calc_intersect_3D_Lines2Point

% intersection point X of two coplanar 3D-lines L and M 
 precondition: lines are not equal

 Usage:
   X = calc_intersect_3D_Lines2Point(L,M)

   L, M - 6x1 Plücker Lines
   X    - 4x1 homogeneous 3D point

 Wolfgang Förstner
 wfoerstn@uni-bonn.de 

 See also calc_intersect_3D_Lines2Point_finite
 calc_join_3D_Lines2Plane, calc_join_3D_Lines2Plane_finite

0001 %% intersection point X of two coplanar 3D-lines L and M
0002 % precondition: lines are not equal
0003 %
0004 % Usage:
0005 %   X = calc_intersect_3D_Lines2Point(L,M)
0006 %
0007 %   L, M - 6x1 Plücker Lines
0008 %   X    - 4x1 homogeneous 3D point
0009 %
0010 % Wolfgang Förstner
0011 % wfoerstn@uni-bonn.de
0012 %
0013 % See also calc_intersect_3D_Lines2Point_finite
0014 % calc_join_3D_Lines2Plane, calc_join_3D_Lines2Plane_finite
0015 
0016 function X = calc_intersect_3D_Lines2Point(L,M)
0017 
0018 % matrix for constraints Gammadual(L)*X=0, ...
0019 T = [calc_Gammadual(L);...
0020      calc_Gammadual(M)];
0021 
0022 % nullspace of T yields the target point X
0023 [~,~,V] = svd(T);
0024 
0025 X = V(:,4);