calc_join_3D_Lines2Plane

% plane through two 3D-lines L and M 
 precondition: lines are coplanar and not equal

 Usage:
   A = calc_join_3D_Lines2Plane(L,M)

   L, M - 6x1 Plücker Lines
   A    - 4x1 plane

 Wolfgang Förstner
 wfoerstn@uni-bonn.de 

 See also calc_intersect_3D_Lines2Point, calc_intersect_3D_Lines2Point_finite
 calc_join_3D_Lines2Plane_finite

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