function [intersects edgeIndices] = intersectLinePolygon(line, poly, varargin)
%INTERSECTLINEPOLYGON Intersection points between a line and a polygon
%
% P = intersectLinePolygon(LINE, POLY)
% Returns the intersection points of the lines LINE with polygon POLY.
% LINE is a 1-by-4 row vector containing parametric representation of the
% line (in the format [x0 y0 dx dy], see the function 'createLine' for
% details).
% POLY is a NV-by-2 array containing coordinates of the polygon vertices
% P is a K-by-2 array containing the coordinates of the K intersection
% points.
%
% P = intersectLinePolygon(LINE, POLY, TOL)
% Specifies the tolerance for geometric tests. Default is 1e-14.
%
% [P INDS] = intersectLinePolygon(...)
% Also returns the indices of edges involved in intersections. INDS is a
% K-by-1 column vector, such that P(i,:) corresponds to intersection of
% the line with the i-th edge of the polygon. If the intersection occurs
% at a polygon vertex, the index of only one of the two neighbor edges is
% returned.
% Note that due to numerical approximations, the use of function
% 'isPointOnEdge' may give results not consistent with this function.
%
%
% Examples
% % compute intersections between a square and an horizontal line
% poly = [0 0;10 0;10 10;0 10];
% line = [5 5 1 0];
% intersectLinePolygon(line, poly)
% ans =
% 10 5
% 0 5
% % also return indices of edges
% [inters inds] = intersectLinePolygon(line, poly)
% inters =
% 10 5
% 0 5
% inds =
% 4
% 2
%
% % compute intersections between a square and a diagonal line
% poly = [0 0;10 0;10 10;0 10];
% line = [5 5 1 1];
% intersectLinePolygon(line, poly)
% ans =
% 0 0
% 10 10
%
% See Also
% lines2d, polygons2d, intersectLines, intersectRayPolygon
%
% ---------
% author : David Legland
% INRA - TPV URPOI - BIA IMASTE
% created the 31/10/2003.
%
% HISTORY
% 2008-11-24 rename 'pi' as 'intersects', update doc
% 2009-07-23 removed forgotten occurence of 'pi' variable (thanks to Bala
% Krishnamoorthy)
% 2010-01-26 rewrite using vectorisation
% 2011-05-20 returns unique results
% 2011-07-20 returns intersected edge indices
% 2012-11-33 add 'diag' option for linePosition
% get computation tolerance
tol = 1e-14;
if ~isempty(varargin)
tol = varargin{1};
end
% create the array of edges
N = size(poly, 1);
edges = [poly(1:N, :) poly([2:N 1], :)];
% compute intersections with supporting lines of polygon edges
supportLines = edgeToLine(edges);
intersects = intersectLines(line, supportLines, tol);
% find edges that are not parallel to the input line
inds = find(isfinite(intersects(:, 1)));
% compute position of intersection points on corresponding lines
pos = linePosition(intersects(inds, :), supportLines(inds, :), 'diag');
% and keep only intersection points located on edges
b = pos > -tol & pos < 1+tol;
inds = inds(b);
intersects = intersects(inds, :);
% remove multiple vertices (can occur for intersections located at polygon
% vertices)
[intersects I J] = unique(intersects, 'rows'); %#ok<NASGU>
if nargout > 1
% return indices of edges involved in intersection
% (in case of intersection located at a vertex, only one of the
% neighbor edges is returned)
edgeIndices = inds(I);
end