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Abstract: 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 G1 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 G1 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. The practical examples reveal the value of the global beautification technique in reverse engineering.
Key words: Computer aided geometric design
Differential manifold Freeform surface
Reverse engineering
CLC No: TP391
国家自然科学基金资助项目(50575098). Received 20060623, received in revised form 20070103
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