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
|
## 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 theta = vectorAngle3d(v1, v2)
%VECTORANGLE3D Angle between two 3D vectors.
%
% THETA = vectorAngle3d(V1, V2)
% Computes the angle between the 2 3D vectors V1 and V2. The result THETA
% is given in radians, between 0 and PI.
%
%
% Example
% % angle between 2 orthogonal vectors
% vectorAngle3d([1 0 0], [0 1 0])
% ans =
% 1.5708
%
% % angle between 2 parallel vectors
% v0 = [3 4 5];
% vectorAngle3d(3*v0, 5*v0)
% ans =
% 0
%
% See also
% vectors3d, vectorNorm3d, crossProduct3d
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2010-10-04, using Matlab 7.9.0.529 (R2009b)
% Copyright 2010-2023 INRA - Cepia Software Platform
% compute angle using arc-tangent to get better precision for angles near
% zero, see the discussion in:
% http://www.mathworks.com/matlabcentral/newsreader/view_thread/151925#381952
theta = atan2(vectorNorm3d(crossProduct3d(v1, v2)), sum(bsxfun(@times, v1, v2),2));
% equivalent to:
% v1 = normalizeVector3d(v1);
% v2 = normalizeVector3d(v2);
% theta = acos(dot(v1, v2, 2));
|
