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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 = projPointOnLine(point, line)
%PROJPOINTONLINE Project a point orthogonally onto a line.
%
% PT2 = projPointOnLine(PT, LINE).
% Computes the (orthogonal) projection of point PT onto the line LINE.
%
% Function works also for multiple points and lines. In this case, it
% returns multiple points.
% Point PT1 is a [N*2] array, and LINE is a [N*4] array (see createLine
% for details). Result PT2 is a [N*2] array, containing coordinates of
% orthogonal projections of PT1 onto lines LINE.
%
% Example
% line = [0 2 2 1];
% projPointOnLine([3 1], line)
% ans =
% 2 3
%
% See also
% lines2d, points2d, isPointOnLine, linePosition, projPointOnEllipse
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-07-04
% Copyright 2005-2023 INRAE - BIA Research Unit - BIBS Platform (Nantes)
% parse input arguments
p = inputParser;
addRequired(p, 'point', @(x)validateattributes(x,{'numeric'},...
{'size',[nan, 2],'nonnan','real','finite'}))
addRequired(p, 'line', @(x)validateattributes(x,{'numeric'},...
{'size',[nan, 4],'nonnan','real','finite'}))
parse(p, point, line)
% direction vector of the line
vx = line(:, 3);
vy = line(:, 4);
% difference of point with line origin
dx = point(:,1) - line(:,1);
dy = point(:,2) - line(:,2);
% Position of projection on line, using dot product
tp = (dx .* vx + dy .* vy ) ./ (vx .* vx + vy .* vy);
% convert position on line to cartesian coordinates
point = [line(:,1) + tp .* vx, line(:,2) + tp .* vy];
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