1## Copyright (C) 2021 David Legland 2## All rights reserved. 3## 4## Redistribution and use in source and binary forms, with or without 5## modification, are permitted provided that the following conditions are met: 6## 7## 1 Redistributions of source code must retain the above copyright notice, 8## this list of conditions and the following disclaimer. 9## 2 Redistributions in binary form must reproduce the above copyright 10## notice, this list of conditions and the following disclaimer in the 11## documentation and/or other materials provided with the distribution. 12## 13## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' 14## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 15## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 16## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR 17## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 18## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR 19## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 20## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, 21## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 22## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 23## 24## The views and conclusions contained in the software and documentation are 25## those of the authors and should not be interpreted as representing official 26## policies, either expressed or implied, of the copyright holders. 27 28function b = isParallel(v1, v2, varargin) 29%ISPARALLEL Check parallelism of two vectors. 30% 31% B = isParallel(V1, V2) 32% where V1 and V2 are two row vectors of length ND, ND being the 33% dimension, returns 1 if the vectors are parallel, and 0 otherwise. 34% 35% Also works when V1 and V2 are two N-by-ND arrays with same number of 36% rows. In this case, return a N-by-1 array containing 1 at the positions 37% of parallel vectors. 38% 39% Also works when one of V1 or V2 is N-by-1 and the other one is N-by-ND 40% array, in this case return N-by-1 results. 41% 42% B = isParallel(V1, V2, ACCURACY) 43% specifies the accuracy for numerical computation. Default value is 44% 1e-14. 45% 46% 47% Example 48% isParallel([1 2], [2 4]) 49% ans = 50% 1 51% isParallel([1 2], [1 3]) 52% ans = 53% 0 54% 55% See also 56% vectors2d, isPerpendicular, lines2d 57% 58 59% ------ 60% Author: David Legland 61% e-mail: david.legland@inra.fr 62% Created: 2006-04-25 63% Copyright 2006 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas). 64 65% HISTORY 66% 2007-09-18 copy from isParallel3d, adapt to any dimension, and add psb 67% to specify precision 68% 2007-01-16 fix bug 69% 2009-09-21 fix bug for array of 3 vectors 70% 2011-01-20 replace repmat by ones-indexing (faster) 71% 2011-06-16 use direct computation (faster) 72% 2017-08-31 use normalized vectors 73 74% default accuracy 75acc = 1e-14; 76if ~isempty(varargin) 77 acc = abs(varargin{1}); 78end 79 80% normalize vectors 81v1 = normalizeVector(v1); 82v2 = normalizeVector(v2); 83 84% adapt size of inputs if needed 85n1 = size(v1, 1); 86n2 = size(v2, 1); 87if n1 ~= n2 88 if n1 == 1 89 v1 = v1(ones(n2,1), :); 90 elseif n2 == 1 91 v2 = v2(ones(n1,1), :); 92 end 93end 94 95% performs computation 96if size(v1, 2) == 2 97 % computation for plane vectors 98 b = abs(v1(:, 1) .* v2(:, 2) - v1(:, 2) .* v2(:, 1)) < acc; 99else 100 % computation in greater dimensions 101 b = vectorNorm(cross(v1, v2, 2)) < acc; 102end 103 104