intersectLinePolygon3d

INTERSECTLINEPOLYGON3D Intersection point of a 3D line and a 3D polygon.

   INTER = intersectLinePolygon3d(LINE, POLY)
   Compute coordinates of intersection point between the 3D line LINE and
   the 3D polygon POLY. LINE is a 1-by-6 row vector containing origin and
   direction vector of the line, POLY is a Np-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 line and polygon do not intersect.

   INTERS = intersectLinePolygon3d(LINES, POLY)
   If LINES is a N-by-6 array representing several lines, the result
   INTERS is a N-by-3 array containing coordinates of intersection of each
   line with the polygon.

   [INTER INSIDE] = intersectLinePolygon3d(LINE, POLY)
   Also return a N-by-1 boolean array containing TRUE if the corresponding
   polygon contains the intersection point.

   Example
     % Compute intersection between a 3D line and a 3D triangle
     pts3d = [3 0 0; 0 6 0;0 0 9];
     line1 = [0 0 0 3 6 9];
     inter = intersectLinePolygon3d(line1, pts3d)
     inter =
           1   2   3

     % keep only valid intersections with several lines
     pts3d = [3 0 0; 0 6 0;0 0 9];
     lines = [0 0 0 1 2 3;10 0 0 1 2 3];
     [inter inside] = intersectLinePolygon3d(line1, pts3d);
     inter(inside, :)
     ans = 
           1   2   3

   See Also
   intersectLinePolygon, intersectRayPolygon3d, intersectLinePlane

0001 function [inter, inside]= intersectLinePolygon3d(line, poly)
0002 %INTERSECTLINEPOLYGON3D Intersection point of a 3D line and a 3D polygon.
0003 %
0004 %   INTER = intersectLinePolygon3d(LINE, POLY)
0005 %   Compute coordinates of intersection point between the 3D line LINE and
0006 %   the 3D polygon POLY. LINE is a 1-by-6 row vector containing origin and
0007 %   direction vector of the line, POLY is a Np-by-3 array containing
0008 %   coordinates of 3D polygon vertices.
0009 %   INTER is a 1-by-3 row vector containing coordinates of intersection
0010 %   point, or [NaN NaN NaN] if line and polygon do not intersect.
0011 %
0012 %   INTERS = intersectLinePolygon3d(LINES, POLY)
0013 %   If LINES is a N-by-6 array representing several lines, the result
0014 %   INTERS is a N-by-3 array containing coordinates of intersection of each
0015 %   line with the polygon.
0016 %
0017 %   [INTER INSIDE] = intersectLinePolygon3d(LINE, POLY)
0018 %   Also return a N-by-1 boolean array containing TRUE if the corresponding
0019 %   polygon contains the intersection point.
0020 %
0021 %   Example
0022 %     % Compute intersection between a 3D line and a 3D triangle
0023 %     pts3d = [3 0 0; 0 6 0;0 0 9];
0024 %     line1 = [0 0 0 3 6 9];
0025 %     inter = intersectLinePolygon3d(line1, pts3d)
0026 %     inter =
0027 %           1   2   3
0028 %
0029 %     % keep only valid intersections with several lines
0030 %     pts3d = [3 0 0; 0 6 0;0 0 9];
0031 %     lines = [0 0 0 1 2 3;10 0 0 1 2 3];
0032 %     [inter inside] = intersectLinePolygon3d(line1, pts3d);
0033 %     inter(inside, :)
0034 %     ans =
0035 %           1   2   3
0036 %
0037 %   See Also
0038 %   intersectLinePolygon, intersectRayPolygon3d, intersectLinePlane
0039 %
0040 
0041 % ------
0042 % Author: David Legland
0043 % e-mail: david.legland@grignon.inra.fr
0044 % Created: 2011-05-22,    using Matlab 7.9.0.529 (R2009b)
0045 % Copyright 2011 INRA - Cepia Software Platform.
0046 
0047 % supporting plane of polygon vertices
0048 plane = createPlane(poly(1:3, :));
0049 
0050 % intersection of 3D line with the plane
0051 inter = intersectLinePlane(line, plane);
0052 
0053 % project all points on reference plane
0054 pts2d = planePosition(poly, plane);
0055 pInt2d = planePosition(inter, plane);
0056 
0057 % need to check polygon orientation
0058 inside = xor(isPointInPolygon(pInt2d, pts2d), polygonArea(pts2d) < 0);
0059 
0060 % intersection points outside the polygon are set to NaN
0061 inter(~inside, :) = NaN;