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# v_polygonwind

## PURPOSE V_POLYGONWIND Test if points are inside a polygon

## SYNOPSIS function w=v_polygonwind(p,x)

## DESCRIPTION ```V_POLYGONWIND Test if points are inside a polygon
Inputs:
P(n,2)  polygon vertices
X(m,2)  points to test

Outputs:
W(m)    winding number for each point

For a normal polygon whose vertices are listed
anti-clockwise, the winding number is 0 or 1 according to whether the
point is outside or inside the polygon. The winding number will
be -1 if the polygon vertices go colckwise around the point.```

## CROSS-REFERENCE INFORMATION This function calls:
This function is called by:

## SOURCE CODE ```0001 function w=v_polygonwind(p,x)
0002 %V_POLYGONWIND Test if points are inside a polygon
0003 % Inputs:
0004 %    P(n,2)  polygon vertices
0005 %    X(m,2)  points to test
0006 %
0007 % Outputs:
0008 %    W(m)    winding number for each point
0009 %
0010 % For a normal polygon whose vertices are listed
0011 % anti-clockwise, the winding number is 0 or 1 according to whether the
0012 % point is outside or inside the polygon. The winding number will
0013 % be -1 if the polygon vertices go colckwise around the point.
0014
0015
0016 %      Copyright (C) Mike Brookes 2009
0017 %      Version: \$Id: v_polygonwind.m 10865 2018-09-21 17:22:45Z dmb \$
0018 %
0019 %   VOICEBOX is a MATLAB toolbox for speech processing.
0021 %
0022 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0023 %   This program is free software; you can redistribute it and/or modify
0024 %   it under the terms of the GNU General Public License as published by
0025 %   the Free Software Foundation; either version 2 of the License, or
0026 %   (at your option) any later version.
0027 %
0028 %   This program is distributed in the hope that it will be useful,
0029 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0030 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0031 %   GNU General Public License for more details.
0032 %
0033 %   You can obtain a copy of the GNU General Public License from
0034 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0035 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0036 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0037 n=size(p,1);
0038 m=size(x,1);
0039 q=zeros(2,n+1);
0040 q(:,1:n)=p';
0041 q(:,n+1)=q(:,1);      % append an extra point
0042 i=1:n;
0043 j=2:n+1;
0044 ym=repmat(2,m,1);
0045 yn=repmat(2,1,n);
0046 w=sum((2*((repmat(q(1,i).*q(2,j)-q(2,i).*q(1,j),m,1)+x(:,1)*(q(2,i)-q(2,j))+x(:,2)*(q(1,j)-q(1,i)))>0)-1).*abs((q(ym,j)>x(:,yn))-(q(ym,i)>x(:,yn))),2)/2;
0047 if ~nargout
0048     w0=w==0;
0049     wp=w>0;
0050     wn=w<0;
0051     plot(q(1,:),q(2,:),'k-',x(w0,1),x(w0,2),'go',x(wp,1),x(wp,2),'r+',x(wn,1),x(wn,2),'bx');
0052     mnx=[1.05 -0.05;-0.05 1.05]*[min([p; x]);max([p; x])];
0053     set(gca,'xlim',mnx(:,1)','ylim',mnx(:,2)');
0054     title('Winding numbers: o=0, +=pos, x=neg');
0055 end```

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