/*
* 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;
// J2SE and extensions
import java.util.List;
import javax.vecmath.MismatchedSizeException;
/**
* Builds {@linkplain org.opengis.referencing.operation.MathTransform
* MathTransform} setup as Affine transformation from a list of {@linkplain
* MappedPosition MappedPosition}. The calculation uses least square method.
* The Affine transform equation:
* <pre>
* [ x'] [ m00 m01 m02 ] [ x ] [ m00x + m01y + m02 ]
* [ y'] = [ m10 m11 m12 ] [ y ] = [ m10x + m11y + m12 ]
* [ 1 ] [ 0 0 1 ] [ 1 ] [ 1 ]
* x' = m * x </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 0 0 ] [ m00 ]
* [ x'<sub>2</sub> ] [ x<sub>2</sub> y<sub>2</sub> 1 0 0 0 ] [ m01 ]
* [ . ] [ . ] [ m02 ]
* [ . ] [ . ] * [ m10 ]
* [ x'<sub>n</sub> ] = [ x<sub>n</sub> y<sub>n</sub> 1 0 0 0 ] [ m11 ]
* [ y'<sub>1</sub> ] [ 0 0 0 x<sub>1</sub> y<sub>1</sub> 1 ] [ m12 ]
* [ y'<sub>2</sub> ] [ 0 0 0 x<sub>2</sub> y<sub>2</sub> 1 ]
* [ . ] [ . ]
* [ . ] [ . ]
* [ y'<sub>n</sub> ] [ 0 0 0 x<sub>n</sub> y<sub>n</sub> 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 AffineTransformBuilder extends ProjectiveTransformBuilder {
protected AffineTransformBuilder() {
}
/**
* Creates AffineTransformBuilder for the set of properties.
*
* @param vectors list of {@linkplain
* MappedPosition MappedPosition}
*/
public AffineTransformBuilder(List <MappedPosition> vectors)
throws MismatchedSizeException, MismatchedDimensionException,
MismatchedReferenceSystemException {
super.setMappedPositions(vectors);
}
/**
* Returns the minimum number of points required by this builder,
* which is 3.
*
* @return the minimum number of points required by this builder, which is
* 3.
*/
public int getMinimumPointCount() {
return 3;
}
/**
* Returns the matrix for Projective transformation setup as
* Affine. The M matrix looks like this:
* <pre>
* [ m00 m01 m02 ]
* [ m10 m11 m12 ]
* [ 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[3], param[4], param[5] };
double[] m2 = { 0, 0, 1 };
M.setRow(0, m0);
M.setRow(1, m1);
M.setRow(2, m2);
return M;
}
protected void fillAMatrix() {
super.A = new GeneralMatrix(2 * getSourcePoints().length, 6);
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, 0, 0
});
}
for (int j = numRow / 2; j < numRow; j++) {
A.setRow(j,
new double[] {0, 0, 0,
getSourcePoints()[j - (numRow / 2)].getCoordinate()[0],
getSourcePoints()[j - (numRow / 2)].getCoordinate()[1], 1
});
}
}
}