isPointInMesh

ISPOINTINMESH Check if a point is inside a 3D mesh.

   B = isPointInMesh(PT, V, F)
   Check if the point PT (given as a 1-by-3 array) is inside the mesh
   defined by the vertices V and the face array F. The result is a
   boolean.

   If PT is a N-by-3 point array, the result is a N-by-1 array of logical.

   Example
     [v, f] = torusMesh([50 50 50 30 10 30 45]);
     [x, y, z] = meshgrid(5:5:100, 5:5:100, 5:5:100);
     res = false(size(x));
     res(:) = isPointInMesh([x(:) y(:) z(:)], v, f);
     figure; plot3(x(res), y(res), z(res), 'b.'); axis equal;

   Algorithm:
   The method computes the intersection with a ray starting from the
   point(s) and with a random orientation. Some errors are possible if
   rays crosses the mesh between two or three faces.

   See also
     meshes3d, intersectLineMesh3d

0001 function res = isPointInMesh(point, v, f, varargin)
0002 %ISPOINTINMESH Check if a point is inside a 3D mesh.
0003 %
0004 %   B = isPointInMesh(PT, V, F)
0005 %   Check if the point PT (given as a 1-by-3 array) is inside the mesh
0006 %   defined by the vertices V and the face array F. The result is a
0007 %   boolean.
0008 %
0009 %   If PT is a N-by-3 point array, the result is a N-by-1 array of logical.
0010 %
0011 %   Example
0012 %     [v, f] = torusMesh([50 50 50 30 10 30 45]);
0013 %     [x, y, z] = meshgrid(5:5:100, 5:5:100, 5:5:100);
0014 %     res = false(size(x));
0015 %     res(:) = isPointInMesh([x(:) y(:) z(:)], v, f);
0016 %     figure; plot3(x(res), y(res), z(res), 'b.'); axis equal;
0017 %
0018 %   Algorithm:
0019 %   The method computes the intersection with a ray starting from the
0020 %   point(s) and with a random orientation. Some errors are possible if
0021 %   rays crosses the mesh between two or three faces.
0022 %
0023 %   See also
0024 %     meshes3d, intersectLineMesh3d
0025  
0026 % ------
0027 % Author: David Legland
0028 % e-mail: david.legland@inra.fr
0029 % Created: 2018-01-26,    using Matlab 9.3.0.713579 (R2017b)
0030 % Copyright 2018 INRA - Cepia Software Platform.
0031 
0032 % choose a random vector
0033 vect = rand(1, 3);
0034 
0035 % initialize array for result
0036 np = size(point, 1);
0037 res = false(np, 1);
0038 
0039 % iterate over the various points
0040 for i = 1:np
0041 %     disp(i);
0042     line = createLine3d(point(i,:), vect);
0043     
0044     [inters, pos] = intersectLineMesh3d(line, v, f); %#ok<ASGLU>
0045     
0046     res(i) = mod(sum(pos > 0), 2) > 0;
0047 end