/usr/share/octave/packages/geometry-1.7.0/geom2d/isPointOnEdge.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## 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
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## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{b} = } isPointOnEdge (@var{point}, @var{edge})
## @deftypefnx {Function File} {@var{b} = } isPointOnEdge (@var{point}, @var{edge}, @var{tol})
## @deftypefnx {Function File} {@var{b} = } isPointOnEdge (@var{point}, @var{edgearray})
## @deftypefnx {Function File} {@var{b} = } isPointOnEdge (@var{pointarray}, @var{edgearray})
## Test if a point belongs to an edge.
#
# with @var{point} being [xp yp], and @var{edge} being [x1 y1 x2 y2], returns TRUE if
# the point is located on the edge, and FALSE otherwise.
#
# Specify an optilonal tolerance value @var{tol}. The tolerance is given as a
# fraction of the norm of the edge direction vector. Default is 1e-14.
#
# When one of the inputs has several rows, return the result of the test
# for each element of the array tested against the single parameter.
#
# When both @var{pointarray} and @var{edgearray} have the same number of rows,
# returns a column vector with the same number of rows.
# When the number of rows are different and both greater than 1, returns
# a Np-by-Ne matrix of booleans, containing the result for each couple of
# point and edge.
#
# @seealso{edges2d, points2d, isPointOnLine}
## @end deftypefn
function b = isPointOnEdge(point, edge, varargin)
# extract computation tolerance
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
# number of edges and of points
Np = size(point, 1);
Ne = size(edge, 1);
# adapt size of inputs if needed, and extract elements for computation
if Np == Ne
# When the number of points and edges is the same, the one-to-one test
# will be computed, so there is no need to repeat matrices
dx = edge(:,3) - edge(:,1);
dy = edge(:,4) - edge(:,2);
lx = point(:,1) - edge(:,1);
ly = point(:,2) - edge(:,2);
elseif Np == 1
# one point, several edges
dx = edge(:, 3) - edge(:, 1);
dy = edge(:, 4) - edge(:, 2);
lx = point(ones(Ne, 1), 1) - edge(:, 1);
ly = point(ones(Ne, 1), 2) - edge(:, 2);
elseif Ne == 1
# several points, one edge
dx = (edge(3) - edge(1)) * ones(Np, 1);
dy = (edge(4) - edge(2)) * ones(Np, 1);
lx = point(:, 1) - edge(1);
ly = point(:, 2) - edge(2);
else
# Np points and Ne edges:
# Create an array for each parameter, so that the result will be a
# Np-by-Ne matrix of booleans (requires more memory, and uses repmat)
x0 = repmat(edge(:, 1)', Np, 1);
y0 = repmat(edge(:, 2)', Np, 1);
dx = repmat(edge(:,3)', Np, 1) - x0;
dy = repmat(edge(:,4)', Np, 1) - y0;
lx = repmat(point(:, 1), 1, Ne) - x0;
ly = repmat(point(:, 2), 1, Ne) - y0;
end
# test if point is located on supporting line
b1 = (abs(lx.*dy - ly.*dx) ./ hypot(dx, dy)) < tol;
# compute position of point with respect to edge bounds
# use different tests depending on line angle
ind = abs(dx) > abs(dy);
t = zeros(size(dx));
t(ind) = lx( ind) ./ dx( ind);
t(~ind) = ly(~ind) ./ dy(~ind);
# check if point is located between edge bounds
b = t >- tol & t-1 < tol & b1;
endfunction
%!shared points, vertices, edges
%!demo
%! # create a point array
%! points = [10 10;15 10; 30 10];
%! # create an edge array
%! vertices = [10 10;20 10;20 20;10 20];
%! edges = [vertices vertices([2:end 1], :)];
%!
%! # Test one point and one edge
%! isPointOnEdge(points(1,:), edges(1,:))
%! isPointOnEdge(points(3,:), edges(1,:))
%!demo
%! # create a point array
%! points = [10 10;15 10; 30 10];
%! # create an edge array
%! vertices = [10 10;20 10;20 20;10 20];
%! edges = [vertices vertices([2:end 1], :)];
%!
%! # Test one point and several edges
%! isPointOnEdge(points(1,:), edges)'
%!demo
%! # create a point array
%! points = [10 10;15 10; 30 10];
%! # create an edge array
%! vertices = [10 10;20 10;20 20;10 20];
%! edges = [vertices vertices([2:end 1], :)];
%!
%! # Test several points and one edge
%! isPointOnEdge(points, edges(1,:))'
%!demo
%! # create a point array
%! points = [10 10;15 10; 30 10];
%! # create an edge array
%! vertices = [10 10;20 10;20 20;10 20];
%! edges = [vertices vertices([2:end 1], :)];
%!
%! # Test N points and N edges
%! isPointOnEdge(points, edges(1:3,:))'
%!demo
%! # create a point array
%! points = [10 10;15 10; 30 10];
%! # create an edge array
%! vertices = [10 10;20 10;20 20;10 20];
%! edges = [vertices vertices([2:end 1], :)];
%!
%! # Test NP points and NE edges
%! isPointOnEdge(points, edges)
%!test
%! p1 = [10 20];
%! p2 = [80 20];
%! edge = [p1 p2];
%! p0 = [10 20];
%! assert (isPointOnEdge(p0, edge));
%! p0 = [80 20];
%! assert (isPointOnEdge(p0, edge));
%! p0 = [50 20];
%! assert (isPointOnEdge(p0, edge));
%! p0 = [9.99 20];
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [80.01 20];
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [50 21];
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [79 19];
%! assert (!isPointOnEdge(p0, edge));
%!test
%! p1 = [20 10];
%! p2 = [20 80];
%! edge = [p1 p2];
%! p0 = [20 10];
%! assert (isPointOnEdge(p0, edge));
%! p0 = [20 80];
%! assert (isPointOnEdge(p0, edge));
%! p0 = [20 50];
%! assert (isPointOnEdge(p0, edge));
%! p0 = [20 9.99];
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [20 80.01];
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [21 50];
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [19 79];
%! assert (!isPointOnEdge(p0, edge));
%!test
%! p1 = [10 20];
%! p2 = [60 70];
%! edge = [p1 p2];
%! assert (isPointOnEdge(p1, edge));
%! assert (isPointOnEdge(p2, edge));
%! p0 = [11 21];
%! assert (isPointOnEdge(p0, edge));
%! p0 = [59 69];
%! assert (isPointOnEdge(p0, edge));
%! p0 = [9.99 19.99];
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [60.01 70.01];
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [30 50.01];
%! assert (!isPointOnEdge(p0, edge));
%!test
%! edge = [10 20 80 20; 20 10 20 80; 20 10 60 70];
%! p0 = [20 20];
%! assert ([true ; true ; false], isPointOnEdge(p0, edge));
%!test
%! k = 1e15;
%! p1 = [10 20]*k;
%! p2 = [60 70]*k;
%! edge = [p1 p2];
%! assert (isPointOnEdge(p1, edge));
%! assert (isPointOnEdge(p2, edge));
%! p0 = [11 21]*k;
%! assert (isPointOnEdge(p0, edge));
%! p0 = [59 69]*k;
%! assert (isPointOnEdge(p0, edge));
%! p0 = [9.99 19.99]*k;
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [60.01 70.01]*k;
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [30 50.01]*k;
%! assert (!isPointOnEdge(p0, edge));
%!test
%! k = 1e-10;
%! p1 = [10 20]*k;
%! p2 = [60 70]*k;
%! edge = [p1 p2];
%! assert (isPointOnEdge(p1, edge));
%! assert (isPointOnEdge(p2, edge));
%! p0 = [11 21]*k;
%! assert (isPointOnEdge(p0, edge));
%! p0 = [59 69]*k;
%! assert (isPointOnEdge(p0, edge));
%! p0 = [9.99 19.99]*k;
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [60.01 70.01]*k;
%! assert (!isPointOnEdge(p0, edge));
%! p0 = [30 50.01]*k;
%! assert (!isPointOnEdge(p0, edge));
%!test
%! p1 = [10 20];
%! p2 = [80 20];
%! edge = [p1 p2];
%! p0 = [10 20; 80 20; 50 20;50 21];
%! exp = [true;true;true;false];
%! assert (exp, isPointOnEdge(p0, edge));
%!test
%! p1 = [10 20];
%! p2 = [80 20];
%! edge = [p1 p2];
%! p0 = [40 20];
%! exp = [true;true;true;true];
%! assert (exp, isPointOnEdge(p0, [edge;edge;edge;edge]));
%!test
%! edge1 = [10 20 80 20];
%! edge2 = [30 10 30 80];
%! edges = [edge1; edge2];
%! p0 = [40 20;30 90];
%! exp = [true;false];
%! assert (exp, isPointOnEdge(p0, edges));
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