linePosition3d

 Return the position of a 3D point projected on a 3D line.

   T = linePosition3d(POINT, LINE)
   Computes position of point POINT on the line LINE, relative to origin
   point and direction vector of the line.
   LINE has the form [x0 y0 z0 dx dy dy],
   POINT has the form [x y z], and is assumed to belong to line.
   The result T is the value such that POINT = LINE(1:3) + T * LINE(4:6).
   If POINT does not belong to LINE, the position of its orthogonal
   projection is computed instead. 

   T = linePosition3d(POINT, LINES)
   If LINES is an array of NL lines, return NL positions, corresponding to
   each line.

   T = linePosition3d(POINTS, LINE)
   If POINTS is an array of NP points, return NP positions, corresponding
   to each point.

   See also:
   lines3d, createLine3d, distancePointLine3d, projPointOnLine3d

   ---------
   author : David Legland
   INRA - TPV URPOI - BIA IMASTE
   created the 17/02/2005.

0001 function pos = linePosition3d(point, line)
0002 % Return the position of a 3D point projected on a 3D line.
0003 %
0004 %   T = linePosition3d(POINT, LINE)
0005 %   Computes position of point POINT on the line LINE, relative to origin
0006 %   point and direction vector of the line.
0007 %   LINE has the form [x0 y0 z0 dx dy dy],
0008 %   POINT has the form [x y z], and is assumed to belong to line.
0009 %   The result T is the value such that POINT = LINE(1:3) + T * LINE(4:6).
0010 %   If POINT does not belong to LINE, the position of its orthogonal
0011 %   projection is computed instead.
0012 %
0013 %   T = linePosition3d(POINT, LINES)
0014 %   If LINES is an array of NL lines, return NL positions, corresponding to
0015 %   each line.
0016 %
0017 %   T = linePosition3d(POINTS, LINE)
0018 %   If POINTS is an array of NP points, return NP positions, corresponding
0019 %   to each point.
0020 %
0021 %   See also:
0022 %   lines3d, createLine3d, distancePointLine3d, projPointOnLine3d
0023 %
0024 %   ---------
0025 %   author : David Legland
0026 %   INRA - TPV URPOI - BIA IMASTE
0027 %   created the 17/02/2005.
0028 %
0029 
0030 %   HISTORY
0031 %   05/01/2007 update doc
0032 %   28/10/2010 change to bsxfun calculation for arbitrary input sizes
0033 %       (Thanks to Sven Holcombe)
0034 
0035 % size of input arguments
0036 np = size(point, 1);
0037 nl = size(line, 1);
0038 
0039 if np == 1 || nl == 1 || np == nl
0040     % standard case where result is either scalar or vector
0041     
0042     % vector from line origin to point
0043     dp = bsxfun(@minus, point, line(:,1:3));
0044     
0045     % direction vector of the line
0046     vl = line(:, 4:6);
0047     
0048     % precompute and check validity of denominator
0049     denom = sum(vl.^2, 2);
0050     invalidLine = denom < eps;
0051     denom(invalidLine) = 1;
0052     
0053     % compute position using dot product normalized with norm of line vector.
0054     pos = bsxfun(@rdivide, sum(bsxfun(@times, dp, vl), 2), denom);
0055     
0056     % position on a degenerated line is set to 0
0057     pos(invalidLine) = 0;
0058 
0059 else
0060     % reshape input
0061     point = reshape(point, [np 1 3]);
0062     line = reshape(line, [1 nl 6]);
0063     
0064     % vector from line origin to point
0065     dp = bsxfun(@minus, point, line(:,:,1:3));
0066     
0067     % direction vector of the line
0068     vl = line(:, :, 4:6);
0069     
0070     % precompute and check validity of denominator
0071     denom = sum(vl.^2, 3);
0072     invalidLine = denom < eps;
0073     denom(invalidLine) = 1;
0074     
0075     % compute position using dot product normalized with norm of line vector.
0076     pos = bsxfun(@rdivide, sum(bsxfun(@times, dp, vl), 3), denom);
0077     
0078     % position on a degenerated line is set to 0
0079     pos(invalidLine) = 0;
0080 end