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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 pos = linePosition3d(point, line)
%LINEPOSITION3D Return the position of a 3D point projected on a 3D line.
%
% T = linePosition3d(POINT, LINE)
% Computes position of point POINT on the line LINE, relative to origin
% point and direction vector of the line.
% LINE has the form [x0 y0 z0 dx dy dy],
% POINT has the form [x y z], and is assumed to belong to line.
% The result T is the value such that POINT = LINE(1:3) + T * LINE(4:6).
% If POINT does not belong to LINE, the position of its orthogonal
% projection is computed instead.
%
% T = linePosition3d(POINT, LINES)
% If LINES is an array of NL lines, return NL positions, corresponding to
% each line.
%
% T = linePosition3d(POINTS, LINE)
% If POINTS is an array of NP points, return NP positions, corresponding
% to each point.
%
% See also
% lines3d, createLine3d, distancePointLine3d, projPointOnLine3d
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-17
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% size of input arguments
np = size(point, 1);
nl = size(line, 1);
if np == 1 || nl == 1 || np == nl
% standard case where result is either scalar or vector
% vector from line origin to point
dp = bsxfun(@minus, point, line(:,1:3));
% direction vector of the line
vl = line(:, 4:6);
% precompute and check validity of denominator
denom = sum(vl.^2, 2);
invalidLine = denom < eps;
denom(invalidLine) = 1;
% compute position using dot product normalized with norm of line vector.
pos = bsxfun(@rdivide, sum(bsxfun(@times, dp, vl), 2), denom);
% position on a degenerated line is set to 0
pos(invalidLine) = 0;
else
% reshape input
point = reshape(point, [np 1 3]);
line = reshape(line, [1 nl 6]);
% vector from line origin to point
dp = bsxfun(@minus, point, line(:,:,1:3));
% direction vector of the line
vl = line(:, :, 4:6);
% precompute and check validity of denominator
denom = sum(vl.^2, 3);
invalidLine = denom < eps;
denom(invalidLine) = 1;
% compute position using dot product normalized with norm of line vector.
pos = bsxfun(@rdivide, sum(bsxfun(@times, dp, vl), 3), denom);
% position on a degenerated line is set to 0
pos(invalidLine) = 0;
end
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