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## Copyright (C) 2024 David Legland
## All rights reserved.
##
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function [inter, valid] = intersectEdgePolygon3d(edge, poly)
%INTERSECTEDGEPOLYGON3D Intersection point of a 3D edge segment and a 3D polygon.
%
% INTER = intersectEdgePolygon3d(EDGE, POLY)
% Compute coordinates of intersection point between the 3D edge EDGE and
% the 3D polygon POLY. EDGE is a 1-by-6 row vector containing source and
% target positions of the edge, POLY is a Nv-by-3 array containing
% coordinates of 3D polygon vertices.
% INTER is a 1-by-3 row vector containing coordinates of intersection
% point, or [NaN NaN NaN] if edge and polygon do not intersect.
%
% INTERS = intersectEdgePolygon3d(EDGES, POLY)
% If EDGES is a N-by-6 array representing several edges, the result
% INTERS is a N-by-3 array containing coordinates of intersection of each
% edge with the polygon.
%
% [INTER, INSIDE] = intersectEdgePolygon3d(EDGE, POLY)
% Also return a N-by-1 boolean array containing TRUE if the corresponding
% edge contains the intersection point.
%
% Example
% % Compute intersection between a 3D edge and a 3D triangle
% pts3d = [3 0 0; 0 6 0;0 0 9];
% edge1 = [0 0 0 3 6 9];
% inter = intersectEdgePolygon3d(edge1, pts3d)
% inter =
% 1 2 3
%
% % keep only valid intersections with several edges
% pts3d = [3 0 0; 0 6 0;0 0 9];
% edges = [0 0 0 3 6 9;10 0 0 10 2 3];
% [inter, inside] = intersectEdgePolygon3d(edges, pts3d);
% inter(inside, :)
% ans =
% 1 2 3
%
% See also
% intersectLinePolygon, intersectRayPolygon3d, intersectLinePlane
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2011-05-22, using Matlab 7.9.0.529 (R2009b)
% Copyright 2011-2023 INRA - Cepia Software Platform
% supporting plane of polygon vertices
plane = createPlane(poly(1:3, :));
% intersection of edge supporting line with the plane
line = edgeToLine3d(edge);
inter = intersectLinePlane(line, plane);
onEdge = isPointOnEdge3d(inter, edge);
% project all points on reference plane
pts2d = planePosition(poly, plane);
pInt2d = planePosition(inter, plane);
% need to check polygon orientation
insidePoly = xor(isPointInPolygon(pInt2d, pts2d), polygonArea(pts2d) < 0);
% intersection points either outside the polygon on outside the edge bounds
% are set to NaN
valid = insidePoly & onEdge;
inter(~valid, :) = NaN;
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