//  Copyright (c) CNES  2008
//
//  This software is part of CelestLab, a CNES toolbox for Scilab
//
//  This software is governed by the CeCILL  license under French law and
//  abiding by the rules of distribution of free software.  You can  use,
//  modify and/ or redistribute the software under the terms of the CeCILL
//  license as circulated by CEA, CNRS and INRIA at the following URL
//  'http://www.cecill.info'.

function [angles1,angles2,Inok] = CL_rot_matrix2angles(M,naxes)
// Frame transformation matrix to Euler or Cardan rotation angles
//
// Calling Sequence
// [angles1,angles2,Inok] = CL_rot_matrix2angles(M,naxes)
//
// Description
// <itemizedlist><listitem>
// <p> Given a frame transformation matrix, this function computes the rotation angles (Euler or Cardan) that correspond to the 
// combination of 3 elementary rotations, each being described by an axis number 
// (1=x-axis, 2=y-axis, 3=z-axis). </p>
// <p></p>
// <p>There are 6 Cardan rotations: XYZ, XZY, YXZ, YZX, ZXY and ZYX;  
// and 6 Euler rotations: XYX, XZX, YXY, YZY, ZXZ and ZYZ.</p>
// <p></p>
// <p></p></listitem>
// <listitem>
// <p><b>Notes:</b></p>
// <p><b>1)</b> There are 2 sets of solutions: </p>
// <p>- For Cardan angles, <b>angles1</b> is the solution for which the second rotation angle is between -pi/2 and pi/2. </p>
// <p>- For Euler angles, <b>angles1</b> is the solution for which the second rotation angle is between 0 and pi.</p>
// <p></p>
// <p><b>2)</b> Cardan and Euler angles have singularities. </p>
// <p>- For Cardan angles, singularities occur when the second angle is close to -pi/2 or +pi/2</p>
// <p>- For Euler angles, singularities occur when the second angle is close to 0 or pi (which implies that 
// the identity rotation is always singular for Euler angles!)</p>
// <p></p>
// <p><b>3)</b> The returned angles for cases close to singularities are approximate.
// The corresponding indices are returned in Inok. </p>
// </listitem>
// </itemizedlist>
//
// Parameters
// M : Frame transformation matrix (3x3xN).
// naxes : Successive axes numbers : 1=x-axis, 2=y-axis or 3=z-axis (1x3 or 3x1)
// angles1 : First set of rotation angles [rad] (3xN)
// angles2 : Second set of rotation angles [rad] (3xN)
// Inok : Indices for which singularities occur (1xP)
//
// Authors
// CNES - DCT/SB
//
// See also
// CL_rot_angles2quat
// CL_rot_angles2matrix
// CL_rot_quat2angles
//
// Examples
// // Cardan angles (XYZ), second rotation angle < %pi/2 
// naxes = [1,2,3];
// angles = [0.1;0.4;0.5];
// M = CL_rot_angles2matrix(naxes,angles);
// [angles1,angles2,Inok] = CL_rot_matrix2angles(M,naxes);
// angles1 - angles  // => 0
//
// // Cardan angles (XYZ), second rotation angle > %pi/2
// angles = [0.1;2.4;0.5];
// M = CL_rot_angles2matrix(naxes,angles);
// [angles1,angles2,Inok] = CL_rot_matrix2angles(M,naxes);
// angles2 - angles // => 0
//
// // Euler angles (ZXZ), second rotation angle close to 0 : singularity
// naxes = [3,1,3];
// angles = [0.1;0;0.5];
// M = CL_rot_angles2matrix(naxes,angles);
// [angles1,angles2,Inok] = CL_rot_matrix2angles(M,naxes);
// Inok // => not empty
// M1 = CL_rot_angles2matrix(naxes,angles1);
// M1*M'  // => identity


// Declarations:


// Code:

[angles1,angles2,Inok] = CL__rot_qM2angles(M,naxes);

endfunction