Triangulation of 3D surfaces

I have a series of data points which describe a surface, i.e. in 3 dimensions. I understand that there is an algorithm, the Delaunay three dimensional algorithm for triangulating the surface. Now it comes down to the question of generating tetrahedrals and a circumscribing sphere where none of the other data points are contained within the sphere.

However whilst I can determine whether points exist or not within the sphere. I have no clear algorithm for determination of a contiguous surface. I don't care about efficiency. Does anyone have any idea about how to proceed??

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