A method, apparatus, system, article of manufacture, and data structure provide the ability to extract a primitive quadric surface from point cloud data. Point cloud data is obtained in 3D space. The point cloud data is segmented to create a disjoined surface and a smooth surface segment based on spatial connectivity and surface smoothness. One or more shapes are extracted from the point cloud data using geometric fitting. The geometric fitting searches for one or more quadric surface parameters of a given type of model that provides a best agreement between selected points from the point cloud data and a resultant model.