/usr/share/octave/packages/geometry-1.7.0/geom3d/private/localToGlobal3d.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## 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
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## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{} =} localToGlobal3d (@var{center}, @var{theta},@var{phi},@var{psi})
## 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 he 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 'createEulerAnglesRotation' function may better suit your needs as
## it is more 'natural'.
##
## @seealso{transforms3d, createEulerAnglesRotation}
## @end deftypefn
function trans = localToGlobal3d(varargin)
## 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;
endfunction
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