Beautification Technique For Freeform Models In Reverse Engineering

As a modern design methodology, reverse engineering has become an essential tool for industrial product development and innovation. Feature based reverse modeling strategy can be used to capture the original design intention accurately and to guide the reverse modeling process conveniently. The beautification theories and methods, focusing on the freeform models, are intensively explored to improve the shape of the final reverse B-rep model in this dissertation.The sectional profile converted by slicing technique from unorganized point cloud may contain unpleasant points wandering away too far from the real-life object and may deteriorate the quality of the final curve/curves. Therefore, an automatic fairing method based on directly geometric modification is proposed to recover the feature structure and shape information of the original curve. Relying on the faired results, a novel knot placement algorithm is presented to improve the shape in the freeform curve fitting process.The multiple surfaces approximated to point cloud subject to tight error are beautified globally by using the infinitesimal deformation technique of differentiable manifold. The deformation energy functional reflecting the overall shape of a surface is defined by using the Beltrami-Laplace operator on the manifold. Also the unique solution of the minimum of the energy functional is formulated according to the property of harmonic function. Then, the necessary and sufficient conditions of G~1 continuity between two B-spline surfaces with single knots are given and simplified, as well as the intrinsic equations of control points of the common boundary curve. Based on the local scheme of convergent G~1 smooth surfaces, a special solution of the family of deformation maps is constructed. The special solution is represented by the smoothly stitched B-rep model. The inevitable local imperfection at the stitching regions caused by constructing the special solution greatly influences on the shape preservation of reverse engineered model. Finally, the final solution is constructed such that the deformation energy clustering round the stitching regions is released gradually to the surface interior. Consequently, the shape of the model is improved.Boundary representation model composed of multiple B-spline surfaces reconstructed from point cloud suffers from various local shape imperfections inevitably caused by noise in the point data and the reverse modeling strategies. A beautification technique is proposed to remove the local shape irregularities of such a model. Based on the topologies of the B-rep model, the basic patterns of local beautification are classified firstly. The shape beautification is compared with the traditional surface fairing according to the pattern classification. Then, the mathematical model of the beautification is given after analyzing acceptable shape optimization criteria and their intrinsic characteristics of differential geometry. Finally, the local irregularities on the model regions are identified by using shape interrogation methods. As the beautifying variables, each control point associated with the regions is modified solely subject to the tolerance constraints and/or G~0 continuity constraints. Simultaneously, an optimization method is used to preserve an approximated G~1 continuity in the local regions. Consequently, the shape is improved without destroying the model topologies.A new local consistent fitting method is presented for dealing with the confluence region, where multiple surfaces meet, to reach global smoothness and keep local feature of normal vector trends. Based on the basic theories of curve and surface in CAGD such as geometric continuity, intersection, bridge, discretization and fitting etc., a reasonable local region definition and feature sensitive surface fitting technique subject to complex boundary constraints are discussed in detail. The final consistent surface, which keeps the fitting precision and reflects the feature trend of the original surfaces, satisfies G~1 continuity with the whole surface model.The algorithms about beautification is embedded in the feature-based reverse modeler—RE-SOFT. Typical industrial examples are used to illustrate the validation of the proposed beautification schemes and to reveal the practical value in reverse engineering. Finally, some topics for future work are discussed briefly.