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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 point = intersectLinePlane(line, plane, varargin)
%INTERSECTLINEPLANE Intersection point between a 3D line and a plane.
%
% PT = intersectLinePlane(LINE, PLANE)
% Returns the intersection point of the given line and the given plane.
% LINE: [x0 y0 z0 dx dy dz]
% PLANE: [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
% PT: [xi yi zi]
% If LINE and PLANE are parallel, return [NaN NaN NaN].
% If LINE (or PLANE) is a matrix with 6 (or 9) columns and N rows, result
% is an array of points with N rows and 3 columns.
%
% PT = intersectLinePlane(LINE, PLANE, TOL)
% Specifies the tolerance factor to test if a line is parallel to a
% plane. Default is 1e-14.
%
% Example
% % define horizontal plane through origin
% plane = [0 0 0 1 0 0 0 1 0];
% % intersection with a vertical line
% line = [2 3 4 0 0 1];
% intersectLinePlane(line, plane)
% ans =
% 2 3 0
% % intersection with a line "parallel" to plane
% line = [2 3 4 1 2 0];
% intersectLinePlane(line, plane)
% ans =
% NaN NaN NaN
%
% See also
% lines3d, planes3d, points3d, clipLine3d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-17
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% extract tolerance if needed
tol = 1e-14;
if nargin > 2
tol = varargin{1};
end
% unify sizes of data
nLines = size(line, 1);
nPlanes = size(plane, 1);
% N planes and M lines not allowed
if nLines ~= nPlanes && min(nLines, nPlanes) > 1
error('MatGeom:geom3d:intersectLinePlane', ...
'Input must have same number of rows, or one must be 1');
end
% plane normal
n = crossProduct3d(plane(:,4:6), plane(:,7:9));
% difference between origins of plane and line
dp = bsxfun(@minus, plane(:, 1:3), line(:, 1:3));
% dot product of line direction with plane normal
denom = sum(bsxfun(@times, n, line(:,4:6)), 2);
% relative position of intersection point on line (can be inf in case of a
% line parallel to the plane)
t = sum(bsxfun(@times, n, dp),2) ./ denom;
% compute coord of intersection point
point = bsxfun(@plus, line(:,1:3), bsxfun(@times, [t t t], line(:,4:6)));
% set indices of line and plane which are parallel to NaN
par = abs(denom) < tol;
point(par,:) = NaN;
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