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## 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 angles3d(varargin)
%ANGLES3D Conventions for manipulating angles in 3D.
%
% The library uses both radians and degrees angles;
% Results of angle computation between shapes usually returns angles in
% radians.
% Representation of 3D shapes use angles in degrees (easier to manipulate
% and to save).
%
% Contrary to the plane, there are no oriented angles in 3D. Angles
% between lines or between planes are comprised between 0 and PI.
%
% Spherical angles
% Spherical angles are defined by 2 angles:
% * THETA, the colatitude, representing angle with Oz axis (between 0 and
% PI)
% * PHI, the azimut, representing angle with Ox axis of horizontal
% projection of the direction (between 0 and 2*PI)
%
% Spherical coordinates can be represented by THETA, PHI, and the
% distance RHO to the origin.
%
% Euler angles
% Some functions for creating rotations use Euler angles. They follow the
% ZYX convention in the global reference system, that is eqivalent to the
% XYZ convention ine a local reference system.
% Euler angles are given by a triplet of angles [PHI THETA PSI] that
% represents the succession of 3 rotations:
% * rotation around X by angle PSI ("roll")
% * rotation around Y by angle THETA ("pitch")
% * rotation around Z by angle PHI ("yaw")
%
% In this library, euler angles are given in degrees. The functions that
% use euler angles use the keyword 'Euler' in their name.
%
%
% See also
% cart2sph2, sph2cart2, cart2sph2d, sph2cart2d
% anglePoints3d, angleSort3d, sphericalAngle, randomAngle3d
% dihedralAngle, polygon3dNormalAngle, eulerAnglesToRotation3d
% rotation3dAxisAndAngle, rotation3dToEulerAngles
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2008-10-13, using Matlab 7.4.0.287 (R2007a)
% Copyright 2008-2023 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas
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