Given a finite set of points P sampling an unknown smooth surface M in R3, our goal is to triangulate M based solely on P. Assuming M is a smooth orientable submanifold of codimension 1 in Rd, we introduce a simple algorithm, Naive Squash, which simplifies the alpha-complex of P by repeatedly applying a new type of collapse called vertical relative to M. Naive Squash also has a practical version that does not require knowledge of M. We establish conditions under which both the naive and practical Squash algorithms output a triangulation of M. We provide a bound on the angle formed by triangles in the alpha-complex with M, yielding sampling conditions on P that are competitive with existing literature for smooth surfaces embedded in R3, while offering a more compartmentalized proof. As a by-product, we obtain that the restricted Delaunay complex of P triangulates M when M is a smooth surface in R3 under weaker conditions than existing ones.