Abstract
In the field of curves and surfaces fairing, arbitrary resolution wavelet fairing algorithm made wavelet fairing technology widely extended to general curves and surfaces, which are determined by any number of control vertices. Unfortunately, accurate wavelet construction algorithm for general curves and surfaces still has not been perfect now. In this article, a concrete algorithm for reconstruction matrix and wavelet construction was emphatically studied, which would be used in the multi-resolution fairing process for curves and surfaces with any number of control vertices. The essence of this algorithm is to generalize wavelet construction into the solution of null space, which could be solved gradually and rapidly by the procedures of decomposition and simplification of coefficient matrix. Certainly, the related compactly supported wavelets could be constructed efficiently and accurately, too. In the last of the article, a complex curve and a complex surface case were provided to verify the stability, high performance, and robustness of this algorithm.
Highlights
In the field of reverse engineering (RE), some kinds of complex parts have high requirements for the fairness of their computer-aided design (CAD) models, such as turbine engine blades, supercharger impellers, compressor rotors, aircrafts, high-speed railway, and so on which must meet the aerodynamics requirements, and household appliances, motor vehicles, and so on which must meet the artistic characteristic requirements
The two primary error sources that affect the fairness of CAD models are measuring accuracy, mainly caused by measuring instruments and measuring methods, and the manufacturing accuracy of the parts themselves
In order to improve the fairness of reconstructed curves and surfaces, fairness operation has always been a good solution and a research focus in the field of RE
Summary
In the field of reverse engineering (RE), some kinds of complex parts have high requirements for the fairness of their computer-aided design (CAD) models, such as turbine engine blades, supercharger impellers, compressor rotors, aircrafts, high-speed railway, and so on which must meet the aerodynamics requirements, and household appliances, motor vehicles, and so on which must meet the artistic characteristic requirements. The idea of this algorithm is to change the knot vector to meet the requirements of literature.[2] So as to realize the wavelet fairing and simplification for non-uniform rational B-splines (NURBS) curves and surfaces by DWFA.
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