Computational topology for reconstruction of surfaces with boundary: integrating experiments and theory

We report new techniques and theory in computational topology for reconstructing surfaces with boundary. This complements and extends known techniques for surfaces without boundary. Our approach is motivated by differential geometry and differential topology. We have also conducted significant experimental work to test our resultant implementations. We discuss some problematic issues that can arise regarding the roles of the medial axis and sampling density. The crucial topics for C2 manifolds are (1) important defining properties of C2 manifolds with boundary, (2) creation of auxiliary surfaces, with emphasis near the boundary,(3) sampling density, and (4) successful practical algorithms and examples.