The shock scaffold is a hierarchical organization of the medial axis in 3D consisting of special medial points and curves connecting these points, thereby forming a geomet-ric directed graph, which is key in applications such as object recognition. In this paper we describe a method for computing the shock scaffold of realistic datasets, which involve tens or hundreds of thousands of points, in a practical time-frame. Our approach is based on propagation along the scaffold from initial sources of flow by considering pairs of input points. We present seven principles which avoid the consideration of those pairs of points which cannot possibly lead to a shock flow; they involve: (i) the "visibility" of a point from another, (ii) the clustering of points, (iii) the visibility of a cluster from another, (iv) the convex hull of a cluster, (v) the vertices of such convex hulls as "virtual" points, (vi) a multi-resolution framework, and, finally, (vii) a search strategy organized in layers.