engleski

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

In the process of reverse engineering a physical part is used to construct a CAD model. The physical part is usually represented as a triangulated point cloud (i.e., mesh). Triangulated mesh parameterization can be achieved by many different methods. When the parameterization is presented as mapping the 3D surface to planar domain, it can be illustrated that different methods result in different distortions in angles and areas. These distortions are important in reverse engineering, as they lead to a distorted B- spline control-point grid after fitting. Ideally, the fitting method based on parameterization should lead to a smooth Bspline control-point grid while keeping fitting error as small as possible. This is usually a problem in which compromises must be made where one objective is sacrificed for the other. The method for parameterization-based B-spline fitting presented in this paper can be regarded as a compromise between the harmonic method (very smooth control- point grid, but possible large fitting error) and the feature sensitive parameterization (low error but distorted control-point grid). In our method, initial parametrization is constructed using the harmonic mapping method. The parameterization is subsequently revised using feature-related and smoothness-related metrics. Different convergence criteria and remapping metrics were investigated on 4 different geometries obtained by 3D scanning. It was shown that the method can be slightly tuned depending on the desired output (small fitting error vs. smooth surface).

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

nije evidentirano