31 const QVector<QgsPointXY> &destinationCoordinates,
32 QgsPointXY &origin,
double &pixelXSize,
double &pixelYSize )
34 const int n = destinationCoordinates.size();
37 throw std::domain_error( QObject::tr(
"Fit to a linear transform requires at least 2 points." ).toLocal8Bit().constData() );
40 double sumPx( 0 ), sumPy( 0 ), sumPx2( 0 ), sumPy2( 0 ), sumPxMx( 0 ), sumPyMy( 0 ), sumMx( 0 ), sumMy( 0 );
41 for (
int i = 0; i < n; ++i )
43 sumPx += sourceCoordinates.at( i ).x();
44 sumPy += sourceCoordinates.at( i ).y();
45 sumPx2 += std::pow( sourceCoordinates.at( i ).x(), 2 );
46 sumPy2 += std::pow( sourceCoordinates.at( i ).y(), 2 );
47 sumPxMx += sourceCoordinates.at( i ).x() * destinationCoordinates.at( i ).x();
48 sumPyMy += sourceCoordinates.at( i ).y() * destinationCoordinates.at( i ).y();
49 sumMx += destinationCoordinates.at( i ).x();
50 sumMy += destinationCoordinates.at( i ).y();
53 const double deltaX = n * sumPx2 - std::pow( sumPx, 2 );
54 const double deltaY = n * sumPy2 - std::pow( sumPy, 2 );
56 const double aX = ( sumPx2 * sumMx - sumPx * sumPxMx ) / deltaX;
57 const double aY = ( sumPy2 * sumMy - sumPy * sumPyMy ) / deltaY;
58 const double bX = ( n * sumPxMx - sumPx * sumMx ) / deltaX;
59 const double bY = ( n * sumPyMy - sumPy * sumMy ) / deltaY;
64 pixelXSize = std::fabs( bX );
65 pixelYSize = std::fabs( bY );
70 const QVector<QgsPointXY> &destinationCoordinates,
75 ( void )sourceCoordinates;
76 ( void )destinationCoordinates;
80 throw QgsNotSupportedException( QObject::tr(
"Calculating a helmert transformation requires a QGIS build based GSL" ) );
82 const int n = destinationCoordinates.size();
85 throw std::domain_error( QObject::tr(
"Fit to a Helmert transform requires at least 2 points." ).toLocal8Bit().constData() );
98 for (
int i = 0; i < n; ++i )
100 A += sourceCoordinates.at( i ).x();
101 B += sourceCoordinates.at( i ).y();
102 C += destinationCoordinates.at( i ).x();
103 D += destinationCoordinates.at( i ).y();
104 E += destinationCoordinates.at( i ).x() * sourceCoordinates.at( i ).x();
105 F += destinationCoordinates.at( i ).y() * sourceCoordinates.at( i ).y();
106 G += std::pow( sourceCoordinates.at( i ).x(), 2 );
107 H += std::pow( sourceCoordinates.at( i ).y(), 2 );
108 I += destinationCoordinates.at( i ).x() * sourceCoordinates.at( i ).y();
109 J += sourceCoordinates.at( i ).x() * destinationCoordinates.at( i ).y();
117 double MData[] = { A, -B, ( double ) n, 0.,
118 B, A, 0., (
double ) n,
123 double bData[] = { C, D, E + F, J - I };
126 gsl_matrix_view M = gsl_matrix_view_array( MData, 4, 4 );
127 const gsl_vector_view b = gsl_vector_view_array( bData, 4 );
128 gsl_vector *x = gsl_vector_alloc( 4 );
129 gsl_permutation *p = gsl_permutation_alloc( 4 );
131 gsl_linalg_LU_decomp( &M.matrix, p, &s );
132 gsl_linalg_LU_solve( &M.matrix, p, &b.vector, x );
133 gsl_permutation_free( p );
135 origin.
setX( gsl_vector_get( x, 2 ) );
136 origin.
setY( gsl_vector_get( x, 3 ) );
137 pixelSize = std::sqrt( std::pow( gsl_vector_get( x, 0 ), 2 ) +
138 std::pow( gsl_vector_get( x, 1 ), 2 ) );
139 rotation = std::atan2( gsl_vector_get( x, 1 ), gsl_vector_get( x, 0 ) );
141 gsl_vector_free( x );
206 double normalizeMatrix[9],
double denormalizeMatrix[9] )
209 double cogX = 0.0, cogY = 0.0;
210 for (
int i = 0; i < coords.size(); i++ )
212 cogX += coords[i].x();
213 cogY += coords[i].y();
215 cogX *= 1.0 / coords.size();
216 cogY *= 1.0 / coords.size();
219 double meanDist = 0.0;
220 for (
int i = 0; i < coords.size(); i++ )
222 const double X = ( coords[i].x() - cogX );
223 const double Y = ( coords[i].y() - cogY );
224 meanDist += std::sqrt( X * X + Y * Y );
226 meanDist *= 1.0 / coords.size();
228 const double OOD = meanDist * M_SQRT1_2;
229 const double D = 1.0 / OOD;
230 normalizedCoords.resize( coords.size() );
231 for (
int i = 0; i < coords.size(); i++ )
233 normalizedCoords[i] =
QgsPointXY( ( coords[i].x() - cogX ) * D, ( coords[i].y() - cogY ) * D );
236 normalizeMatrix[0] = D;
237 normalizeMatrix[1] = 0.0;
238 normalizeMatrix[2] = -cogX * D;
239 normalizeMatrix[3] = 0.0;
240 normalizeMatrix[4] = D;
241 normalizeMatrix[5] = -cogY * D;
242 normalizeMatrix[6] = 0.0;
243 normalizeMatrix[7] = 0.0;
244 normalizeMatrix[8] = 1.0;
246 denormalizeMatrix[0] = OOD;
247 denormalizeMatrix[1] = 0.0;
248 denormalizeMatrix[2] = cogX;
249 denormalizeMatrix[3] = 0.0;
250 denormalizeMatrix[4] = OOD;
251 denormalizeMatrix[5] = cogY;
252 denormalizeMatrix[6] = 0.0;
253 denormalizeMatrix[7] = 0.0;
254 denormalizeMatrix[8] = 1.0;
260 const QVector<QgsPointXY> &destinationCoordinates,
264 ( void )sourceCoordinates;
265 ( void )destinationCoordinates;
267 throw QgsNotSupportedException( QObject::tr(
"Calculating a projective transformation requires a QGIS build based GSL" ) );
269 Q_ASSERT( sourceCoordinates.size() == destinationCoordinates.size() );
271 if ( destinationCoordinates.size() < 4 )
273 throw std::domain_error( QObject::tr(
"Fitting a projective transform requires at least 4 corresponding points." ).toLocal8Bit().constData() );
276 QVector<QgsPointXY> sourceCoordinatesNormalized;
277 QVector<QgsPointXY> destinationCoordinatesNormalized;
279 double normSource[9], denormSource[9];
280 double normDest[9], denormDest[9];
281 normalizeCoordinates( sourceCoordinates, sourceCoordinatesNormalized, normSource, denormSource );
282 normalizeCoordinates( destinationCoordinates, destinationCoordinatesNormalized, normDest, denormDest );
286 const uint m = std::max( 9u, ( uint )destinationCoordinatesNormalized.size() * 2u );
288 gsl_matrix *S = gsl_matrix_alloc( m, n );
290 for (
int i = 0; i < destinationCoordinatesNormalized.size(); i++ )
292 gsl_matrix_set( S, i * 2, 0, sourceCoordinatesNormalized[i].x() );
293 gsl_matrix_set( S, i * 2, 1, sourceCoordinatesNormalized[i].y() );
294 gsl_matrix_set( S, i * 2, 2, 1.0 );
296 gsl_matrix_set( S, i * 2, 3, 0.0 );
297 gsl_matrix_set( S, i * 2, 4, 0.0 );
298 gsl_matrix_set( S, i * 2, 5, 0.0 );
300 gsl_matrix_set( S, i * 2, 6, -destinationCoordinatesNormalized[i].x()*sourceCoordinatesNormalized[i].x() );
301 gsl_matrix_set( S, i * 2, 7, -destinationCoordinatesNormalized[i].x()*sourceCoordinatesNormalized[i].y() );
302 gsl_matrix_set( S, i * 2, 8, -destinationCoordinatesNormalized[i].x() * 1.0 );
304 gsl_matrix_set( S, i * 2 + 1, 0, 0.0 );
305 gsl_matrix_set( S, i * 2 + 1, 1, 0.0 );
306 gsl_matrix_set( S, i * 2 + 1, 2, 0.0 );
308 gsl_matrix_set( S, i * 2 + 1, 3, sourceCoordinatesNormalized[i].x() );
309 gsl_matrix_set( S, i * 2 + 1, 4, sourceCoordinatesNormalized[i].y() );
310 gsl_matrix_set( S, i * 2 + 1, 5, 1.0 );
312 gsl_matrix_set( S, i * 2 + 1, 6, -destinationCoordinatesNormalized[i].y()*sourceCoordinatesNormalized[i].x() );
313 gsl_matrix_set( S, i * 2 + 1, 7, -destinationCoordinatesNormalized[i].y()*sourceCoordinatesNormalized[i].y() );
314 gsl_matrix_set( S, i * 2 + 1, 8, -destinationCoordinatesNormalized[i].y() * 1.0 );
317 if ( destinationCoordinatesNormalized.size() == 4 )
325 for (
int j = 0; j < 9; j++ )
327 gsl_matrix_set( S, 8, j, gsl_matrix_get( S, 7, j ) );
335 gsl_matrix *V = gsl_matrix_alloc( n, n );
336 gsl_vector *singular_values = gsl_vector_alloc( n );
337 gsl_vector *work = gsl_vector_alloc( n );
341 gsl_linalg_SV_decomp( S, V, singular_values, work );
344 for (
unsigned int i = 0; i < n; i++ )
346 H[i] = gsl_matrix_get( V, i, n - 1 );
349 gsl_matrix *prodMatrix = gsl_matrix_alloc( 3, 3 );
351 gsl_matrix_view Hmatrix = gsl_matrix_view_array( H, 3, 3 );
352 const gsl_matrix_view normSourceMatrix = gsl_matrix_view_array( normSource, 3, 3 );
353 const gsl_matrix_view denormDestMatrix = gsl_matrix_view_array( denormDest, 3, 3 );
357 gsl_blas_dgemm( CblasNoTrans, CblasNoTrans, 1.0, &Hmatrix.matrix, &normSourceMatrix.matrix, 0.0, prodMatrix );
358 gsl_blas_dgemm( CblasNoTrans, CblasNoTrans, 1.0, &denormDestMatrix.matrix, prodMatrix, 0.0, &Hmatrix.matrix );
360 gsl_matrix_free( prodMatrix );
361 gsl_matrix_free( S );
362 gsl_matrix_free( V );
363 gsl_vector_free( singular_values );
364 gsl_vector_free( work );