Global beautification technique for freeform surface model

Abstract

The multiple surfaces approximated to point cloud subject to tight error are beautified globally by using the infini- tesimal 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 en- ergy functional is formulated according to the property of har- monic 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 solu- tion of the family of deformation maps is constructed. The spe- cial 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 en- ergy 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.