# v_rotro2lu

## PURPOSE

V_ROTRO2QR converts a 3x3 rotation matrix to look and up directions

## SYNOPSIS

function [l,u]=v_rotro2lu(r)

## DESCRIPTION

    V_ROTRO2QR converts a 3x3 rotation matrix to look and up directions
      Inputs:  R(3,3,...)  Input rotation matrix

     Outputs:  L(3,...)    Unit vector specifying look direction
               U(3,...)    Unit vector specifying up direction

     The rotation maps the look direction to the negative z-axis and the up direction
     to lie in the y-z plane with a positive y component. That is, R*L=a*[0 0 -1]' and
     R*U=b*[0 1 c] for postive constants a and b. After applying this rotation to an object,
     the 2-D data obtained by omitting the z-component represents an orthographic projection
     performed by a camera looking in the direction L.

## CROSS-REFERENCE INFORMATION

This function calls:

- v_rotro2qr V_ROTRO2QR converts a 3x3 rotation matrix to a real quaternion

This function is called by:

## SOURCE CODE

    0001 function [l,u]=v_rotro2lu(r)
    0002 %V_ROTRO2QR converts a 3x3 rotation matrix to look and up directions
    0003 %  Inputs:  R(3,3,...)  Input rotation matrix
    0004 %
    0005 % Outputs:  L(3,...)    Unit vector specifying look direction
    0006 %           U(3,...)    Unit vector specifying up direction
    0007 %
    0008 % The rotation maps the look direction to the negative z-axis and the up direction
    0009 % to lie in the y-z plane with a positive y component. That is, R*L=a*[0 0 -1]' and
    0010 % R*U=b*[0 1 c] for postive constants a and b. After applying this rotation to an object,
    0011 % the 2-D data obtained by omitting the z-component represents an orthographic projection
    0012 % performed by a camera looking in the direction L.
    0013
    0014 %      Copyright (C) Mike Brookes 2023
    0015 %      Version: $Id: v_rotro2lu.m 10865 2018-09-21 17:22:45Z dmb $
    0016 %
    0017 %   VOICEBOX is a MATLAB toolbox for speech processing.
    0018 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
    0019 %
    0020 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0021 %   This program is free software; you can redistribute it and/or modify
    0022 %   it under the terms of the GNU Lesser General Public License as published by
    0023 %   the Free Software Foundation; either version 3 of the License, or
    0024 %   (at your option) any later version.
    0025 %
    0026 %   This program is distributed in the hope that it will be useful,
    0027 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
    0028 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    0029 %   GNU Lesser General Public License for more details.
    0030 %
    0031 %   You can obtain a copy of the GNU Lesser General Public License from
    0032 %   https://www.gnu.org/licenses/ .
    0033 %
    0034 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0035
    0036 sz=size(r);
    0037 r=reshape(r,9,[]);                  % make 2-dimensional
    0038 if size(r,2)>1                      % multiple rotation matrices
    0039     l=reshape(-r([3 6 9],:),[3 sz(3:end)]);
    0040     u=reshape(r([2 5 8],:),[3 sz(3:end)]);
    0041 else                                % only one rotation matrix
    0042     l=-r([3 6 9],:);
    0043     u=r([2 5 8],:);
    0044 end
    0045 if ~nargout
    0046     v_rotro2qr(reshape(r(:,1),3,3));           % plot a cube
    0047     set(gca,'CameraPosition',[0 0 1]);
    0048 end