parallelPlane

PARALLELPLANE Parallel to a plane through a point or at a given distance.

   PL2 = parallelPlane(PL, PT)
   Constructs the plane parallel to plane PL and containing the point PT.

   PL2 = parallelPlane(PL, D)
   Constructs the plane parallel to plane PL, and located at the given
   signed distance D.

   Example
     % Create a plane normal to the 3D vector DIR
     dir = [3 4 5];
     plane = createPlane([3 4 5], dir);
     % Create plane at a specific distance 
     plane2 = parallelPlane(plane, 5);
     % Create a line perpendicular to both planes
     line = [2 4 1 3 4 5];
     pi1 = intersectLinePlane(line, plane);
     pi2 = intersectLinePlane(line, plane2);
     % check the distance between intersection points
     distancePoints3d(pi1, pi2)
     ans = 
         5

   See also
   geom3d, parallelLine3d

 ------
 Author: David Legland
 e-mail: david.legland@grignon.inra.fr
 Created: 2012-08-22,    using Matlab 7.9.0.529 (R2009b)
 Copyright 2012 INRA - Cepia Software Platform.

0001 function res = parallelPlane(plane, point)
0002 %PARALLELPLANE Parallel to a plane through a point or at a given distance.
0003 %
0004 %   PL2 = parallelPlane(PL, PT)
0005 %   Constructs the plane parallel to plane PL and containing the point PT.
0006 %
0007 %   PL2 = parallelPlane(PL, D)
0008 %   Constructs the plane parallel to plane PL, and located at the given
0009 %   signed distance D.
0010 %
0011 %   Example
0012 %     % Create a plane normal to the 3D vector DIR
0013 %     dir = [3 4 5];
0014 %     plane = createPlane([3 4 5], dir);
0015 %     % Create plane at a specific distance
0016 %     plane2 = parallelPlane(plane, 5);
0017 %     % Create a line perpendicular to both planes
0018 %     line = [2 4 1 3 4 5];
0019 %     pi1 = intersectLinePlane(line, plane);
0020 %     pi2 = intersectLinePlane(line, plane2);
0021 %     % check the distance between intersection points
0022 %     distancePoints3d(pi1, pi2)
0023 %     ans =
0024 %         5
0025 %
0026 %   See also
0027 %   geom3d, parallelLine3d
0028 %
0029 % ------
0030 % Author: David Legland
0031 % e-mail: david.legland@grignon.inra.fr
0032 % Created: 2012-08-22,    using Matlab 7.9.0.529 (R2009b)
0033 % Copyright 2012 INRA - Cepia Software Platform.
0034 
0035 if size(point, 2) == 1
0036     % use a distance. Compute position of point located at distance DIST on
0037     % the line normal to the plane.
0038     normal = normalizeVector3d(planeNormal(plane));
0039     point = plane(:, 1:3) + bsxfun(@times, point, normal);
0040 end
0041 
0042 % change origin, and keep direction vectors
0043 res = [point plane(:, 4:9)];