{"id":4797,"date":"2013-09-06T09:00:20","date_gmt":"2013-09-06T13:00:20","guid":{"rendered":"https:\/\/blogs.mathworks.com\/pick\/?p=4797"},"modified":"2013-12-05T13:58:38","modified_gmt":"2013-12-05T18:58:38","slug":"inpolyhedron","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/pick\/2013\/09\/06\/inpolyhedron\/","title":{"rendered":"INPOLYHEDRON"},"content":{"rendered":"
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Sean<\/a>'s pick this week is inpolyhedron<\/a> by Sven<\/a>.\r\n <\/p>\r\n <\/introduction>\r\n

Polygons, Polyhedra and Convexity<\/a><\/h3>\r\n

It's often useful to know if a point is inside of a polygon (two dimensions) and sometimes if a point is inside of a polyhedron\r\n (three dimensions). For two dimensions, MATLAB ships with inpolygon<\/a>, a nice function to handle this. However, this same operation in three dimensions becomes more complicated. It is simplified\r\n if the object is convex. In this case, the vertices can be represented as a set of constraints and we can apply these constraints\r\n to the points to test whether they are inside or not. Matt J<\/a> does this in his vert2lcon<\/a> function (The runner-up, who will also get some MathWorks swag, for this week's post!).\r\n <\/p>\r\n

But what about when the polydehron is not necessarily convex? Now we no longer have this luxury and have to resort to more\r\n complex algorithms.\r\n <\/p>\r\n

Fortunately, Sven has done the work for us!<\/p>\r\n

Let's use Paul's three dimensional L-Shaped Membrane<\/a>.\r\n <\/p>

% Load shellVertices, shellfaces from Paul's Blog:<\/span>\r\nload PaulsMembrane.mat<\/span>\r\n\r\n% Draw the membrane:<\/span>\r\npatch('Vertices'<\/span>,shellVertices,...<\/span>\r\n    'Faces'<\/span>,shellFaces,...<\/span>\r\n    'FaceColor'<\/span>,'r'<\/span>);\r\naxis tight<\/span>\r\nview(-51,24)<\/pre>
 <\/p>\r\n   
Add 10000 random points to it<\/p>
pts = rand([10000,3]); %Generate a random 10000pts<\/span>\r\nhold on<\/span>;\r\nplot3(pts(:,1),pts(:,2),pts(:,3),'b*'<\/span>); %add points to plot<\/span><\/pre>
 <\/p>\r\n   
Find the points in the polyhedron<\/p>
in = inpolyhedron(shellFaces,shellVertices,pts,'FlipNormals'<\/span>,true);\r\ndelete(hLine); %clean up<\/span>\r\nplot3(pts(in,1),pts(in,2),pts(in,3),'b*'<\/span>); %add points to plot<\/span>\r\nset(hPatch,'FaceAlpha'<\/span>,0.3,...<\/span>\r\n    'EdgeColor'<\/span>,'none'<\/span>); %make the points inside visible<\/span><\/pre>
 <\/p>\r\n   
Woohoo!<\/p>\r\n   
Comments<\/a><\/h3>\r\n   
In addition to everything you saw here, there is also excellent help and many options built into inpolyhedron.  Give it a\r\n      try and let us know what you think here<\/a> or leave a comment<\/a> for Sven.\r\n   <\/p>