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@inrae.fr
0022 % Created: 2003-10-31
0023 % Copyright 2003-2024 INRA - TPV URPOI - BIA IMASTE
0024 
0025 % extract computation tolerance
0026 tol = 1e-14;
0027 if ~isempty(varargin)
0028     tol = varargin{1};
0029 end
0030 
0031 % size of inputs
0032 np = size(point,1);
0033 nl = size(line, 1);
0034 
0035 if np == 1 || nl == 1 || np == nl
0036     % test if lines are colinear, using norm of the cross product
0037     b = bsxfun(@rdivide, vectorNorm3d( ...
0038         crossProduct3d(bsxfun(@minus, line(:,1:3), point), line(:,4:6))), ...
0039         vectorNorm3d(line(:,4:6))) < tol;
0040 else
0041     % same test, but after reshaping arrays to manage difference of
0042     % dimensionality
0043     point = reshape(point, [np 1 3]);
0044     line = reshape(line, [1 nl 6]);
0045     b = bsxfun(@rdivide, vectorNorm3d( ...
0046         cross(bsxfun(@minus, line(:,:,1:3), point), line(ones(1,np),:,4:6), 3)), ...
0047         vectorNorm3d(line(:,:,4:6))) < tol;
0048 end