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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 plane2 = normalizePlane(plane1)
%NORMALIZEPLANE Normalize parametric representation of a plane.
%
% PLANE2 = normalizePlane(PLANE1);
% Transforms the plane PLANE1 in the following format:
% [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], where:
% - (X0, Y0, Z0) is a point belonging to the plane
% - (DX1, DY1, DZ1) is a first direction vector
% - (DX2, DY2, DZ2) is a second direction vector
% into another plane, with the same format, but with:
% - (x0 y0 z0) is the closest point of plane to the origin
% - (DX1 DY1 DZ1) has norm equal to 1
% - (DX2 DY2 DZ2) has norm equal to 1 and is orthogonal to (DX1 DY1 DZ1)
%
% See also
% planes3d, createPlane
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-21
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% compute first direction vector
d1 = normalizeVector3d(plane1(:,4:6));
% compute second direction vector
n = normalizeVector3d(planeNormal(plane1));
d2 = -normalizeVector3d(crossProduct3d(d1, n));
% compute origin point of the plane
origins = repmat([0 0 0], [size(plane1, 1) 1]);
p0 = projPointOnPlane(origins, [plane1(:,1:3) d1 d2]);
% create the resulting plane
plane2 = [p0 d1 d2];
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