/usr/share/octave/packages/geometry-1.7.0/polygons2d/expandPolygon.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{loops} = } expandPolygon (@var{poly}, @var{dist})
## Expand a polygon by a given (signed) distance
##
## Associates to each edge of the polygon @var{poly} the parallel line located
## at distance @var{dist} from the current edge, and compute intersections with
## neighbor parallel lines. The resulting polygon is simplified to remove
## inner "loops", and can be disconnected.
## The result is a cell array, each cell containing a simple linear ring.
##
## This is a kind of dilation, but behaviour on corners is different.
## This function keeps angles of polygons, but there is no direct relation
## between length of 2 polygons.
##
## It is also possible to specify negative distance, and get all points
## inside the polygon. If the polygon is convex, the result equals
## morphological erosion of polygon by a ball with radius equal to the
## given distance.
##
## @seealso{polygons2d}
## @end deftypefn
function loops = expandPolygon(poly, dist)
# eventually copy first point at the end to ensure closed polygon
if sum(poly(end, :)==poly(1,:))~=2
poly = [poly; poly(1,:)];
end
# number of vertices of the polygon
N = size(poly, 1)-1;
# find lines parallel to polygon edges located at distance DIST
lines = zeros(N, 4);
for i=1:N
side = createLine(poly(i,:), poly(i+1,:));
lines(i, 1:4) = parallelLine(side, dist);
end
# compute intersection points of consecutive lines
lines = [lines;lines(1,:)];
poly2 = zeros(N, 2);
for i=1:N
poly2(i,1:2) = intersectLines(lines(i,:), lines(i+1,:));
end
# split result polygon into set of loops (simple polygons)
loops = polygonLoops(poly2);
# keep only loops whose distance to original polygon is correct
distLoop = zeros(length(loops), 1);
for i=1:length(loops)
distLoop(i) = distancePolygons(loops{i}, poly);
end
loops = loops(abs(distLoop-abs(dist))<abs(dist)/1000);
endfunction
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