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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 = intersectEdgePlane(edge, plane, varargin)
%INTERSECTEDGEPLANE Return intersection point between a plane and a edge.
%
% PT = intersectEdgePlane(edge, PLANE) return the intersection point of
% the given edge and the given plane.
% PLANE : [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
% edge : [x1 y1 z1 x2 y2 z2]
% PT : [xi yi zi]
% If EDGE and PLANE are parallel, return [NaN NaN NaN].
% If EDGE (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.
%
% Example:
% edge = [5 5 -1 5 5 1];
% plane = [0 0 0 1 0 0 0 1 0];
% intersectEdgePlane(edge, plane) % should return [5 5 0].
% ans =
% 5 5 0
%
% See also
% planes3d, intersectLinePlane, createLine3d, createPlane
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2007-04-24, from intersectLinePlane
% Copyright 2007-2023 INRA - TPV URPOI - BIA IMASTE
% extract tolerance for determination of parallel edges and planes
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
% number of planes and edges
np = size(plane, 1);
ne = size(edge, 1);
% unify sizes of data
if np ~= ne
if ne == 1
% one edge and many planes
edge = edge(ones(np, 1), :);
elseif np == 1
% one plane possible many edges
plane = plane(ones(ne, 1), :);
else
% N planes and M edges, not allowed for now.
error('Should have the same number of planes and edges');
end
end
% initialize empty arrays
point = zeros(size(plane, 1), 3);
t = zeros(size(plane,1),3);
% plane normal
n = cross(plane(:,4:6), plane(:,7:9), 2);
% create line supporting edge
line = createLine3d(edge(:,1:3), edge(:,4:6));
% get indices of edge and plane which are parallel
par = abs(dot(n, line(:,4:6), 2)) < tol;
point(par,:) = NaN;
t(par) = NaN;
% difference between origins of plane and edge
dp = plane(:, 1:3) - line(:, 1:3);
% relative position of intersection on line
%t = dot(n(~par,:), dp(~par,:), 2)./dot(n(~par,:), line(~par,4:6), 2);
t(~par) = dot(n(~par,:), dp(~par,:), 2) ./ dot(n(~par,:), line(~par,4:6), 2);
% compute coord of intersection point
%point(~par, :) = line(~par,1:3) + repmat(t,1,3).*line(~par,4:6);
point(~par, :) = line(~par,1:3) + repmat(t(~par),1,3) .* line(~par,4:6);
% set points outside of edge to [NaN NaN NaN]
point(t<0, :) = NaN;
point(t>1, :) = NaN;
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