angles3d

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

0001 function angles3d(varargin)
0002 %ANGLES3D Conventions for manipulating angles in 3D.
0003 %
0004 %   The library uses both radians and degrees angles;
0005 %   Results of angle computation between shapes usually returns angles in
0006 %   radians.
0007 %   Representation of 3D shapes use angles in degrees (easier to manipulate
0008 %   and to save).
0009 %
0010 %   Contrary to the plane, there are no oriented angles in 3D. Angles
0011 %   between lines or between planes are comprised between 0 and PI.
0012 %
0013 %   Spherical angles
0014 %   Spherical angles are defined by 2 angles:
0015 %   * THETA, the colatitude, representing angle with Oz axis (between 0 and
0016 %       PI)
0017 %   * PHI, the azimut, representing angle with Ox axis of horizontal
0018 %       projection of the direction (between 0 and 2*PI)
0019 %
0020 %   Spherical coordinates can be represented by THETA, PHI, and the
0021 %   distance RHO to the origin.
0022 %
0023 %   Euler angles
0024 %   Some functions for creating rotations use Euler angles. They follow the
0025 %   ZYX convention in the global reference system, that is eqivalent to the
0026 %   XYZ convention ine a local reference system.
0027 %   Euler angles are given by a triplet of angles [PHI THETA PSI] that
0028 %   represents the succession of 3 rotations:
0029 %   * rotation around X by angle PSI    ("roll")
0030 %   * rotation around Y by angle THETA  ("pitch")
0031 %   * rotation around Z by angle PHI    ("yaw")
0032 %
0033 %   In this library, euler angles are given in degrees. The functions that
0034 %   use euler angles use the keyword 'Euler' in their name.
0035 %
0036 %
0037 %   See also
0038 %   cart2sph2, sph2cart2, cart2sph2d, sph2cart2d
0039 %   anglePoints3d, angleSort3d, sphericalAngle, randomAngle3d
0040 %   dihedralAngle, polygon3dNormalAngle, eulerAnglesToRotation3d
0041 %   rotation3dAxisAndAngle, rotation3dToEulerAngles
0042 %
0043 
0044 % ------
0045 % Author: David Legland
0046 % e-mail: david.legland@inra.fr
0047 % Created: 2008-10-13,    using Matlab 7.4.0.287 (R2007a)
0048 % Copyright 2008 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas.