import org.apache.commons.math.linear.*;
import java.awt.geom.*;

public void insertPoint2DInMatrix(RealMatrix m, Point2D.Double pt, int row) {
	// Set row to [x,y,1]:
	m.setEntry(row, 0, pt.x);
	m.setEntry(row, 1, pt.y);
	m.setEntry(row, 2, 1);
}

public AffineTransform generateAffineTransformFromPointPairs(Map pointPairs) {
	u = new Array2DRowRealMatrix(pointPairs.size(),3);
	v = new Array2DRowRealMatrix(pointPairs.size(),3);

	// Create u (source) and v (dest) matrices whose row vectors
	// are [x,y,1] for each Point2D.Double:

	int i = 0;
	for (Map.Entry pair:pointPairs.entrySet()) {
		uPt = pair.getKey();
		vPt = pair.getValue();
	
		insertPoint2DInMatrix(u,uPt,i);
		insertPoint2DInMatrix(v,vPt,i);
	
		i++;
	}

	// Find the 3x3 linear least squares solution to u*m'=v
	// (the last row should be [0,0,1]):
	solver = (new QRDecompositionImpl(u)).getSolver();
	double[][] m = solver.solve(v).transpose().getData();

	// Create an AffineTransform object from the elements of m
	// (the last row is omitted as specified in AffineTransform class):
	return new AffineTransform(m[0][0], m[1][0], m[0][1], m[1][1], m[0][2], m[1][2]);
}

public void runAffineTest() {

	pointPairs = new HashMap();


	// Create sample src and dest points:
	pointPairs.put(new Point2D.Double(1,1),new Point2D.Double(18,2));
	pointPairs.put(new Point2D.Double(1,9),new Point2D.Double(2,2));
	pointPairs.put(new Point2D.Double(9,9),new Point2D.Double(2,18));
	pointPairs.put(new Point2D.Double(9,1),new Point2D.Double(18,18));

	// Run the computation to be tested:
	affineTransform = generateAffineTransformFromPointPairs(pointPairs);

	// Print input and output:
	print(pointPairs);
	print(affineTransform);

	// Check that affineTransform works correctly:
	for (Map.Entry pair:pointPairs.entrySet()) {
		uPt = pair.getKey();
		vPt = pair.getValue();
		result = new Point2D.Double();	
		affineTransform.transform(uPt,result);
		print(uPt+"->"+result+" residual: "+vPt.distance(result));
	
		i++;
	}
}

update();