1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
|
## 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 b = isPerpendicular(v1, v2, varargin)
%ISPERPENDICULAR Check orthogonality of two vectors.
%
% B = isPerpendicular(V1, V2)
% where V1 and V2 are two 1-by-2 row arrays, returns 1 if the vectors are
% perpendicular, and 0 otherwise.
%
% Also works when V1 and V2 are two N-by-2 arrays with same number of
% rows. In this case, return a N-by-1 array containing 1 at the positions
% of perpendicular vectors.
%
% Also works when one of V1 or V2 is 1-by-2 and the other one is a N-by-2
% array. In this case the result has size N-by-1.
%
% B = isPerpendicular(V1, V2, ACCURACY)
% specifies accuracy of numerical tests, default is 1e-14.
%
%
% Example
% isPerpendicular([1 2 1], [2 4 2])
% ans =
% 1
%
% isPerpendicular([1 2 1], [1 3 2])
% ans =
% 0
%
% See also
% vectors2d, isParallel, lines2d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2006-04-25
% Copyright 2006-2023 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
% default accuracy
acc = 1e-14;
if ~isempty(varargin)
acc = abs(varargin{1});
end
% normalize vectors
v1 = normalizeVector(v1);
v2 = normalizeVector(v2);
% adapt size of inputs
n1 = size(v1, 1);
n2 = size(v2, 1);
if n1 ~= n2
if n1 == 1
v1 = v1(ones(n2, 1), :);
elseif n2==1
v2 = v2(ones(n1, 1), :);
else
error('Inputs must either have same size, or one must be scalar');
end
end
% performs test
b = abs(dot(v1, v2, 2)) < acc;
|
