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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function res = polynomialTransform2d(pts, coeffs)
%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
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2013-09-04, using Matlab 7.9.0.529 (R2009b)
% Copyright 2013-2023 INRA - Cepia Software Platform
x = pts(:,1);
y = pts(:,2);
nPoints = length(x);
xCoeffs = coeffs(1:2:end);
yCoeffs = coeffs(2:2:end);
nCoeffs = length(xCoeffs);
% allocate memory for result
x2 = zeros(nPoints, 1);
y2 = zeros(nPoints, 1);
% degree from coefficient number
degree = sqrt(9/4 - 4*(1 - nCoeffs)/2) - 1.5;
% iterate over degrees
iCoeff = 0;
for iDegree = 0:degree
% iterate over binomial coefficients of a given degree
for k = 0:iDegree
iCoeff = iCoeff + 1;
tmp = power(x, iDegree-k) .* power(y, k);
x2 = x2 + xCoeffs(iCoeff) .* tmp;
y2 = y2 + yCoeffs(iCoeff) .* tmp;
end
end
res = [x2 y2];
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