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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 bis = planesBisector(plane1, plane2)
%PLANESBISECTOR Bisector plane between two other planes.
%
% BIS = planesBisector(PLANE1, PLANE2);
% Returns the planes that contains the intersection line between PLANE1
% and PLANE2 and that bisect the dihedral angle of PLANE1 and PLANE2.
% Note that computing the bisector of PLANE2 and PLANE1 (in that order)
% returns the same plane but with opposite orientation.
%
% Example
% % Draw two planes together with their bisector
% pl1 = createPlane([3 4 5], [1 2 3]);
% pl2 = createPlane([3 4 5], [2 -3 4]);
% % compute bisector
% bis = planesBisector(pl1, pl2);
% % setup display
% figure; hold on; axis([0 10 0 10 0 10]);
% set(gcf, 'renderer', 'opengl')
% view(3);
% % draw the planes
% drawPlane3d(pl1, 'g');
% drawPlane3d(pl2, 'g');
% drawPlane3d(bis, 'b');
%
% See also
% planes3d, dihedralAngle, intersectPlanes
%
% ------
% Author: Ben X. Kang
% E-mail: N/A
% Created: ?
% Copyright ?
% Let the two planes be defined by equations
%
% a1*x + b1*y + c1*z + d1 = 0
%
% and
%
% a2*x + b2*y + c2*z + d2 = 0
%
% in which vectors [a1,b1,c1] and [a2,b2,c2] are normalized to be of unit
% length (a^2+b^2+c^2 = 1). Then
%
% (a1+a2)*x + (b1+b2)*y + (c1+c2)*z + (d1+d2) = 0
%
% is the equation of the desired plane which bisects the dihedral angle
% between the two planes. These coefficients cannot be all zero because
% the two given planes are not parallel.
%
% Notice that there is a second solution to this problem
%
% (a1-a2)*x + (b1-b2)*y + (c1-c2)*z + (d1-d2) = 0
%
% which also is a valid plane and orthogonal to the first solution. One of
% these planes bisects the acute dihedral angle, and the other the
% supplementary obtuse dihedral angle, between the two given planes.
p1 = plane1(1:3); % a point on the plane
n1 = planeNormal(plane1); % the normal of the plane
p2 = plane2(1:3);
n2 = planeNormal(plane2);
if ~isequal(p1(1:3), p2(1:3))
L = intersectPlanes(plane1, plane2); % intersection of the given two planes
pt = L(1:3); % a point on the line intersection
else
pt = p1(1:3);
end
% use column-wise vector
bis = createPlane(pt, n1 - n2);
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