polynomialTransform2d

POLYNOMIALTRANSFORM2D Apply a polynomial transform to a set of points.

   RES = polynomialTransform2d(PTS, COEFFS)
   Transforms the input points PTS given as a N-by-2 array of coordinates
   using the polynomial transform defined by PARAMS.
   PARAMS given as [a0 b0 a1 b1 ... an bn]

   Example
   coeffs = [0 0  1 0  0 1   0.1 0  0 0  0 0.1];
       %     cte   x    y     x^2   x*y   y^2
   pts = rand(200, 2) * 2 - 1;
   pts2 = polynomialTransform2d(pts, coeffs);
   figure; hold on;
   drawPoint(pts);
   drawPoint(pts2, 'g');

   See also
     transformPoint, fitPolynomialTransform2d

0001 function res = polynomialTransform2d(pts, coeffs)
0002 %POLYNOMIALTRANSFORM2D Apply a polynomial transform to a set of points.
0003 %
0004 %   RES = polynomialTransform2d(PTS, COEFFS)
0005 %   Transforms the input points PTS given as a N-by-2 array of coordinates
0006 %   using the polynomial transform defined by PARAMS.
0007 %   PARAMS given as [a0 b0 a1 b1 ... an bn]
0008 %
0009 %   Example
0010 %   coeffs = [0 0  1 0  0 1   0.1 0  0 0  0 0.1];
0011 %       %     cte   x    y     x^2   x*y   y^2
0012 %   pts = rand(200, 2) * 2 - 1;
0013 %   pts2 = polynomialTransform2d(pts, coeffs);
0014 %   figure; hold on;
0015 %   drawPoint(pts);
0016 %   drawPoint(pts2, 'g');
0017 %
0018 %   See also
0019 %     transformPoint, fitPolynomialTransform2d
0020 
0021 % ------
0022 % Author: David Legland
0023 % e-mail: david.legland@grignon.inra.fr
0024 % Created: 2013-09-04,    using Matlab 7.9.0.529 (R2009b)
0025 % Copyright 2013 INRA - Cepia Software Platform.
0026 
0027 x = pts(:,1);
0028 y = pts(:,2);
0029 nPoints = length(x);
0030 
0031 
0032 xCoeffs = coeffs(1:2:end);
0033 yCoeffs = coeffs(2:2:end);
0034 nCoeffs = length(xCoeffs);
0035 
0036 % allocate memory for result
0037 x2 = zeros(nPoints, 1);
0038 y2 = zeros(nPoints, 1);
0039 
0040 % degree from coefficient number
0041 degree = sqrt(9/4 - 4*(1 - nCoeffs)/2) - 1.5;
0042 
0043 % iterate over degrees
0044 iCoeff = 0;
0045 for iDegree = 0:degree
0046     
0047     % iterate over binomial coefficients of a given degree
0048     for k = 0:iDegree
0049         iCoeff = iCoeff + 1;
0050         tmp = power(x, iDegree-k) .* power(y, k);
0051         x2 = x2 + xCoeffs(iCoeff) .* tmp;
0052         y2 = y2 + yCoeffs(iCoeff) .* tmp;
0053     end
0054 end
0055 
0056 res = [x2 y2];