| Transforming a real-life arbitrary solid topology into a computerized model is challenging. Traditional spline and least square interpolation methods can become labor-intensive and cumbersome when dealing with complex 3D surfaces. The piece-wise spline (i.e., parameterized cubic spline), least square, and other power basis polynomial methods can still be used to approximate such complex curves and surfaces. Conformal mapping can also be used to approximate complex curves but it is not applicable for 3D problems. Moreover, these methods do not offer the interactive geometric modeling capability. In this work an automated technique is introduced for modeling smooth shapes of 3D arbitrary topology. This automated method combines the unification of finite element analysis (FEA) and non-uniform rational B-spline (NURBS). Due to the unification of these two methods, it is called the unified automated surface approximation method (USAM). The numerical algorithm of USAM is based on non-linear FEA and NURBS. It is systematically designed as a versatile, self-contained, equation-solving module for incorporating in existing CAD tools. Prior to applying USAM, it is necessary to have a given sculptured geometry scanned. The scanned grid point locations are obtained via an optical scanner. Through this scanning process, the point cloud density is formed. The data points are then transferred to a computer for surface approximation process via USAM. Through the process of surface approximation, the numerical algorithm systematically and iteratively computes the nodal displacement and its derivatives. Once the surface approximation process has converged, USAM then generates a smooth, interactive surface of the sculptured geometry up to C2 continuity. The computer solid model can then be interactively modified either locally or globally due to NURBS property enhancement. USAM eliminates the need for building another sculptured model. Therefore, it is an ideal tool for concurrent engineering applications. Ultimately, USAM offers great potential application in design and analysis for all industries: entertainment, medical, aerospace, and automobile. |
