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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
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##
## 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
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## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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##
## 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 = intersectLines(line1, line2, varargin)
%INTERSECTLINES Return all intersection points of N lines in 2D.
%
% PT = intersectLines(L1, L2);
% returns the intersection point of lines L1 and L2. L1 and L2 are 1-by-4
% row arrays, containing parametric representation of each line (in the
% form [x0 y0 dx dy], see 'createLine' for details).
%
% In case of colinear lines, returns [Inf Inf].
% In case of parallel but not colinear lines, returns [NaN NaN].
%
% If each input is [N*4] array, the result is a [N*2] array containing
% intersections of each couple of lines.
% If one of the input has N rows and the other 1 row, the result is a
% [N*2] array.
%
% PT = intersectLines(L1, L2, EPS);
% Specifies the tolerance for detecting parallel lines. Default is 1e-14.
%
% Example
% line1 = createLine([0 0], [10 10]);
% line2 = createLine([0 10], [10 0]);
% point = intersectLines(line1, line2)
% point =
% 5 5
%
% See also
% lines2d, edges2d, intersectEdges, intersectLineEdge
% intersectLineCircle
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2003-10-31
% Copyright 2003-2023 INRA - TPV URPOI - BIA IMASTE
%% Process input arguments
% extract tolerance
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
% check size of each input
N1 = size(line1, 1);
N2 = size(line2, 1);
N = max(N1, N2);
if N1 ~= N2 && N1*N2 ~= N
error('matGeom:IntersectLines:IllegalArgument', ...
'The two input arguments must have same number of lines');
end
%% Check parallel and colinear lines
% coordinate differences of origin points
dx = bsxfun(@minus, line2(:,1), line1(:,1));
dy = bsxfun(@minus, line2(:,2), line1(:,2));
% indices of parallel lines
denom = line1(:,3) .* line2(:,4) - line2(:,3) .* line1(:,4);
par = abs(denom) < tol;
% indices of colinear lines
col = abs(dx .* line1(:,4) - dy .* line1(:,3)) < tol & par ;
% initialize result array
x0 = zeros(N, 1);
y0 = zeros(N, 1);
% initialize result for parallel lines
x0(col) = Inf;
y0(col) = Inf;
x0(par & ~col) = NaN;
y0(par & ~col) = NaN;
% in case all line couples are parallel, return
if all(par)
point = [x0 y0];
return;
end
%% Extract coordinates of itnersecting lines
% indices of intersecting lines
inds = ~par;
% extract base coordinates of first lines
if N1 > 1
line1 = line1(inds,:);
end
x1 = line1(:,1);
y1 = line1(:,2);
dx1 = line1(:,3);
dy1 = line1(:,4);
% extract base coordinates of second lines
if N2 > 1
line2 = line2(inds,:);
end
x2 = line2(:,1);
y2 = line2(:,2);
dx2 = line2(:,3);
dy2 = line2(:,4);
% re-compute coordinate differences of origin points
dx = bsxfun(@minus, line2(:,1), line1(:,1));
dy = bsxfun(@minus, line2(:,2), line1(:,2));
%% Compute intersection points
denom = denom(inds);
x0(inds) = (x2 .* dy2 .* dx1 - dy .* dx1 .* dx2 - x1 .* dy1 .* dx2) ./ denom ;
y0(inds) = (dx .* dy1 .* dy2 + y1 .* dx1 .* dy2 - y2 .* dx2 .* dy1) ./ denom ;
% concatenate result
point = [x0 y0];
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