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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 [dist, t] = distancePointEdge3d(point, edge)
%DISTANCEPOINTEDGE3D Minimum distance between a 3D point and a 3D edge.
%
% DIST = distancePointEdge3d(POINT, EDGE);
% Return the euclidean distance between edge EDGE and point POINT.
% EDGE has the form: [x1 y1 z1 x2 y2 z2], and POINT is [x y z].
%
% If EDGE is N-by-6 array, result is N-by-1 array computed for each edge.
% If POINT is a N-by-3 array, the result is computed for each point.
% If both POINT and EDGE are array, they must have the same number of
% rows, and the result is computed for each couple point(i,:);edge(i,:).
%
% [DIST POS] = distancePointEdge3d(POINT, EDGE);
% Also returns the position of closest point on the edge. POS is
% comprised between 0 (first point) and 1 (last point).
%
% See also
% edges3d, points3d, distancePoints3d, distancePointLine3d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-04-07
% Copyright 2004-2023 INRA - CEPIA URPOI - MIA MathCell
% direction vector of each edge
vl = edge(:, 4:6) - edge(:, 1:3);
% compute position of points projected on the supporting line
% (Size of t is the max number of edges or points)
t = linePosition3d(point, [edge(:,1:3) vl]);
% change position to ensure projected point is located on the edge
t(t < 0) = 0;
t(t > 1) = 1;
% difference of coordinates between projected point and base point
p0 = bsxfun(@plus, edge(:,1:3), [t .* vl(:,1) t .* vl(:,2) t .* vl(:,3)]);
p0 = bsxfun(@minus, point, p0);
% compute distance between point and its projection on the edge
dist = sqrt(sum(p0 .* p0, 2));
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