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
|
## 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 = dihedralAngle(plane1, plane2)
%DIHEDRALANGLE Compute dihedral angle between 2 planes.
%
% THETA = dihedralAngle(PLANE1, PLANE2)
% PLANE1 and PLANE2 are plane representations given in the following
% format:
% [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
% THETA is the angle between the two vectors given by plane normals,
% given between 0 and PI.
%
% References
% http://en.wikipedia.org/wiki/Dihedral_angle
% http://mathworld.wolfram.com/DihedralAngle.html
%
% See also
% planes3d, lines3d, angles3d, planesBisector
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-21
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% compute plane normals
v1 = planeNormal(plane1);
v2 = planeNormal(plane2);
% number of vectors
n1 = size(v1, 1);
n2 = size(v2, 1);
% ensures vectors have same dimension
if n1 ~= n2
if n1 == 1
v1 = repmat(v1, [n2 1]);
elseif n2 == 1
v2 = repmat(v2, [n1 1]);
else
error('Arguments V1 and V2 must have the same size');
end
end
% compute dihedral angle(s)
theta = atan2(vectorNorm3d(cross(v1, v2, 2)), dot(v1, v2, 2));
% % equivalent to following formula, but more precise for small angles:
% n1 = normalizeVector3d(planeNormal(plane1));
% n2 = normalizeVector3d(planeNormal(plane2));
% theta = acos(dot(n1, n2, 2));
|
