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    <p>If your surface enclosing the points can be described as a <a href="http://mathworld.wolfram.com/ConvexPolyhedron.html" rel="noreferrer">convex polyhedron</a> (i.e. like the surface of a cube or a <a href="http://en.wikipedia.org/wiki/Dodecahedron" rel="noreferrer">dodecahedron</a>, without concave pits or <a href="http://en.wikipedia.org/wiki/Small_stellated_dodecahedron" rel="noreferrer">jagged pointy parts</a>), then I would start by creating a 3-D <a href="http://www.mathworks.com/help/techdoc/ref/delaunaytriclass.html" rel="noreferrer">Delaunay triangulation</a> of the points. This will fill the volume around the points with a series of tetrahedral elements with the points as their vertices, and you can then find the set of triangular faces that form the outer shell of the volume using the <a href="http://www.mathworks.com/help/techdoc/ref/delaunaytri.convexhull.html" rel="noreferrer"><code>convexHull</code></a> method of the <code>DelaunayTri</code> class.</p> <p>Here's an example that generates 200 random points uniformly distributed within the unit cube, creates a tetrahedral mesh for these points, then finds the 3-D convex hull for the volume:</p> <pre><code>interiorPoints = rand(200,3); %# Generate 200 3-D points DT = DelaunayTri(interiorPoints); %# Create the tetrahedral mesh hullFacets = convexHull(DT); %# Find the facets of the convex hull %# Plot the scattered points: subplot(2,2,1); scatter3(interiorPoints(:,1),interiorPoints(:,2),interiorPoints(:,3),'.'); axis equal; title('Interior points'); %# Plot the tetrahedral mesh: subplot(2,2,2); tetramesh(DT); axis equal; title('Tetrahedral mesh'); %# Plot the 3-D convex hull: subplot(2,2,3); trisurf(hullFacets,DT.X(:,1),DT.X(:,2),DT.X(:,3),'FaceColor','c') axis equal; title('Convex hull'); </code></pre> <p><img src="https://i.stack.imgur.com/qn1P8.png" alt="enter image description here"></p>
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    1. POPlotting a surface from a set of interior 3D scatter points in MATLAB
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    1. COI don't have the latest version of Matlab, but was able to find essentially equivalent versions of the same functions. Unfortunately my surface is not convex, so the methods above obscured some of the important detail. I'll amend my question to clarify this point.
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      1. USAdam Wuerl
 

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