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## Copyright (C) 2004 Josep Mones i Teixidor
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
## -*- texinfo -*-
## @deftypefn {Function File} {@var{BW} = } poly2mask (@var{x},@var{y},@var{m},@var{n})
## Convert a polygon to a region mask
##
## BW=poly2mask(x,y,m,n) converts a polygon, specified by a list of
## vertices in @var{x} and @var{y} and returns in a @var{m}-by-@var{n}
## logical mask @var{BW} the filled polygon. Region inside the polygon
## is set to 1, values outside the shape are set to 0.
##
## @var{x} and @var{y} should always represent a closed polygon, first
## and last points should be coincident. If they are not poly2mask will
## close it for you. If @var{x} or @var{y} are fractional they are
## nearest integer.
##
## If all the polygon or part of it falls outside the masking area
## (1:m,1:n), it is discarded or clipped.
##
## This function uses scan-line polygon filling algorithm as described
## in http://www.cs.rit.edu/~icss571/filling/ with some minor
## modifications: capability of clipping and scan order, which can
## affect the results of the algorithm (algorithm is described not to
## reach ymax, xmax border when filling to avoid enlarging shapes). In
## this function we scan the image backwards (we begin at ymax and end
## at ymin), and we don't reach ymin, xmin, which we believe should be
## compatible with MATLAB.
## @end deftypefn
## TODO: check how to create a logical BW without any conversion
## Author: Josep Mones i Teixidor <jmones@puntbarra.com>
function BW = poly2mask(x, y, m, n)
if (nargin!=4)
usage("BW = poly2mask(x, y, m, n)");
endif
## check x and y
x=round(x(:)');
y=round(y(:)');
if(length(x)<3)
error("poly2mask: polygon must have at least 3 vertices.");
endif
if(length(x)!=length(y))
error("poly2mask: length of x doesn't match length of y.");
endif
## create output matrix
uint8(0); ## This fails for octave < 2.1.58
BW=logical(zeros(m,n,"uint8"));
## close polygon if needed
if((x(1)!=x(length(x)))||(y(1)!=y(length(y))))
x=horzcat(x,x(1));
y=horzcat(y,y(1));
endif
## build global edge table
ex=[x(1:length(x)-1);x(1,2:length(x))]; ## x values for each edge
ey=[y(1:length(y)-1);y(1,2:length(y))]; ## y values for each edge
idx=find(ey(1,:)!=ey(2,:)); ## eliminate horizontal edges
ex=ex(:,idx);
ey=ey(:,idx);
eminy=min(ey); ## minimum y for each edge
emaxy=max(ey); ## maximum y for each edge
t=ey==[eminy;eminy]; ## values associated to miny
exminy=ex(:)(find(t)); ## x values associated to min y
exmaxy=ex(:)(find(!t)); ## x values associated to max y
emaxy=emaxy'; ## we want them vertical now...
eminy=eminy';
m_inv=(exmaxy-exminy)./(emaxy-eminy); ## calculate inverse slope
ge=[emaxy, eminy, exmaxy, m_inv]; ## build global edge table
ge=sortrows(ge,[1,3]); ## sort on eminy and exminy
## we add an extra dummy edge at the end just to avoid checking
## while indexing it
ge=[-Inf,-Inf,-Inf,-Inf;ge];
## initial parity is even (0)
parity=0;
## init scan line set to bottom line
sl=ge(size(ge,1),1);
## init active edge table
## we use a loop because the table is sorted and edge list could be
## huge
ae=[];
gei=size(ge,1);
while sl==ge(gei,1)
ae=[ge(gei,2:4);ae];
gei-=1;
endwhile
## calc minimum y to draw
miny=min(y);
if (miny<1)
miny=1;
endif
while sl>=miny
## check vert clipping
if(sl<=m)
## draw current scan line
## we have to round because 1/m is fractional
ie=round(reshape(ae(:,2),2,size(ae)/2));
## this discards left border of image (this differs from version at
## http://www.cs.rit.edu/~icss571/filling/ which discards right
## border) but keeps an exception when the point is a vertex.
ie(1,:)+=ie(1,:)!=ie(2,:);
## we'll clip too, just in case m,n is not big enough
ie(1,find(ie(1,:)<1))=1;
ie(2,find(ie(2,:)>n))=n;
## we eliminate segments outside window
ie=ie(:,find(ie(1,:)<=n));
ie=ie(:,find(ie(2,:)>=1));
for i=1:columns(ie)
BW(sl,ie(1,i):ie(2,i))=true;
endfor
endif
## decrement scan line
sl-=1;
## eliminate edges that eymax==sl
## this discards ymin border of image (this differs from version at
## http://www.cs.rit.edu/~icss571/filling/ which discards ymax).
ae=ae(find(ae(:,1)!=sl),:);
## update x (x1=x0-1/m)
ae(:,2)-=ae(:,3);
## update ae with new values
while sl==ge(gei,1)
ae=vertcat(ae,ge(gei,2:4));
gei-=1;
endwhile
## order the edges in ae by x value
if(rows(ae)>0)
ae=sortrows(ae,2);
endif
endwhile
endfunction
%!demo
%! s=[0:pi/4:2*pi];
%! x=cos(s)*90+101;
%! y=sin(s)*90+101;
%! bw=poly2mask(x,y,200,200);
%! imshow(bw);
%! %Creates a filled octagon
%!demo
%! s=[0:2*pi/5:pi*4];
%! s=s([1,3,5,2,4,6]);
%! x=cos(s)*90+101;
%! y=sin(s)*90+101;
%! bw=poly2mask(x,y,200,200);
%! imshow(bw);
%! %Creates a 5-vertex star
%!# Convex polygons
%!shared xs, ys, Rs, xt, yt, Rt
%! xs=[3,3,10,10];
%! ys=[4,12,12,4];
%! Rs=zeros(16,14);
%! Rs(5:12,4:10)=1;
%! Rs=logical(Rs);
%! xt=[1,4,7];
%! yt=[1,4,1];
%! Rt=[0,0,0,0,0,0,0;
%! 0,0,1,1,1,1,0;
%! 0,0,0,1,1,0,0;
%! 0,0,0,1,0,0,0;
%! 0,0,0,0,0,0,0];
%! Rt=logical(Rt);
%!assert(poly2mask(xs,ys,16,14),Rs); # rectangle
%!assert(poly2mask(xs,ys,8,7),Rs(1:8,1:7)); # clipped
%!assert(poly2mask(xs-7,ys-8,8,7),Rs(9:16,8:14)); # more clipping
%!assert(poly2mask(xt,yt,5,7),Rt); # triangle
%!assert(poly2mask(xt,yt,3,3),Rt(1:3,1:3)); # clipped
%!# Concave polygons
%!test
%! x=[3,3,5,5,8,8,10,10];
%! y=[4,12,12,8,8,11,11,4];
%! R=zeros(16,14);
%! R(5:12,4:5)=1;
%! R(5:8,6:8)=1;
%! R(5:11,9:10)=1;
%! R=logical(R);
%! assert(poly2mask(x,y,16,14), R);
%!# Complex polygons
%!test
%! x=[1,5,1,5];
%! y=[1,1,4,4];
%! R=[0,0,0,0,0,0;
%! 0,0,1,1,0,0;
%! 0,0,1,1,0,0;
%! 0,1,1,1,1,0;
%! 0,0,0,0,0,0];
%! R=logical(R);
%! assert(poly2mask(x,y,5,6), R);
%
% $Log$
% Revision 1.5 2004/09/07 14:47:50 pkienzle
% Avoid segfaults on pre-2.1.58 octave. Invisible whitespace changes.
%
% Revision 1.4 2004/09/03 17:12:36 jmones
% Uses uint8 to save some temporal memory (suggested by David Bateman)
%
% Revision 1.3 2004/09/03 13:32:07 jmones
% Work with logical arrays from BW creation
%
% Revision 1.2 2004/08/11 17:39:51 jmones
% Algorithm url in docs corrected.
%
% Revision 1.1 2004/08/11 17:34:11 jmones
% poly2mask added: creates filled polygon bw mask
%
%