1 : /******************************************************************************
2 : * $Id: thinplatespline.cpp 22879 2011-08-07 01:00:45Z rouault $
3 : *
4 : * Project: GDAL Warp API
5 : * Purpose: Implemenentation of 2D Thin Plate Spline transformer.
6 : * Author: VIZRT Development Team.
7 : *
8 : * This code was provided by Gilad Ronnen (gro at visrt dot com) with
9 : * permission to reuse under the following license.
10 : *
11 : ******************************************************************************
12 : * Copyright (c) 2004, VIZRT Inc.
13 : *
14 : * Permission is hereby granted, free of charge, to any person obtaining a
15 : * copy of this software and associated documentation files (the "Software"),
16 : * to deal in the Software without restriction, including without limitation
17 : * the rights to use, copy, modify, merge, publish, distribute, sublicense,
18 : * and/or sell copies of the Software, and to permit persons to whom the
19 : * Software is furnished to do so, subject to the following conditions:
20 : *
21 : * The above copyright notice and this permission notice shall be included
22 : * in all copies or substantial portions of the Software.
23 : *
24 : * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
25 : * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
26 : * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
27 : * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
28 : * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
29 : * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
30 : * DEALINGS IN THE SOFTWARE.
31 : ****************************************************************************/
32 :
33 : #ifdef HAVE_ARMADILLO
34 : /* Include before #define A(r,c) because armadillo uses A in its include files */
35 : #include "armadillo"
36 : #endif
37 :
38 : #include "thinplatespline.h"
39 :
40 : #ifdef HAVE_FLOAT_H
41 : # include <float.h>
42 : #elif defined(HAVE_VALUES_H)
43 : # include <values.h>
44 : #endif
45 :
46 : #ifndef FLT_MAX
47 : # define FLT_MAX 1e+37
48 : # define FLT_MIN 1e-37
49 : #endif
50 :
51 : VizGeorefSpline2D* viz_xy2llz;
52 : VizGeorefSpline2D* viz_llz2xy;
53 :
54 : /////////////////////////////////////////////////////////////////////////////////////
55 : //// vizGeorefSpline2D
56 : /////////////////////////////////////////////////////////////////////////////////////
57 :
58 : #define A(r,c) _AA[ _nof_eqs * (r) + (c) ]
59 : #define Ainv(r,c) _Ainv[ _nof_eqs * (r) + (c) ]
60 :
61 :
62 : #define VIZ_GEOREF_SPLINE_DEBUG 0
63 :
64 : static int matrixInvert( int N, double input[], double output[] );
65 :
66 40 : void VizGeorefSpline2D::grow_points()
67 :
68 : {
69 40 : int new_max = _max_nof_points*2 + 2 + 3;
70 : int i;
71 :
72 40 : if( _max_nof_points == 0 )
73 : {
74 20 : x = (double *) VSIMalloc( sizeof(double) * new_max );
75 20 : y = (double *) VSIMalloc( sizeof(double) * new_max );
76 20 : u = (double *) VSIMalloc( sizeof(double) * new_max );
77 20 : unused = (int *) VSIMalloc( sizeof(int) * new_max );
78 20 : index = (int *) VSIMalloc( sizeof(int) * new_max );
79 60 : for( i = 0; i < VIZGEOREF_MAX_VARS; i++ )
80 : {
81 40 : rhs[i] = (double *) VSICalloc( sizeof(double), new_max );
82 40 : coef[i] = (double *) VSICalloc( sizeof(double), new_max );
83 : }
84 : }
85 : else
86 : {
87 20 : x = (double *) VSIRealloc( x, sizeof(double) * new_max );
88 20 : y = (double *) VSIRealloc( y, sizeof(double) * new_max );
89 20 : u = (double *) VSIRealloc( u, sizeof(double) * new_max );
90 20 : unused = (int *) VSIRealloc( unused, sizeof(int) * new_max );
91 20 : index = (int *) VSIRealloc( index, sizeof(int) * new_max );
92 60 : for( i = 0; i < VIZGEOREF_MAX_VARS; i++ )
93 : {
94 40 : rhs[i] = (double *)
95 40 : VSIRealloc( rhs[i], sizeof(double) * new_max );
96 40 : coef[i] = (double *)
97 40 : VSIRealloc( coef[i], sizeof(double) * new_max );
98 : }
99 : }
100 :
101 40 : _max_nof_points = new_max - 3;
102 40 : }
103 :
104 80 : int VizGeorefSpline2D::add_point( const double Px, const double Py, const double *Pvars )
105 : {
106 80 : type = VIZ_GEOREF_SPLINE_POINT_WAS_ADDED;
107 : int i;
108 :
109 80 : if( _nof_points == _max_nof_points )
110 20 : grow_points();
111 :
112 80 : i = _nof_points;
113 : //A new point is added
114 80 : x[i] = Px;
115 80 : y[i] = Py;
116 240 : for ( int j = 0; j < _nof_vars; j++ )
117 160 : rhs[j][i+3] = Pvars[j];
118 80 : _nof_points++;
119 80 : return 1;
120 : }
121 :
122 0 : bool VizGeorefSpline2D::change_point(int index, double Px, double Py, double* Pvars)
123 : {
124 0 : if ( index < _nof_points )
125 : {
126 0 : int i = index;
127 0 : x[i] = Px;
128 0 : y[i] = Py;
129 0 : for ( int j = 0; j < _nof_vars; j++ )
130 0 : rhs[j][i+3] = Pvars[j];
131 : }
132 :
133 0 : return( true );
134 : }
135 :
136 0 : bool VizGeorefSpline2D::get_xy(int index, double& outX, double& outY)
137 : {
138 : bool ok;
139 :
140 0 : if ( index < _nof_points )
141 : {
142 0 : ok = true;
143 0 : outX = x[index];
144 0 : outY = y[index];
145 : }
146 : else
147 : {
148 0 : ok = false;
149 0 : outX = outY = 0.0f;
150 : }
151 :
152 0 : return(ok);
153 : }
154 :
155 0 : int VizGeorefSpline2D::delete_point(const double Px, const double Py )
156 : {
157 0 : for ( int i = 0; i < _nof_points; i++ )
158 : {
159 0 : if ( ( fabs(Px - x[i]) <= _tx ) && ( fabs(Py - y[i]) <= _ty ) )
160 : {
161 0 : for ( int j = i; j < _nof_points - 1; j++ )
162 : {
163 0 : x[j] = x[j+1];
164 0 : y[j] = y[j+1];
165 0 : for ( int k = 0; k < _nof_vars; k++ )
166 0 : rhs[k][j+3] = rhs[k][j+3+1];
167 : }
168 0 : _nof_points--;
169 0 : type = VIZ_GEOREF_SPLINE_POINT_WAS_DELETED;
170 0 : return(1);
171 : }
172 : }
173 0 : return(0);
174 : }
175 :
176 20 : int VizGeorefSpline2D::solve(void)
177 : {
178 : int r, c, v;
179 : int p;
180 :
181 : // No points at all
182 20 : if ( _nof_points < 1 )
183 : {
184 0 : type = VIZ_GEOREF_SPLINE_ZERO_POINTS;
185 0 : return(0);
186 : }
187 :
188 : // Only one point
189 20 : if ( _nof_points == 1 )
190 : {
191 0 : type = VIZ_GEOREF_SPLINE_ONE_POINT;
192 0 : return(1);
193 : }
194 : // Just 2 points - it is necessarily 1D case
195 20 : if ( _nof_points == 2 )
196 : {
197 0 : _dx = x[1] - x[0];
198 0 : _dy = y[1] - y[0];
199 0 : double fact = 1.0 / ( _dx * _dx + _dy * _dy );
200 0 : _dx *= fact;
201 0 : _dy *= fact;
202 :
203 0 : type = VIZ_GEOREF_SPLINE_TWO_POINTS;
204 0 : return(2);
205 : }
206 :
207 : // More than 2 points - first we have to check if it is 1D or 2D case
208 :
209 20 : double xmax = x[0], xmin = x[0], ymax = y[0], ymin = y[0];
210 : double delx, dely;
211 : double xx, yy;
212 20 : double sumx = 0.0f, sumy= 0.0f, sumx2 = 0.0f, sumy2 = 0.0f, sumxy = 0.0f;
213 : double SSxx, SSyy, SSxy;
214 :
215 100 : for ( p = 0; p < _nof_points; p++ )
216 : {
217 80 : xx = x[p];
218 80 : yy = y[p];
219 :
220 80 : xmax = MAX( xmax, xx );
221 80 : xmin = MIN( xmin, xx );
222 80 : ymax = MAX( ymax, yy );
223 80 : ymin = MIN( ymin, yy );
224 :
225 80 : sumx += xx;
226 80 : sumx2 += xx * xx;
227 80 : sumy += yy;
228 80 : sumy2 += yy * yy;
229 80 : sumxy += xx * yy;
230 : }
231 20 : delx = xmax - xmin;
232 20 : dely = ymax - ymin;
233 :
234 20 : SSxx = sumx2 - sumx * sumx / _nof_points;
235 20 : SSyy = sumy2 - sumy * sumy / _nof_points;
236 20 : SSxy = sumxy - sumx * sumy / _nof_points;
237 :
238 20 : if ( delx < 0.001 * dely || dely < 0.001 * delx ||
239 : fabs ( SSxy * SSxy / ( SSxx * SSyy ) ) > 0.99 )
240 : {
241 : int p1;
242 :
243 0 : type = VIZ_GEOREF_SPLINE_ONE_DIMENSIONAL;
244 :
245 0 : _dx = _nof_points * sumx2 - sumx * sumx;
246 0 : _dy = _nof_points * sumy2 - sumy * sumy;
247 0 : double fact = 1.0 / sqrt( _dx * _dx + _dy * _dy );
248 0 : _dx *= fact;
249 0 : _dy *= fact;
250 :
251 0 : for ( p = 0; p < _nof_points; p++ )
252 : {
253 0 : double dxp = x[p] - x[0];
254 0 : double dyp = y[p] - y[0];
255 0 : u[p] = _dx * dxp + _dy * dyp;
256 0 : unused[p] = 1;
257 : }
258 :
259 0 : for ( p = 0; p < _nof_points; p++ )
260 : {
261 0 : int min_index = -1;
262 0 : double min_u = 0;
263 0 : for ( p1 = 0; p1 < _nof_points; p1++ )
264 : {
265 0 : if ( unused[p1] )
266 : {
267 0 : if ( min_index < 0 || u[p1] < min_u )
268 : {
269 0 : min_index = p1;
270 0 : min_u = u[p1];
271 : }
272 : }
273 : }
274 0 : index[p] = min_index;
275 0 : unused[min_index] = 0;
276 : }
277 :
278 0 : return(3);
279 : }
280 :
281 20 : type = VIZ_GEOREF_SPLINE_FULL;
282 : // Make the necessary memory allocations
283 20 : if ( _AA )
284 0 : CPLFree(_AA);
285 20 : if ( _Ainv )
286 0 : CPLFree(_Ainv);
287 :
288 20 : _nof_eqs = _nof_points + 3;
289 :
290 20 : _AA = ( double * )CPLCalloc( _nof_eqs * _nof_eqs, sizeof( double ) );
291 20 : _Ainv = ( double * )CPLCalloc( _nof_eqs * _nof_eqs, sizeof( double ) );
292 :
293 : // Calc the values of the matrix A
294 80 : for ( r = 0; r < 3; r++ )
295 240 : for ( c = 0; c < 3; c++ )
296 180 : A(r,c) = 0.0;
297 :
298 100 : for ( c = 0; c < _nof_points; c++ )
299 : {
300 80 : A(0,c+3) = 1.0;
301 80 : A(1,c+3) = x[c];
302 80 : A(2,c+3) = y[c];
303 :
304 80 : A(c+3,0) = 1.0;
305 80 : A(c+3,1) = x[c];
306 80 : A(c+3,2) = y[c];
307 : }
308 :
309 100 : for ( r = 0; r < _nof_points; r++ )
310 280 : for ( c = r; c < _nof_points; c++ )
311 : {
312 200 : A(r+3,c+3) = base_func( x[r], y[r], x[c], y[c] );
313 200 : if ( r != c )
314 120 : A(c+3,r+3 ) = A(r+3,c+3);
315 : }
316 :
317 : #if VIZ_GEOREF_SPLINE_DEBUG
318 :
319 : for ( r = 0; r < _nof_eqs; r++ )
320 : {
321 : for ( c = 0; c < _nof_eqs; c++ )
322 : fprintf(stderr, "%f", A(r,c));
323 : fprintf(stderr, "\n");
324 : }
325 :
326 : #endif
327 :
328 : // Invert the matrix
329 20 : int status = matrixInvert( _nof_eqs, _AA, _Ainv );
330 :
331 20 : if ( !status )
332 : {
333 0 : fprintf(stderr, " There is a problem to invert the interpolation matrix\n");
334 0 : return 0;
335 : }
336 :
337 : // calc the coefs
338 60 : for ( v = 0; v < _nof_vars; v++ )
339 320 : for ( r = 0; r < _nof_eqs; r++ )
340 : {
341 280 : coef[v][r] = 0.0;
342 2240 : for ( c = 0; c < _nof_eqs; c++ )
343 1960 : coef[v][r] += Ainv(r,c) * rhs[v][c];
344 : }
345 :
346 20 : return(4);
347 : }
348 :
349 5124 : int VizGeorefSpline2D::get_point( const double Px, const double Py, double *vars )
350 : {
351 : int v, r;
352 : double tmp, Pu;
353 : double fact;
354 5124 : int leftP=0, rightP=0, found = 0;
355 :
356 5124 : switch ( type )
357 : {
358 : case VIZ_GEOREF_SPLINE_ZERO_POINTS :
359 0 : for ( v = 0; v < _nof_vars; v++ )
360 0 : vars[v] = 0.0;
361 0 : break;
362 : case VIZ_GEOREF_SPLINE_ONE_POINT :
363 0 : for ( v = 0; v < _nof_vars; v++ )
364 0 : vars[v] = rhs[v][3];
365 0 : break;
366 : case VIZ_GEOREF_SPLINE_TWO_POINTS :
367 0 : fact = _dx * ( Px - x[0] ) + _dy * ( Py - y[0] );
368 0 : for ( v = 0; v < _nof_vars; v++ )
369 0 : vars[v] = ( 1 - fact ) * rhs[v][3] + fact * rhs[v][4];
370 0 : break;
371 : case VIZ_GEOREF_SPLINE_ONE_DIMENSIONAL :
372 0 : Pu = _dx * ( Px - x[0] ) + _dy * ( Py - y[0] );
373 0 : if ( Pu <= u[index[0]] )
374 : {
375 0 : leftP = index[0];
376 0 : rightP = index[1];
377 : }
378 0 : else if ( Pu >= u[index[_nof_points-1]] )
379 : {
380 0 : leftP = index[_nof_points-2];
381 0 : rightP = index[_nof_points-1];
382 : }
383 : else
384 : {
385 0 : for ( r = 1; !found && r < _nof_points; r++ )
386 : {
387 0 : leftP = index[r-1];
388 0 : rightP = index[r];
389 0 : if ( Pu >= u[leftP] && Pu <= u[rightP] )
390 0 : found = 1;
391 : }
392 : }
393 :
394 0 : fact = ( Pu - u[leftP] ) / ( u[rightP] - u[leftP] );
395 0 : for ( v = 0; v < _nof_vars; v++ )
396 0 : vars[v] = ( 1.0 - fact ) * rhs[v][leftP+3] +
397 0 : fact * rhs[v][rightP+3];
398 0 : break;
399 : case VIZ_GEOREF_SPLINE_FULL :
400 15372 : for ( v = 0; v < _nof_vars; v++ )
401 10248 : vars[v] = coef[v][0] + coef[v][1] * Px + coef[v][2] * Py;
402 :
403 25620 : for ( r = 0; r < _nof_points; r++ )
404 : {
405 20496 : tmp = base_func( Px, Py, x[r], y[r] );
406 61488 : for ( v= 0; v < _nof_vars; v++ )
407 40992 : vars[v] += coef[v][r+3] * tmp;
408 : }
409 5124 : break;
410 : case VIZ_GEOREF_SPLINE_POINT_WAS_ADDED :
411 0 : fprintf(stderr, " A point was added after the last solve\n");
412 0 : fprintf(stderr, " NO interpolation - return values are zero\n");
413 0 : for ( v = 0; v < _nof_vars; v++ )
414 0 : vars[v] = 0.0;
415 0 : return(0);
416 : break;
417 : case VIZ_GEOREF_SPLINE_POINT_WAS_DELETED :
418 0 : fprintf(stderr, " A point was deleted after the last solve\n");
419 0 : fprintf(stderr, " NO interpolation - return values are zero\n");
420 0 : for ( v = 0; v < _nof_vars; v++ )
421 0 : vars[v] = 0.0;
422 0 : return(0);
423 : break;
424 : default :
425 0 : return(0);
426 : break;
427 : }
428 5124 : return(1);
429 : }
430 :
431 20696 : double VizGeorefSpline2D::base_func( const double x1, const double y1,
432 : const double x2, const double y2 )
433 : {
434 20696 : if ( ( x1 == x2 ) && (y1 == y2 ) )
435 198 : return 0.0;
436 :
437 20498 : double dist = ( x2 - x1 ) * ( x2 - x1 ) + ( y2 - y1 ) * ( y2 - y1 );
438 :
439 20498 : return dist * log( dist );
440 : }
441 :
442 : #ifdef HAVE_ARMADILLO
443 :
444 20 : static int matrixInvert( int N, double input[], double output[] )
445 : {
446 : try
447 : {
448 20 : arma::mat matInput(input,N,N,false);
449 20 : const arma::mat& matInv = arma::inv(matInput);
450 : int row, col;
451 160 : for(row = 0; row < N; row++)
452 1120 : for(col = 0; col < N; col++)
453 1960 : output[row * N + col] = matInv.at(row, col);
454 20 : return true;
455 : //arma::mat matInv(output,N,N,false);
456 : //return arma::inv(matInv, matInput);
457 : }
458 0 : catch(...)
459 : {
460 0 : fprintf(stderr, "matrixInvert(): error occured.\n");
461 0 : return false;
462 : }
463 4029 : }
464 :
465 : #else
466 :
467 : static int matrixInvert( int N, double input[], double output[] )
468 : {
469 : // Receives an array of dimension NxN as input. This is passed as a one-
470 : // dimensional array of N-squared size. It produces the inverse of the
471 : // input matrix, returned as output, also of size N-squared. The Gauss-
472 : // Jordan Elimination method is used. (Adapted from a BASIC routine in
473 : // "Basic Scientific Subroutines Vol. 1", courtesy of Scott Edwards.)
474 :
475 : // Array elements 0...N-1 are for the first row, N...2N-1 are for the
476 : // second row, etc.
477 :
478 : // We need to have a temporary array of size N x 2N. We'll refer to the
479 : // "left" and "right" halves of this array.
480 :
481 : int row, col;
482 :
483 : #if 0
484 : fprintf(stderr, "Matrix Inversion input matrix (N=%d)\n", N);
485 : for ( row=0; row<N; row++ )
486 : {
487 : for ( col=0; col<N; col++ )
488 : {
489 : fprintf(stderr, "%5.2f ", input[row*N + col ] );
490 : }
491 : fprintf(stderr, "\n");
492 : }
493 : #endif
494 :
495 : int tempSize = 2 * N * N;
496 : double* temp = (double*) new double[ tempSize ];
497 : double ftemp;
498 :
499 : if (temp == 0) {
500 :
501 : fprintf(stderr, "matrixInvert(): ERROR - memory allocation failed.\n");
502 : return false;
503 : }
504 :
505 : // First create a double-width matrix with the input array on the left
506 : // and the identity matrix on the right.
507 :
508 : for ( row=0; row<N; row++ )
509 : {
510 : for ( col=0; col<N; col++ )
511 : {
512 : // Our index into the temp array is X2 because it's twice as wide
513 : // as the input matrix.
514 :
515 : temp[ 2*row*N + col ] = input[ row*N+col ]; // left = input matrix
516 : temp[ 2*row*N + col + N ] = 0.0f; // right = 0
517 : }
518 : temp[ 2*row*N + row + N ] = 1.0f; // 1 on the diagonal of RHS
519 : }
520 :
521 : // Now perform row-oriented operations to convert the left hand side
522 : // of temp to the identity matrix. The inverse of input will then be
523 : // on the right.
524 :
525 : int max;
526 : int k=0;
527 : for (k = 0; k < N; k++)
528 : {
529 : if (k+1 < N) // if not on the last row
530 : {
531 : max = k;
532 : for (row = k+1; row < N; row++) // find the maximum element
533 : {
534 : if (fabs( temp[row*2*N + k] ) > fabs( temp[max*2*N + k] ))
535 : {
536 : max = row;
537 : }
538 : }
539 :
540 : if (max != k) // swap all the elements in the two rows
541 : {
542 : for (col=k; col<2*N; col++)
543 : {
544 : ftemp = temp[k*2*N + col];
545 : temp[k*2*N + col] = temp[max*2*N + col];
546 : temp[max*2*N + col] = ftemp;
547 : }
548 : }
549 : }
550 :
551 : ftemp = temp[ k*2*N + k ];
552 : if ( ftemp == 0.0f ) // matrix cannot be inverted
553 : {
554 : delete[] temp;
555 : return false;
556 : }
557 :
558 : for ( col=k; col<2*N; col++ )
559 : {
560 : temp[ k*2*N + col ] /= ftemp;
561 : }
562 :
563 : int i2 = k*2*N ;
564 : for ( row=0; row<N; row++ )
565 : {
566 : if ( row != k )
567 : {
568 : int i1 = row*2*N;
569 : ftemp = temp[ i1 + k ];
570 : for ( col=k; col<2*N; col++ )
571 : {
572 : temp[ i1 + col ] -= ftemp * temp[ i2 + col ];
573 : }
574 : }
575 : }
576 : }
577 :
578 : // Retrieve inverse from the right side of temp
579 :
580 : for (row = 0; row < N; row++)
581 : {
582 : for (col = 0; col < N; col++)
583 : {
584 : output[row*N + col] = temp[row*2*N + col + N ];
585 : }
586 : }
587 :
588 : #if 0
589 : fprintf(stderr, "Matrix Inversion result matrix:\n");
590 : for ( row=0; row<N; row++ )
591 : {
592 : for ( col=0; col<N; col++ )
593 : {
594 : fprintf(stderr, "%5.2f ", output[row*N + col ] );
595 : }
596 : fprintf(stderr, "\n");
597 : }
598 : #endif
599 :
600 : delete [] temp; // free memory
601 : return true;
602 : }
603 : #endif
|
