Implicit curve and surface reconstruction attracts the attention of many researchers and gains a wide range of applications, due to its ability to describe objects with complicated geometry and topology. However, extra zero-level sets or spurious sheets arise in the reconstruction process makes the reconstruction result challenging to be interpreted and damage the final result. In this paper, we proposed an implicit curve and surface reconstruction method based on the progressive-iterative approximation method, named implicit progressive-iterative approximation (I-PIA). The proposed method elegantly eliminates the spurious sheets naturally without requiring any explicit minimization procedure, thus reducing the computational cost greatly and providing high-quality reconstruction results. Numerical examples are provided to demonstrate the efficiency and effectiveness of the proposed method.

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In this paper, we propose methods to find a G k -multi-degree reduction of disk Bézier curves for k = 0, 1. The methods are based on degree reducing the center and radius curves using G k -continuity and minimizing the corresponding errors. Some examples and comparisons are given to illustrate the efficiency and simplicity of the proposed methods. The examples show that by using our proposed methods, we get G 0 -, and G 1 -degree reductions, while having less errors than existing methods, which are without any continuity conditions.

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