# v_atan2sc

## PURPOSE

V_ATAN2SC sin and cosine of atan(y/x) [S,C,R,T]=(Y,X)

## SYNOPSIS

function [s,c,r,t]=v_atan2sc(y,x)

## DESCRIPTION

```V_ATAN2SC    sin and cosine of atan(y/x) [S,C,R,T]=(Y,X)

Outputs:
s    sin(t) where tan(t) = y/x
c    cos(t) where tan(t) = y/x
r    sqrt(x^2 + y^2)
t    arctan of y/x

Note y and x can be arrays but must be the same size. The outputs will
all be the same size as y.```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:
• v_rotpl2ro V_ROTPL2RO find matrix to rotate in the plane containing u and v r=[u,v,t]
• v_rotro2eu V_ROTRO2EU converts a 3x3 rotation matrix into the corresponding euler angles
• v_rotro2pl V_ROTRO2PL find the plane and rotation angle of a rotation matrix [u,v,t]=r

## SOURCE CODE

```0001 function [s,c,r,t]=v_atan2sc(y,x)
0002 %V_ATAN2SC    sin and cosine of atan(y/x) [S,C,R,T]=(Y,X)
0003 %
0004 % Outputs:
0005 %    s    sin(t) where tan(t) = y/x
0006 %    c    cos(t) where tan(t) = y/x
0007 %    r    sqrt(x^2 + y^2)
0008 %    t    arctan of y/x
0009 %
0010 % Note y and x can be arrays but must be the same size. The outputs will
0011 % all be the same size as y.
0012
0013 %      Copyright (C) Mike Brookes 2007
0014 %      Version: \$Id: v_atan2sc.m 10865 2018-09-21 17:22:45Z dmb \$
0015 %
0016 %   VOICEBOX is a MATLAB toolbox for speech processing.
0018 %
0019 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0020 %   This program is free software; you can redistribute it and/or modify
0022 %   the Free Software Foundation; either version 2 of the License, or
0023 %   (at your option) any later version.
0024 %
0025 %   This program is distributed in the hope that it will be useful,
0026 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0027 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0028 %   GNU General Public License for more details.
0029 %
0030 %   You can obtain a copy of the GNU General Public License from
0031 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0032 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0033 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0034
0035 sz=size(y);
0036 s=zeros(sz);
0037 c=NaN(sz);
0038 r=zeros(sz);
0039 t=NaN(sz);
0040 m=y==0;
0041 if any(m(:)) % handle case when y=0 and possibly x=0 also
0042     t(m)=(x(m)<0);
0043     c(m)=1-2*t(m);
0044     r(m)=abs(x(m));
0045     t(m)=t(m)*pi;
0046 end
0047 m=abs(y)>abs(x) & isnan(c);
0048 if any(m(:))
0049     q = x(m)./y(m);
0050     u = sqrt(1+q.^2).*sign(y(m)); % avoids underflow even if x and y are very small
0051     s(m) = 1./u;
0052     c(m) = s(m).*q;
0053     r(m) = y(m).*u;
0054 end
0055 m=isnan(c);
0056 if any(m(:))
0057     q = y(m)./x(m);
0058     u = sqrt(1+q.^2).*sign(x(m));
0059     c(m) = 1./u;
0060     s(m) = c(m).*q;
0061     r(m) = x(m).*u;
0062 end
0063 m=isnan(t);
0064 if nargout>3 && any(m(:))
0065     t(m)=atan2(s(m),c(m));
0066 end```