The relaxed implicit randomized algebraic reconstruction technique for curve and surface reconstruction

Abstract

Implicit curve and surface reconstruction has wide applications in computer graphics, which attracts great attention of many researchers. In this paper, we propose the relaxed implicit randomized algebraic reconstruction technique (RIR-ART) for curve and surface reconstruction. The RIR-ART method generates a sequence of curves and surfaces by adjusting the control coefficients with the relaxation parameters iteratively. It is proved that the sequence of curves and surfaces generated by the RIR-ART method with the suitable relaxation parameters converge to the least-norm results in terms of the mean square error. The RIR-ART method can eliminate the extra zero-level sets effectively during its iterative process, and converge faster than the implicit progressive-iterative approximation method (Hamza et al. 2020). Numerical examples present the efficiency and effectiveness of the proposed method.