function mat = eulerAnglesToRotation3d(phi, theta, psi, varargin)
%EULERANGLESTOROTATION3D Convert 3D Euler angles to 3D rotation matrix
% MAT = eulerAnglesToRotation3d(PHI, THETA, PSI)
% Creates a rotation matrix from the 3 euler angles PHI THETA and PSI,
% given in degrees, using the 'XYZ' convention (local basis), or the
% 'ZYX' convention (global basis). The result MAT is a 4-by-4 rotation
% matrix in homogeneous coordinates.
% PHI: rotation angle around Z-axis, in degrees, corresponding to the
% 'Yaw'. PHI is between -180 and +180.
% THETA: rotation angle around Y-axis, in degrees, corresponding to the
% 'Pitch'. THETA is between -90 and +90.
% PSI: rotation angle around X-axis, in degrees, corresponding to the
% 'Roll'. PSI is between -180 and +180.
% These angles correspond to the "Yaw-Pitch-Roll" convention, also known
% as "TaitBryan angles".
% The resulting rotation is equivalent to a rotation around X-axis by an
% angle PSI, followed by a rotation around the Y-axis by an angle THETA,
% followed by a rotation around the Z-axis by an angle PHI.
% That is:
% ROT = Rz * Ry * Rx;
% MAT = eulerAnglesToRotation3d(ANGLES)
% Concatenates all angles in a single 1-by-3 array.
% [n e f] = createCube;
% phi = 20;
% theta = 30;
% psi = 10;
% rot = eulerAnglesToRotation3d(phi, theta, psi);
% n2 = transformPoint3d(n, rot);
% drawPolyhedron(n2, f);
% See also
% transforms3d, createRotationOx, createRotationOy, createRotationOz
% Author: David Legland
% e-mail: email@example.com
% Created: 2010-07-22, using Matlab 22.214.171.1249 (R2009b)
% Copyright 2010 INRA - Cepia Software Platform.
% 2011-06-20 rename and use degrees
% Process input arguments
if size(phi, 2) == 3
% manages arguments given as one array
theta = phi(:, 2);
psi = phi(:, 3);
phi = phi(:, 1);
% create individual rotation matrices
k = pi / 180;
rotX = createRotationOx(psi * k);
rotY = createRotationOy(theta * k);
rotZ = createRotationOz(phi * k);
% concatenate matrices
mat = rotZ * rotY * rotX;