We present a simple and fast algorithm for computing the exact holes in discrete two-dimensional manifolds embedded in a three-dimensional Euclidean space. We deal with the intentionally created “through holes” or “tunnel holes” in the geometry as opposed to missing triangles. The algorithm detects the holes in the geometry directly without any simplified geometry approximation. Discrete Gaussian curvature is used for approximating the local curvature flow in the geometry and for removing outliers from the collection of feature edges. We present an algorithm with varying degrees of flexibility. The algorithm is demonstrated separately for sheets and solid geometries. This article demonstrates the algorithm on triangulated surfaces. However, the algorithm and the underlying data structure are also applicable for surfaces with mixed polygons.