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## Copyright (C) 2024 David Legland
## 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
## documentation and/or other materials provided with the distribution.
##
## 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
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function [points, edgeInds, linePositions] = 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.
%
% [P, INDS, POS] = intersectLinePolygon(...)
% Also returns the relative position of each intersection point along the
% line. The position can be used to sort the points.
%
% 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
%
% % Potentially prolematic case
% % create a polygon with various configurations at y=50
% poly = [10 30;30 50;45 30; 50 50; 60 70; 70 50; ...
% 90 30; 80 80; 50 80; 40 50; 30 80; 20 80];
% figure; axis([0 100 0 100]); hold on;
% drawPolygon(poly, 'b'); drawPoint(poly, 'b.');
% % Computes intersection with horizontal line at y=50
% line = [10 50 2 0]; drawLine(line, 'm');
% points = intersectLinePolygon(line, poly);
% % result is a 6-by-2 numeric array, with a double intersection
% % (indices 2 and 3), resulting in five displayed intersections.
% drawPoint(points, 'ko');
% % sort intersection points according to x-coordinate
% points2 = sortrows(points, 1);
% % display pairs of successive intersection points as colored lines
% for i = 1:2:size(points2, 1)
% drawEdge(points2(i,:), points2(i+1,:), 'linewidth', 2);
% end
%
% References
% https://web.cs.ucdavis.edu/~ma/ECS175_S00/Notes/0411_b.pdf
% https://alienryderflex.com/polygon_fill/
%
% See also
% lines2d, polygons2d, intersectLines, intersectRayPolygon, polygonEdges
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2003-10-31, using Matlab 7.9.0.529 (R2009b)
% Copyright 2003-2023 INRA - Cepia Software Platform
% line origin and angle
ox = line(1);
oy = line(2);
dx = line(3);
dy = line(4);
% create transform matrix that project line onto the horizontal axis
% (then, computation of intersections rely only on the y-coordinate)
theta = atan2(dy, dx);
s = hypot(dx, dy);
cot = cos(theta) / s;
sit = sin(theta) / s;
transfo = [cot sit 0; -sit cot 0; 0 0 1] * [1 0 -ox; 0 1 -oy; 0 0 1];
% number of vertices in polygon
nVertices = size(poly, 1);
% create arrays for storing x-coordinates and edge inds of intersections
linePositions = [];
edgeInds = [];
% retrieve previous vertex and its y-coordinate
ivp = nVertices;
previousVertex = transformPoint(poly(ivp,:), transfo);
yvp = previousVertex(2);
% iterate over indices of first edge vertex
for iv = 1:nVertices
% current vertex and its y-coordinate
currentVertex = transformPoint(poly(iv,:), transfo);
yv = currentVertex(2);
% check conditions for intersection
% either if:
% 1) previous vertex is above or on, and current vertex is strictly below
% 2) previous vertex is strictly below, and current vertex is above or on
if yvp >= 0 && yv < 0 || yvp < 0 && yv >= 0
% slope of current edge (dy cannot be zero due to above condition)
edgeDx = currentVertex(1) - previousVertex(1);
edgeDy = currentVertex(2) - previousVertex(2);
% position of intersection on the horizontal line
currentPos = currentVertex(1) - yv * edgeDx / edgeDy ;
% add to list of intersections
linePositions = [linePositions ; currentPos]; %#ok<AGROW>
% keep list if edge indices
edgeInds = [edgeInds ; ivp]; %#ok<AGROW>
end
% switch current vertex to previous vertex
previousVertex = currentVertex;
ivp = iv; % keep edge index for optional output
yvp = yv;
end
% format output result into a N-by-2 array of points
if ~isempty(linePositions)
points = [linePositions zeros(size(linePositions))];
points = transformPoint(points, inv(transfo));
else
points = [];
end
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