 |
|
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int ingrid = 1; |
290 |
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|
291 |
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if (ip == NULL) /* paranoia */ |
292 |
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return(-1); |
293 |
|
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/* need to compute interpolant? */ |
294 |
|
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if (ip->da == NULL && !interp2_analyze(ip)) |
295 |
|
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return(-1); |
296 |
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/* get grid position */ |
297 |
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fgi[0] = (x - ip->smin[0]) * NI2DIM / (ip->smax[0] - ip->smin[0]); |
298 |
|
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if (fgi[0] >= NI2DIM) { |
299 |
|
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fgi[0] = NI2DIM-1; |
300 |
|
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ingrid = 0; |
301 |
|
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} else if (fgi[0] < 0) { |
302 |
|
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fgi[0] = 0; |
303 |
|
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ingrid = 0; |
304 |
|
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} |
305 |
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fgi[1] = (y - ip->smin[1]) * NI2DIM / (ip->smax[1] - ip->smin[1]); |
306 |
|
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if (fgi[1] >= NI2DIM) { |
307 |
|
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fgi[1] = NI2DIM-1; |
308 |
|
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ingrid = 0; |
309 |
|
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} else if (fgi[1] < 0) { |
310 |
|
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fgi[1] = 0; |
311 |
|
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ingrid = 0; |
312 |
|
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} |
313 |
|
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return(ingrid); |
314 |
|
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} |
315 |
|
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|
316 |
|
|
/* private call to set black flag if not too close to the given sample */ |
317 |
|
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static void |
318 |
|
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setblk(INTERP2 *ip, const int i, const int gi[2]) |
319 |
|
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{ |
320 |
|
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double dx = (gi[0]+.5)*(1./NI2DIM)*(ip->smax[0] - ip->smin[0]) + |
321 |
|
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ip->smin[0] - ip->spt[i][0]; |
322 |
|
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double dy = (gi[1]+.5)*(1./NI2DIM)*(ip->smax[1] - ip->smin[1]) + |
323 |
|
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ip->smin[1] - ip->spt[i][1]; |
324 |
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|
325 |
|
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if (dx*dx + dy*dy > 2.*ip->grid2) |
326 |
|
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ip->da[i].blkflg[gi[1]] |= 1<<gi[0]; |
327 |
|
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} |
328 |
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|
329 |
|
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#define chkblk(ip,i,gi) ((ip)->da[i].blkflg[(gi)[1]]>>(gi)[0] & 1) |
330 |
|
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|
331 |
greg |
2.1 |
/* Assign full set of normalized weights to interpolate the given position */ |
332 |
|
|
int |
333 |
|
|
interp2_weights(float wtv[], INTERP2 *ip, double x, double y) |
334 |
|
|
{ |
335 |
|
|
double wnorm; |
336 |
greg |
2.11 |
int fgi[2]; |
337 |
|
|
int ingrid; |
338 |
greg |
2.1 |
int i; |
339 |
|
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|
340 |
greg |
2.11 |
if (wtv == NULL) |
341 |
|
|
return(0); |
342 |
|
|
/* get flag position */ |
343 |
|
|
if ((ingrid = interp2_flagpos(fgi, ip, x, y)) < 0) |
344 |
greg |
2.1 |
return(0); |
345 |
|
|
|
346 |
|
|
wnorm = 0; /* compute raw weights */ |
347 |
greg |
2.11 |
for (i = ip->ns; i--; ) |
348 |
|
|
if (chkblk(ip, i, fgi)) { |
349 |
|
|
wtv[i] = 0; |
350 |
|
|
} else { |
351 |
greg |
2.10 |
double wt = interp2_wti(ip, i, x, y); |
352 |
greg |
2.1 |
wtv[i] = wt; |
353 |
|
|
wnorm += wt; |
354 |
greg |
2.11 |
if (wt <= 1e-9 && ingrid) |
355 |
|
|
setblk(ip, i, fgi); |
356 |
|
|
} |
357 |
greg |
2.1 |
if (wnorm <= 0) /* too far from all our samples! */ |
358 |
|
|
return(0); |
359 |
|
|
wnorm = 1./wnorm; /* normalize weights */ |
360 |
|
|
for (i = ip->ns; i--; ) |
361 |
|
|
wtv[i] *= wnorm; |
362 |
|
|
return(ip->ns); /* all done */ |
363 |
|
|
} |
364 |
|
|
|
365 |
|
|
|
366 |
|
|
/* Get normalized weights and indexes for n best samples in descending order */ |
367 |
|
|
int |
368 |
|
|
interp2_topsamp(float wt[], int si[], const int n, INTERP2 *ip, double x, double y) |
369 |
|
|
{ |
370 |
|
|
int nn = 0; |
371 |
greg |
2.11 |
int fgi[2]; |
372 |
|
|
int ingrid; |
373 |
greg |
2.1 |
double wnorm; |
374 |
|
|
int i, j; |
375 |
|
|
|
376 |
greg |
2.11 |
if ((n <= 0) | (wt == NULL) | (si == NULL)) |
377 |
|
|
return(0); |
378 |
|
|
/* get flag position */ |
379 |
|
|
if ((ingrid = interp2_flagpos(fgi, ip, x, y)) < 0) |
380 |
greg |
2.1 |
return(0); |
381 |
|
|
/* identify top n weights */ |
382 |
greg |
2.11 |
for (i = ip->ns; i--; ) |
383 |
|
|
if (!chkblk(ip, i, fgi)) { |
384 |
greg |
2.10 |
const double wti = interp2_wti(ip, i, x, y); |
385 |
greg |
2.11 |
if (wti <= 1e-9) { |
386 |
|
|
if (ingrid) |
387 |
|
|
setblk(ip, i, fgi); |
388 |
greg |
2.9 |
continue; |
389 |
greg |
2.11 |
} |
390 |
greg |
2.1 |
for (j = nn; j > 0; j--) { |
391 |
greg |
2.3 |
if (wt[j-1] >= wti) |
392 |
greg |
2.1 |
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 |
greg |
2.3 |
wt[j] = wti; |
400 |
greg |
2.1 |
si[j] = i; |
401 |
|
|
nn += (nn < n); |
402 |
|
|
} |
403 |
greg |
2.11 |
} |
404 |
greg |
2.3 |
wnorm = 0; /* normalize sample weights */ |
405 |
|
|
for (j = nn; j--; ) |
406 |
|
|
wnorm += wt[j]; |
407 |
greg |
2.1 |
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 |
greg |
2.4 |
if (ip->da != NULL) |
422 |
|
|
free(ip->da); |
423 |
greg |
2.1 |
free(ip); |
424 |
|
|
} |