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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 = createBasisTransform3d(source, target)
%CREATEBASISTRANSFORM3D Compute matrix for transforming a basis into another basis.
%
% TRANSFO = createBasisTransform3d(SOURCE, TARGET) will create a 4-by-4
% transformation matrix representing the transformation from SOURCE basis
% to TARGET basis.
% SOURCE and TARGET are either standard 1-by-9 geom3d PLANE
% representations of the form: [x0 y0 z0 ex1 ey1 ez1 ex2 ey2 ez2]
% OR
% SOURCE and TARGET may be any string such as 'global' or 'g' in which
% case they represent the global plane [0 0 0 1 0 0 0 1 0].
%
% The resulting TRANSFO matrix is such that a point expressed with
% coordinates of the first basis will be represented by new coordinates
% P2 = transformPoint3d(P1, TRANSFO) in the target basis.
%
% Either (or both) SOURCE or TARGET may be an N-by-9 set of N planes. In
% that case, TRANSFO will be a 4-by-4-by-N array of N transformation
% matrices.
%
% Example:
% % Calculate local plane coords. of a point given in global coords.
% plane = [10 10 10 1 0 0 0 1 0];
% transfo = createBasisTransform3d('global', plane);
% PT_IN_PLANE = transformPoint3d([3 8 2], transfo)
% PT_IN_PLANE =
% 13 18 12
%
% See also
% transforms3d, transformPoint3d, planePosition, createBasisTransform
% ------
% 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
% size of input arguments
srcSz = size(source, 1);
tgtSz = size(target, 1);
maxSz = max(srcSz, tgtSz);
% check case of multiple inputs
if maxSz > 1
[t1, t2] = deal( bsxfun(@times, eye(4), ones(1,1,maxSz)) );
if srcSz > 1
source = permute(source, [3 2 1]);
end
if tgtSz > 1
target = permute(target, [3 2 1]);
end
else
[t1, t2] = deal(eye(4));
end
% Place source and target planes into t1 and t2 t-form matrices. If either
% input is non-numeric it is assumed to mean 'global', or identity t-form.
if isnumeric(source)
if maxSz > 1 && srcSz == 1
source = bsxfun(@times, source, ones(1,1,maxSz));
end
t1(1:3, 1, :) = source(1, 4:6, :);
t1(1:3, 2, :) = source(1, 7:9, :);
t1(1:3, 3, :) = crossProduct3d(source(1,4:6,:), source(1,7:9,:));
t1(1:3, 4, :) = source(1, 1:3, :);
end
if isnumeric(target)
if maxSz > 1 && tgtSz == 1
target = bsxfun(@times, target, ones(1,1,maxSz));
end
t2(1:3, 1, :) = target(1, 4:6, :);
t2(1:3, 2, :) = target(1, 7:9, :);
t2(1:3, 3, :) = crossProduct3d(target(1,4:6,:), target(1,7:9,:));
t2(1:3, 4, :) = target(1, 1:3, :);
end
% compute transform matrix
transfo = zeros(4, 4, maxSz);
for i = 1:maxSz
% coordinate of four reference points in source basis
po = t1(1:3, 4, i)';
px = po + t1(1:3, 1, i)';
py = po + t1(1:3, 2, i)';
pz = po + t1(1:3, 3, i)';
% express coordinates of reference points in the new basis
t2i = inv(t2(:,:,i));
pot = transformPoint3d(po, t2i);
pxt = transformPoint3d(px, t2i);
pyt = transformPoint3d(py, t2i);
pzt = transformPoint3d(pz, t2i);
% compute direction vectors in new basis
vx = pxt - pot;
vy = pyt - pot;
vz = pzt - pot;
% concatenate result in a 4-by-4 affine transform matrix
transfo(:,:,i) = [vx' vy' vz' pot' ; 0 0 0 1];
end
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