projPointOnLine3d

PROJPOINTONLINE3D Project a 3D point orthogonally onto a 3D line.

   PT2 = projPointOnLine3d(PT, LINE).
   Computes the (orthogonal) projection of 3D point PT onto the 3D line
   LINE. 
   
   Function works also for multiple points and lines. In this case, it
   returns multiple points.
   Point PT1 is a N-by-3 array, and LINE is a N-by-6 array.
   Result PT2 is a N-by-3 array, containing coordinates of orthogonal
   projections of PT1 onto lines LINE. 


   See also:
   projPointOnLine, distancePointLine3d

   ---------
   author : David Legland
   INRA - TPV URPOI - BIA IMASTE
   created the 2012-08-23.

0001 function point = projPointOnLine3d(point, line)
0002 %PROJPOINTONLINE3D Project a 3D point orthogonally onto a 3D line.
0003 %
0004 %   PT2 = projPointOnLine3d(PT, LINE).
0005 %   Computes the (orthogonal) projection of 3D point PT onto the 3D line
0006 %   LINE.
0007 %
0008 %   Function works also for multiple points and lines. In this case, it
0009 %   returns multiple points.
0010 %   Point PT1 is a N-by-3 array, and LINE is a N-by-6 array.
0011 %   Result PT2 is a N-by-3 array, containing coordinates of orthogonal
0012 %   projections of PT1 onto lines LINE.
0013 %
0014 %
0015 %   See also:
0016 %   projPointOnLine, distancePointLine3d
0017 %
0018 %   ---------
0019 %   author : David Legland
0020 %   INRA - TPV URPOI - BIA IMASTE
0021 %   created the 2012-08-23.
0022 %
0023 
0024 %   HISTORY
0025 
0026 % direction vector of the line
0027 vx = line(:, 4);
0028 vy = line(:, 5);
0029 vz = line(:, 6);
0030 
0031 % difference of point with line origin
0032 dx = point(:,1) - line(:,1);
0033 dy = point(:,2) - line(:,2);
0034 dz = point(:,3) - line(:,3);
0035 
0036 % Position of projection on line, using dot product
0037 delta = vx .* vx + vy .* vy + vz .* vz;
0038 tp = (dx .* vx + dy .* vy + dz .* vz) ./ delta;
0039 
0040 % convert position on line to cartesian coordinates
0041 point = [line(:,1) + tp .* vx, line(:,2) + tp .* vy, line(:,3) + tp .* vz];