Compute the affine transform that best register two point sets.

   TRANSFO = fitAffineTransform2d(REF, SRC)
   Returns the affine transform matrix that minimizes the distance between
   the reference point set REF and the point set SRC after transformation.
   Both REF and SRC must by N-by-2 arrays with the same number of rows,
   and the points must be in correspondence.
   The function minimizes the sum of the squared distances:
   CRIT = sum(distancePoints(REF, transformPoint(PTS, TRANSFO)).^2);

   Example
     % computes the transform the register two ellipses
     % create the reference poitn set
     elli = [50 50 40 20 30];
     poly = resamplePolygonByLength(ellipseToPolygon(elli, 200), 5);
     figure; axis equal; axis([0 100 0 100]); hold on;
     drawPoint(poly, 'kx')
     % create the point set to fit on the reference
     trans0 = createRotation([20 60], -pi/8);
     poly2 = transformPoint(poly, trans0);
     poly2 = poly2 + randn(size(poly)) * 2;
     drawPoint(poly2, 'b+');
     % compute the transform that project poly2 onto poly.
     transfo = fitAffineTransform2d(poly, poly2);
     poly2t = transformPoint(poly2, transfo);
     drawPoint(poly2t, 'mo')
     legend('Reference', 'Initial', 'Transformed');

   See also
     transforms2d, transformPoint, transformVector,
     fitPolynomialTransform2d, registerICP, fitAffineTransform3d

Package: matgeom