Effective re-parameterization and GA based knot structure optimization for high quality T-spline surface fitting

T-spline surface fitting from input triangular mesh is a common task in T-splines related CAD applications. One major objective to this problem is creating T-spline surface with fewer control points and higher accuracy. This paper proposes several effective approaches to improve fitting results. The proposed approaches include an incremental sampling strategy for robust initial fitting, a global effective re-parameterization algorithm called NUFR (non-uniform faithful re-parameterization) for a proper mesh parameterization, and a GA (genetic algorithm) based T-mesh knot structure optimization process for an optimal knot structure. The tradeoff between mesh simplicity and fitting accuracy can be adjusted with a few input parameters. Experiments on different models are provided to demonstrate the effectiveness of these approaches. Compared with the classic adaptive fitting result, the result of the proposed algorithm has smaller RMS error. And typically, the number of control points will be reduced by about 30%. (C) 2019 Elsevier B.V. All rights reserved.