Automatic reconstruction of 3D CAD models from digital scans

We present an approach for the reconstruction and approximation of 3D CAD models from an unorganized collection of points. Applications include rapid reverse engineering of existing objects for use in a virtual prototyping environment, including computer aided design and manufacturing. Our reconstruction approach is flexible enough to permit interpolation of both smooth surfaces and sharp features, while placing few restrictions on the geometry or topology of the object. Our algorithm is based on alpha-shapes to compute an initial triangle mesh approximating the surface of the object. A mesh reduction technique is applied to the dense triangle mesh to build a simplified approximation, while retaining important topological and geometric characteristics of the model. The reduced mesh is interpolated with piecewise algebraic surface patches which approximate the original points. The process is fully automatic, and the reconstruction is guaranteed to be homeomorphic and error bounded with respect to the original model when certain sampling requirements are satisfied. The resulting model is suitable for typical CAD modeling and analysis applications.