/usr/share/octave/packages/geometry-1.7.0/polygons2d/medialAxisConvex.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
## notice, this list of conditions and the following disclaimer in the
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##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
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## -*- texinfo -*-
## @deftypefn {Function File} {[@var{n} @var{e}] = } medialAxisConvex (@var{polygon})
## Compute medial axis of a convex polygon
##
## @var{polygon} is given as a set of points [x1 y1;x2 y2 ...], returns
## the medial axis of the polygon as a graph.
## @var{n} is a set of nodes. The first elements of @var{n} are the vertices of the
## original polygon.
## @var{e} is a set of edges, containing indices of source and target nodes.
## Edges are sorted according to order of creation. Index of first vertex
## is lower than index of last vertex, i.e. edges always point to newly
## created nodes.
##
## Notes:
## - Is not fully implemented, need more development (usually crashes for
## polygons with more than 6-7 points...)
## - Works only for convex polygons.
## - Complexity is not optimal: this algorithm is O(n*log n), but linear
## algorithms exist.
##
## @seealso{polygons2d, bisector}
## @end deftypefn
function [nodes, edges] = medialAxisConvex(points)
# eventually remove the last point if it is the same as the first one
if points(1,:) == points(end, :)
nodes = points(1:end-1, :);
else
nodes = points;
end
# special case of triangles:
# compute directly the gravity center, and simplify computation.
if size(nodes, 1)==3
nodes = [nodes; mean(nodes, 1)];
edges = [1 4;2 4;3 4];
return
end
# number of nodes, and also of initial rays
N = size(nodes, 1);
# create ray of each vertex
rays = zeros(N, 4);
rays(1, 1:4) = bisector(nodes([2 1 N], :));
rays(N, 1:4) = bisector(nodes([1 N N-1], :));
for i=2:N-1
rays(i, 1:4) = bisector(nodes([i+1, i, i-1], :));
end
# add indices of edges producing rays (indices of first vertex, second
# vertex is obtained by adding one modulo N).
rayEdges = [[N (1:N-1)]' (1:N)'];
pint = intersectLines(rays, rays([2:N 1], :));
#ti = linePosition(pint, rays);
#ti = min(linePosition(pint, rays), linePosition(pint, rays([2:N 1], :)));
ti = distancePointLine(pint, ...
createLine(points([N (1:N-1)]', :), points((1:N)', :)));
# create list of events.
# terms are : R1 R2 X Y t0
# R1 and R2 are indices of involved rays
# X and Y is coordinate of intersection point
# t0 is position of point on rays
events = sortrows([ (1:N)' [2:N 1]' pint ti], 5);
# initialize edges
edges = zeros(0, 2);
# -------------------
# process each event until there is no more
# start after index of last vertex, and process N-3 intermediate rays
for i=N+1:2*N-3
# add new node at the rays intersection
nodes(i,:) = events(1, 3:4);
# add new couple of edges
edges = [edges; events(1,1) i; events(1,2) i];
# find the two edges creating the new emanating ray
n1 = rayEdges(events(1, 1), 1);
n2 = rayEdges(events(1, 2), 2);
# create the new ray
line1 = createLine(nodes(n1, :), nodes(mod(n1,N)+1, :));
line2 = createLine(nodes(mod(n2,N)+1, :), nodes(n2, :));
ray0 = bisector(line1, line2);
# set its origin to emanating point
ray0(1:2) = nodes(i, :);
# add the new ray to the list
rays = [rays; ray0];
rayEdges(size(rayEdges, 1)+1, 1:2) = [n1 n2];
# find the two neighbour rays
ind = sum(ismember(events(:,1:2), events(1, 1:2)), 2)==0;
ir = unique(events(ind, 1:2));
ir = ir(~ismember(ir, events(1,1:2)));
# create new intersections
pint = intersectLines(ray0, rays(ir, :));
#ti = min(linePosition(pint, ray0), linePosition(pint, rays(ir, :))) + events(1,5);
ti = distancePointLine(pint, line1);
# remove all events involving old intersected rays
ind = sum(ismember(events(:,1:2), events(1, 1:2)), 2)==0;
events = events(ind, :);
# add the newly formed events
events = [events; ir(1) i pint(1,:) ti(1); ir(2) i pint(2,:) ti(2)];
# and sort them according to 'position' parameter
events = sortrows(events, 5);
end
# centroid computation for last 3 rays
nodes = [nodes; mean(events(:, 3:4))];
edges = [edges; [unique(events(:,1:2)) ones(3, 1)*(2*N-2)]];
endfunction
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