MATLAB: What is the maximum diameter of convex polygons

convexhull

is it the maximum distance between the vertices or something else ?

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This is not a question about MATLAB, but since it already has an answer...

Yes. You should be able to prove that the maximal diameter must lie between two vertices of the polygonal region. I would do that by starting with a pair of parallel lines in the plane that do not intersect the polygon, but contain the polygon between them. You can move them closer together, until they just touch the polygonal region. Clearly that event will happen when one or more of the vertices of the polygon lie along each of the parallel enclosing lines. The diameter of the polygon in that direction is just the distance between the lines.

Now rotate the lines you would consider, implicitly creating a function of the dameter of the polygon at any rotation angle. Clearly this function is continuous, though not differentiable. Still it will have a well defined maximum. That maximum need not be unique (consider a square).

In the end, you will have shown that the maximum diameter will be given by the maximum Euclidean distance between any pair of vertices of the polygon, so pdist, applied to the polygonal vertices, will suffice.

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MATLAB: Convert a tetrahedron mesh to triangular mesh or surface mesh.

Easy. Assume that tess is an nx4 array, composed of references into the set of vertices.

Then surely is it true that:

facets = [tess(:,[1 2 3]);tess(:,[1 2 4]);tess(:,[1 3 4]);tess(:,[2 3 4])];

is a set of facets of those simplexes? So facets is the set of triangular facets as requested. But I think you asked for the outer boundary surface of the mesh.

The only problem is that some of those facets are replicated. That is, facets that are shared between a pair of touching simplexes will happen exactly twice. A facet that is on the surface will occur exactly once.

But in fact, these replicates are actually a good thing! If you are only looking for the surface triangulation, then you can discard those facets that occurred twice. It is important to sort them though. (Think! why?)

facets = sort(facets,2);

Now, how do we discard those duplicated?

facets = sortrows(facets);
duploc = find(all(diff(facets) == 0,2));
facets([duploc;duploc + 1],:) = [];

MATLAB: To calculate or estimate a center of a convex hull

FEX has (at least) one

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MATLAB: Convert a tetrahedron mesh to triangular mesh or surface mesh.

MATLAB: To calculate or estimate a center of a convex hull

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