  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.
