function pos = linePosition3d(point, line)
%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.
% 05/01/2007 update doc
% 28/10/2010 change to bsxfun calculation for arbitrary input sizes
% (Thanks to Sven Holcombe)
% vector from line origin to point
dp = bsxfun(@minus, point, line(:,1:3));
% direction vector of the line
vl = line(:, 4:6);
% precompute and check validity of denominator
denom = sum(vl.^2, 2);
invalidLine = denom < eps;
denom(invalidLine) = 1;
% compute position using dot product normalized with norm of line vector.
pos = bsxfun(@rdivide, sum(bsxfun(@times, dp, vl), 2), denom);
% position on a degenerated line is set to 0
pos(invalidLine) = 0;