19 Jun 2009
11 Jun 2014)
Library to handle 3D geometric primitives: create, intersect, display, and make basic computations
%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
% 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
% * 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: email@example.com
% Created: 2008-10-13, using Matlab 220.127.116.117 (R2007a)
% Copyright 2008 INRA - BIA PV Nantes - MIAJ Jouy-en-Josas.