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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 line = intersectPlanes(plane1, plane2, varargin)
%INTERSECTPLANES Return intersection line between 2 planes in space.
%
% LINE = intersectPlanes(PLANE1, PLANE2)
% Returns the straight line belonging to both planes.
% PLANE: [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
% LINE: [x0 y0 z0 dx dy dz]
% In case of parallel planes, returns line with NaN values.
%
% LINE = intersectPlanes(PLANE1, PLANE2, TOL)
% Also specifies the tolerance for detecting parallel planes.
%
% See also
% planes3d, lines3d, intersectLinePlane
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-17
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
% plane normal
n1 = normalizeVector3d(cross(plane1(:,4:6), plane1(:, 7:9), 2));
n2 = normalizeVector3d(cross(plane2(:,4:6), plane2(:, 7:9), 2));
% test if planes are parallel
if abs(cross(n1, n2, 2)) < tol
line = [NaN NaN NaN NaN NaN NaN];
return;
end
% Uses Hessian form, ie : N.p = d
% I this case, d can be found as : -N.p0, when N is normalized
d1 = dot(n1, plane1(:,1:3), 2);
d2 = dot(n2, plane2(:,1:3), 2);
% compute dot products
dot1 = dot(n1, n1, 2);
dot2 = dot(n2, n2, 2);
dot12 = dot(n1, n2, 2);
% intermediate computations
det = dot1*dot2 - dot12*dot12;
c1 = (d1*dot2 - d2*dot12)./det;
c2 = (d2*dot1 - d1*dot12)./det;
% compute line origin and direction
p0 = c1*n1 + c2*n2;
dp = cross(n1, n2, 2);
line = [p0 dp];
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