/*
* GeoTools - The Open Source Java GIS Toolkit
* http://geotools.org
*
* (C) 2002-2008, Open Source Geospatial Foundation (OSGeo)
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation;
* version 2.1 of the License.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*/
package org.geotools.referencing.operation.builder;
import org.geotools.referencing.operation.matrix.GeneralMatrix;
import org.opengis.geometry.MismatchedDimensionException;
import org.opengis.geometry.MismatchedReferenceSystemException;
import java.util.List;
// J2SE and extensions
import javax.vecmath.MismatchedSizeException;
/**
* Builds {@linkplain org.opengis.referencing.operation.MathTransform
* MathTransform} setup as Similar transformation from a list of {@linkplain
* org.geotools.referencing.operation.builder.MappedPosition MappedPosition}.
* The The calculation uses least square method. The similar transform
* equation:<pre>
* [ x'] [ a -b Tx ] [ x ] [ a*x - b*y + Tx ]
* [ y'] = [ b a Ty ] [ y ] = [ b*x + a*y + Ty ] </pre>In the case
* that we have more identical points we can write it like this (in Matrix):
* <pre>
* [ x'<sub>1</sub> ] [ x<sub>1</sub> -y<sub>1</sub> 1 0 ] [ a ]
* [ x'<sub>2</sub> ] [ x<sub>2</sub> -y<sub>2</sub> 1 0 ] [ b ]
* [ . ] [ . ] [ Tx ]
* [ . ] [ . ] * [ Ty ]
* [ x'<sub>n</sub> ] = [ x<sub>n</sub> y<sub>n</sub> 1 0 ]
* [ y'<sub>1</sub> ] [ y<sub>1</sub> x<sub>1</sub> 0 1 ]
* [ y'<sub>2</sub> ] [ y<sub>2</sub> x<sub>2</sub> 0 1 ]
* [ . ] [ . ]
* [ . ] [ . ]
* [ y'<sub>n</sub> ] [ y<sub>n</sub> x<sub>n</sub> 0 1 ]
* x' = A*m </pre>Using the least square method we get this result:
* <pre><blockquote>
* m = (A<sup>T</sup>A)<sup>-1</sup> A<sup>T</sup>x' </blockquote> </pre>
*
* @since 2.4
*
* @source $URL$
* @version $Id$
* @author Jan Jezek
*/
public class SimilarTransformBuilder extends ProjectiveTransformBuilder {
/**
* Creates SimilarTransformBuilder for the set of properties. The {@linkplain java.util.List List} of {@linkplain
* org.geotools.referencing.operation.builder.MappedPosition MappedPosition} is expected.
*
* @param vectors list of {@linkplain
* org.geotools.referencing.operation.builder.MappedPosition MappedPosition}
*/
public SimilarTransformBuilder(List <MappedPosition> vectors)
throws MismatchedSizeException, MismatchedDimensionException,
MismatchedReferenceSystemException {
super.setMappedPositions(vectors);
}
protected void fillAMatrix() {
super.A = new GeneralMatrix(2 * getSourcePoints().length, 4);
int numRow = getSourcePoints().length * 2;
// Creates X matrix
for (int j = 0; j < (numRow / 2); j++) {
A.setRow(j,
new double[] {
getSourcePoints()[j].getCoordinate()[0],
-getSourcePoints()[j].getCoordinate()[1], 1, 0
});
}
for (int j = numRow / 2; j < numRow; j++) {
A.setRow(j,
new double[] {
getSourcePoints()[j - (numRow / 2)].getCoordinate()[1],
getSourcePoints()[j - (numRow / 2)].getCoordinate()[0], 0,
1
});
}
}
/**
* Returns the minimum number of points required by this builder,
* which is 2.
*
* @return Returns the minimum number of points required by this builder,
* which is 2.
*/
public int getMinimumPointCount() {
return 2;
}
/**
* Returns the matrix for Projective transformation setup as
* Affine. The M matrix looks like this:
* <pre>
* [ a -b Tx ]
* [ b a Ty ]
* [ 0 0 1 ]
* </pre>
*
* @return Matrix M.
*/
protected GeneralMatrix getProjectiveMatrix() {
GeneralMatrix M = new GeneralMatrix(3, 3);
double[] param = calculateLSM();
double[] m0 = { param[0], -param[1], param[2] };
double[] m1 = { param[1], param[0], param[3] };
double[] m2 = { 0, 0, 1 };
M.setRow(0, m0);
M.setRow(1, m1);
M.setRow(2, m2);
return M;
}
}