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Convergence and Remeshing Criteria for Fitting Method Based on Iterative Reparameterization via Plane-Stress Model

In the process of reverse engineering [10] a physical part is used to construct a CAD model. Two main steps of the reverse engineering process are: first part is the digitalization of physical object which commonly performed by the object 3D surface scanning and the second step is constructing a compact surface CAD model. In one of the reverse engineering paths, the object can be divided in a userselected patches which can be represented by a NURBS surface. For example, in ship hull representation a user might select each side of the hull to be a separate surface patch. In this case, a NURBS surface fitting algorithm is required for each patch separately. As surface fitting is common topic in computer-aided design there already exists a large amount of literature [11] on these topics. The techniques for surface fitting can be divided to parameterization-based and the ones that do not use parameterization. In the parameterization-based methods, the crucial part of the fitting method is the point-cloud parameterization in which parameters u, v are allocated to all points of the 3D pointcloud. These methods can be divided to parameterization of organized [2] and unorganized points [3]. This paper deals with reverse engineering methods in which we assume that 3D model exists in a form of triangulated point cloud (surface mesh), and the objective is to construct a B-spline surface using a user-defined part of the surface.

Reverse Engineering, Parametric Surface Fitting, Shape Parameterization, Shape Optimization, B-spline

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