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We present a new method for extracting the feature primitives of a 3D object directly from the point cloud of its surface scan. The objective is to identify a subset of points that provides the same information about the structure and the topology of the object geometry as the point cloud itself. The entire process is carried out with the least human intervention possible. The only information we receive as input is the point cloud of the 3D scan of the object. First, the point cloud is sliced in cross sections. Each cross section consists of a 2D point cloud. A collection of curve patches is derived for each slice, describing the cross section, and providing a featurebased CAD model appropriate for further editing. For the extraction of the feature points and the interpolating curve patches we use properties of the convex hull and the voronoi diagram of the point cloud.