calc_distance_3D_point_from_linesegment

% distance of a point T to line segment K(X,Y)

 Usage:
   dist = calc_distance_3D_point_from_linesegment(T,X,Y)

   T, X, Y - 3D points, euclidean
   dist    - double, shortest distance from T to segment X-Y 

 Wolfgang Förstner
 wfoerstn@uni-bonn.de 

 See also calc_distance_3D_point_from_3D_line, calc_distance_3D_point_from_triangle

0001 %% distance of a point T to line segment K(X,Y)
0002 %
0003 % Usage:
0004 %   dist = calc_distance_3D_point_from_linesegment(T,X,Y)
0005 %
0006 %   T, X, Y - 3D points, euclidean
0007 %   dist    - double, shortest distance from T to segment X-Y
0008 %
0009 % Wolfgang Förstner
0010 % wfoerstn@uni-bonn.de
0011 %
0012 % See also calc_distance_3D_point_from_3D_line, calc_distance_3D_point_from_triangle
0013 
0014 function dist = calc_distance_3D_point_from_linesegment(T,X,Y)
0015 
0016 % direction
0017 Lh = Y - X;
0018 t = (T-X)'*Lh/norm(Lh)^2;
0019 if t < 0
0020     dist = norm(T - X);
0021 else
0022     if t>1
0023         dist = norm(T - Y);
0024     else
0025         L0   = cross(X,Y);
0026         dist = norm(cross( T,Lh)-L0)/norm(Lh);
0027     end
0028 end
0029