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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 transfo = createBasisTransform(source, target)
%CREATEBASISTRANSFORM Compute matrix for transforming a basis into another basis.
%
% TRANSFO = createBasisTransform(SOURCE, TARGET)
% Both SOURCE and TARGET represent basis, in the following form:
% [x0 y0 ex1 ey1 ex2 ey2]
% [y0 y0] is the origin of the basis, [ex1 ey1] is the first direction
% vector, and [ex2 ey2] is the second direction vector.
%
% The result TRANSFO is a 3-by-3 matrix such that a point expressed with
% coordinates of the first basis will be represented by new coordinates
% P2 = transformPoint(P1, TRANSFO) in the target basis.
%
% TRANSFO = createBasisTransform(TARGET)
% Assumes the source is the standard (Oij) basis, with origin at (0,0),
% first direction vector equal to (1,0) and second direction vector
% equal to (0,1).
%
%
% Example
% % define source and target bases
% src = [ 0 0 1 0 0 1];
% tgt = [20 0 .5 .5 -.5 .5];
% trans = createBasisTransform(src, tgt);
% % create a polygon in source basis
% poly = [10 10;30 10; 30 20; 20 20;20 40; 10 40];
% figure;
% subplot(121); drawPolygon(poly, 'b'); axis equal; axis([-10 50 -10 50]);
% hold on; drawLine([0 0 1 0], 'k'); drawLine([0 0 0 1], 'k');
% drawLine([20 0 1 1], 'r'); drawLine([20 0 -1 1], 'r');
% t = -1:5; plot(t*5+20, t*5, 'r.'); plot(-t*5+20, t*5, 'r.');
% % transform the polygon in target basis
% poly2 = transformPoint(poly, trans);
% subplot(122); drawPolygon(poly2, 'b'); axis equal; axis([-10 50 -10 50]);
% hold on; drawLine([0 0 1 0], 'r'); drawLine([0 0 0 1], 'r');
% t = -1:5; plot(t*10, zeros(size(t)), 'r.'); plot(zeros(size(t)), t*10, 'r.');
%
% See also
% transforms2d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2010-12-03, using Matlab 7.9.0.529 (R2009b)
% Copyright 2010-2023 INRA - Cepia Software Platform
% init basis transform to identity
t1 = eye(3);
t2 = eye(3);
if nargin == 2
% from source to reference basis
t1(1:2, 1) = source(3:4);
t1(1:2, 2) = source(5:6);
t1(1:2, 3) = source(1:2);
else
% if only one input, use first input as target basis, and leave the
% first matrix to identity
target = source;
end
% from reference to target basis
t2(1:2, 1) = target(3:4);
t2(1:2, 2) = target(5:6);
t2(1:2, 3) = target(1:2);
% compute transform matrix
transfo = zeros(3, 3);
maxSz = 1;
for i = 1:maxSz
% coordinate of three reference points in source basis
po = t1(1:2, 3, i)';
px = po + t1(1:2, 1, i)';
py = po + t1(1:2, 2, i)';
% express coordinates of reference points in the new basis
t2i = inv(t2(:,:,i));
pot = transformPoint(po, t2i);
pxt = transformPoint(px, t2i);
pyt = transformPoint(py, t2i);
% compute direction vectors in new basis
vx = pxt - pot;
vy = pyt - pot;
% concatenate result in a 3-by-3 affine transform matrix
transfo(:,:,i) = [vx' vy' pot' ; 0 0 1];
end
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