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
|
## 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 trans = localToGlobal3d(varargin)
%LOCALTOGLOBAL3D Transformation matrix from local to global coordinate system.
%
% TRANS = localToGlobal3d(CENTER, THETA, PHI, PSI)
% Compute the transformation matrix from a local (or modelling)
% coordinate system to the global (or world) coordinate system.
% This is a low-level function, used by several drawing functions.
%
% The transform is defined by:
% - CENTER: the position of the local origin into the world coordinate
% system
% - THETA: colatitude, defined as the angle with the Oz axis (between 0
% and 180 degrees), positive in the direction of the of Oy axis.
% - PHI: azimut, defined as the angle of the normal with the Ox axis,
% between 0 and 360 degrees
% - PSI: intrinsic rotation, corresponding to the rotation of the object
% around the direction vector, between 0 and 360 degrees
%
% The resulting transform is obtained by applying (in that order):
% - Rotation by PSI around the Z-axis
% - Rotation by THETA around the Y-axis
% - Rotation by PHI around the Z-axis
% - Translation by vector CENTER
% This corresponds to Euler ZYZ rotation, using angles PHI, THETA and
% PSI.
%
% The 'eulerAnglesToRotation3d' function may better suit your needs as
% it is more 'natural'.
%
% Example
% localToGlobal3d
%
% See also
% transforms3d, eulerAnglesToRotation3d
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2009-06-19, using Matlab 7.7.0.471 (R2008b)
% Copyright 2009-2023 INRA - Cepia Software Platform
% extract the components of the transform
if nargin == 1
% all components are bundled in the first argument
var = varargin{1};
center = var(1:3);
theta = var(4);
phi = var(5);
psi = 0;
if length(var) > 5
psi = var(6);
end
elseif nargin == 4
% arguments = center, then the 3 angles
center = varargin{1};
theta = varargin{2};
phi = varargin{3};
psi = varargin{4};
elseif nargin > 4
% center is given in 3 arguments, then 3 angles
center = [varargin{1} varargin{2} varargin{3}];
theta = varargin{4};
phi = varargin{5};
psi = 0;
if nargin > 5
psi = varargin{6};
end
end
% conversion from degrees to radians
k = pi / 180;
% rotation around normal vector axis
rot1 = createRotationOz(psi * k);
% colatitude
rot2 = createRotationOy(theta * k);
% longitude
rot3 = createRotationOz(phi * k);
% shift center
tr = createTranslation3d(center);
% create final transform by concatenating transforms
trans = tr * rot3 * rot2 * rot1;
|
