File: eulerAnglesToRotation3d.m

package info (click to toggle)
octave-matgeom 1.2.4-2
  • links: PTS, VCS
  • area: main
  • in suites: forky, sid, trixie
  • size: 3,584 kB
  • sloc: objc: 469; makefile: 10
file content (155 lines) | stat: -rw-r--r-- 6,068 bytes parent folder | download
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
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
## 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 mat = eulerAnglesToRotation3d(phi, theta, psi, varargin)
%EULERANGLESTOROTATION3D Convert 3D Euler angles to 3D rotation matrix.
%
%   MAT = eulerAnglesToRotation3d(PHI, THETA, PSI)
%   Creates a rotation matrix from the 3 euler angles PHI THETA and PSI,
%   given in degrees, using the 'XYZ' convention (local basis), or the
%   'ZYX' convention (global basis). The result MAT is a 4-by-4 rotation
%   matrix in homogeneous coordinates.
%
%   PHI:    rotation angle around Z-axis, in degrees, corresponding to the
%       'Yaw'. PHI is between -180 and +180.
%   THETA:  rotation angle around Y-axis, in degrees, corresponding to the
%       'Pitch'. THETA is between -90 and +90.
%   PSI:    rotation angle around X-axis, in degrees, corresponding to the
%       'Roll'. PSI is between -180 and +180.
%   These angles correspond to the "Yaw-Pitch-Roll" convention, also known
%   as "Tait-Bryan angles".
%
%   The resulting rotation is equivalent to a rotation around X-axis by an
%   angle PSI, followed by a rotation around the Y-axis by an angle THETA,
%   followed by a rotation around the Z-axis by an angle PHI.
%   That is:
%       ROT = Rz * Ry * Rx;
%
%   MAT = eulerAnglesToRotation3d(ANGLES)
%   Concatenates all angles in a single 1-by-3 array.
%   
%   ... = eulerAnglesToRotation3d(ANGLES, CONVENTION)
%   CONVENTION specifies the axis rotation sequence. Default is 'ZYX'.
%   Supported conventions are: 
%       'ZYX','ZXY','YXZ','YZX','XYZ','XZY'
%       'ZYZ','ZXZ','YZY','YXY','XZX','XYX'
%
%   Example
%   [n e f] = createCube;
%   phi     = 20;
%   theta   = 30;
%   psi     = 10;
%   rot = eulerAnglesToRotation3d(phi, theta, psi);
%   n2 = transformPoint3d(n, rot);
%   drawPolyhedron(n2, f);
%
%   See also 
%   transforms3d, createRotationOx, createRotationOy, createRotationOz
%   rotation3dAxisAndAngle
%

% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2010-07-22, using Matlab 7.9.0.529 (R2009b)
% Copyright 2010-2023 INRA - Cepia Software Platform

% Process input arguments
if size(phi, 2) == 3
    if nargin > 1
        varargin{1} = theta;
    end
    % manages arguments given as one array
    psi     = phi(:, 3);
    theta   = phi(:, 2);
    phi     = phi(:, 1);
end

p = inputParser;
validStrings = {...
    'ZYX','ZXY','YXZ','YZX','XYZ','XZY',...
    'ZYZ','ZXZ','YZY','YXY','XZX','XYX'};
addOptional(p,'convention','ZYX',@(x) any(validatestring(x,validStrings)));
parse(p,varargin{:});
convention=p.Results.convention;

% create individual rotation matrices
k = pi / 180;

switch convention
    case 'ZYX'
        rot1 = createRotationOx(psi * k);
        rot2 = createRotationOy(theta * k);
        rot3 = createRotationOz(phi * k);
    case 'ZXY'
        rot1 = createRotationOy(psi * k);
        rot2 = createRotationOx(theta * k);
        rot3 = createRotationOz(phi * k);
    case 'YXZ'
        rot1 = createRotationOz(psi * k);
        rot2 = createRotationOx(theta * k);
        rot3 = createRotationOy(phi * k);
    case 'YZX'
        rot1 = createRotationOx(psi * k);
        rot2 = createRotationOz(theta * k);
        rot3 = createRotationOy(phi * k);
    case 'XYZ'
        rot1 = createRotationOz(psi * k);
        rot2 = createRotationOy(theta * k);
        rot3 = createRotationOx(phi * k);
    case 'XZY'
        rot1 = createRotationOy(psi * k);
        rot2 = createRotationOz(theta * k);
        rot3 = createRotationOx(phi * k);
    case 'ZYZ'
        rot1 = createRotationOz(psi * k);
        rot2 = createRotationOy(theta * k);
        rot3 = createRotationOz(phi * k);
    case 'ZXZ'
        rot1 = createRotationOz(psi * k);
        rot2 = createRotationOx(theta * k);
        rot3 = createRotationOz(phi * k);
    case 'YZY'
        rot1 = createRotationOy(psi * k);
        rot2 = createRotationOz(theta * k);
        rot3 = createRotationOy(phi * k);
    case 'YXY'
        rot1 = createRotationOy(psi * k);
        rot2 = createRotationOx(theta * k);
        rot3 = createRotationOy(phi * k);
    case 'XZX'
        rot1 = createRotationOx(psi * k);
        rot2 = createRotationOz(theta * k);
        rot3 = createRotationOx(phi * k);
    case 'XYX'
        rot1 = createRotationOx(psi * k);
        rot2 = createRotationOy(theta * k);
        rot3 = createRotationOx(phi * k);
end

% concatenate matrices
mat = rot3 * rot2 * rot1;