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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 = linePosition(point, line, varargin)
%LINEPOSITION Position of a point on a line.
%
% POS = linePosition(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 dx dy],
% POINT has the form [x y], and is assumed to belong to line.
%
% POS = linePosition(POINT, LINES);
% If LINES is an array of NL lines, return NL positions, corresponding to
% each line.
%
% POS = linePosition(POINTS, LINE);
% If POINTS is an array of NP points, return NP positions, corresponding
% to each point.
%
% POS = linePosition(POINTS, LINES);
% If POINTS is an array of NP points and LINES is an array of NL lines,
% return an array of [NP NL] position, corresponding to each couple
% point-line.
%
% POS = linePosition(POINTS, LINES, 'diag');
% When POINTS and LINES have the same number of rows, computes positions
% only for couples POINTS(i,:) and LINES(i,:). The result POS is a column
% vector with as many rows as the number of points/lines.
%
%
% Example
% line = createLine([10 30], [30 90]);
% linePosition([20 60], line)
% ans =
% .5
%
% See also
% lines2d, createLine, projPointOnLine, isPointOnLine
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2004-05-25
% Copyright 2004-2023 INRA - TPV URPOI - BIA IMASTE
% if diag is true, we need only to compute position of i-th point with i-th
% line.
diag = ~isempty(varargin) && ischar(varargin{1}) && strcmpi(varargin{1}, 'diag');
if diag
% In the case of 'diag' option, use direct correspondence between
% points and lines
% check input have same size
np = size(point, 1);
nl = size(line, 1);
if np ~= nl
error('matGeom:linePosition', ...
'Using diag option, number of points and lines should be the same');
end
% direction vector of the lines
vx = line(:, 3);
vy = line(:, 4);
% difference of coordinates between point and line origins
dx = point(:, 1) - line(:, 1);
dy = point(:, 2) - line(:, 2);
else
% General case -> return NP-by-NL array
% direction vector of the lines
vx = line(:, 3)';
vy = line(:, 4)';
% difference of coordinates between point and line origins
dx = bsxfun(@minus, point(:, 1), line(:, 1)');
dy = bsxfun(@minus, point(:, 2), line(:, 2)');
end
% squared norm of direction vector, with a check of validity
delta = vx .* vx + vy .* vy;
invalidLine = delta < eps;
delta(invalidLine) = 1;
% compute position of points projected on the line, by using normalised dot
% product (NP-by-NL array)
pos = bsxfun(@rdivide, bsxfun(@times, dx, vx) + bsxfun(@times, dy, vy), delta);
% ensure degenerated edges are correclty processed (consider the first
% vertex is the closest one)
if diag
pos(invalidLine) = 0;
else
pos(:, invalidLine) = 0;
end
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