isPointOnLine3d

ISPOINTONLINE3D Test if a 3D point belongs to a 3D line.

   B = isPointOnLine3d(POINT, LINE)
   with POINT being [xp yp zp], and LINE being [x0 y0 z0 dx dy dz].
   Returns 1 if point lies on the line, 0 otherwise.

   If POINT is an N-by-3 array of points, B is a N-by-1 array of booleans.

   If LINE is a N-by-6 array of lines, B is a N-by-1 array of booleans.

   B = isPointOnLine3d(POINT, LINE, TOL)
   Specifies the tolerance used for testing location on 3D line.

   See also:
   lines3d, distancePointLine3d, linePosition3d, isPointOnLine

0001 function b = isPointOnLine3d(point, line, varargin)
0002 %ISPOINTONLINE3D Test if a 3D point belongs to a 3D line.
0003 %
0004 %   B = isPointOnLine3d(POINT, LINE)
0005 %   with POINT being [xp yp zp], and LINE being [x0 y0 z0 dx dy dz].
0006 %   Returns 1 if point lies on the line, 0 otherwise.
0007 %
0008 %   If POINT is an N-by-3 array of points, B is a N-by-1 array of booleans.
0009 %
0010 %   If LINE is a N-by-6 array of lines, B is a N-by-1 array of booleans.
0011 %
0012 %   B = isPointOnLine3d(POINT, LINE, TOL)
0013 %   Specifies the tolerance used for testing location on 3D line.
0014 %
0015 %   See also:
0016 %   lines3d, distancePointLine3d, linePosition3d, isPointOnLine
0017 %
0018 
0019 % ---------
0020 % author : David Legland
0021 % e-mail: david.legland@inra.fr
0022 % INRA - TPV URPOI - BIA IMASTE
0023 % created the 31/10/2003.
0024 %
0025 
0026 %   HISTORY
0027 %   17/12/2013 create from isPointOnLine
0028 
0029 % extract computation tolerance
0030 tol = 1e-14;
0031 if ~isempty(varargin)
0032     tol = varargin{1};
0033 end
0034 
0035 % size of inputs
0036 np = size(point,1);
0037 nl = size(line, 1);
0038 
0039 if np == 1 || nl == 1 || np == nl
0040     % test if lines are colinear, using norm of the cross product
0041     b = bsxfun(@rdivide, vectorNorm3d( ...
0042         crossProduct3d(bsxfun(@minus, line(:,1:3), point), line(:,4:6))), ...
0043         vectorNorm3d(line(:,4:6))) < tol;
0044 else
0045     % same test, but after reshaping arrays to manage difference of
0046     % dimensionality
0047     point = reshape(point, [np 1 3]);
0048     line = reshape(line, [1 nl 6]);
0049     b = bsxfun(@rdivide, vectorNorm3d( ...
0050         cross(bsxfun(@minus, line(:,:,1:3), point), line(ones(1,np),:,4:6), 3)), ...
0051         vectorNorm3d(line(:,:,4:6))) < tol;
0052 end