Two efficient algorithms for surface construction

Abstract

In this paper, we are concerned with two efficient algorithms for surface construction. Based on the Gauss equations, a discretized nonlinear equation of the form should be solved in the process of surface construction. We first consider a regularized fixed-point iterative algorithm for solving the discretized equation, in which we determine the actual regularization parameter by the Morozov discrepancy principle. A two-parameter algorithm is employed for solving the Morozov equation, and the convergence of the regularized fixed-point iterative algorithm is demonstrated. Secondly, we also propose the regularizing Levenberg–Marquardt scheme to solve the discretized equation, in which the regularization parameter is chosen to be a small constant. Numerical experiments are provided to demonstrate the robustness and efficiency of the two algorithms.

Keywords:

• regularization
• surface modelling
• fundamental theorem of surface

AMS Subject Classifications:

• 65J22
• 65J20
• 47J06

Acknowledgments

The authors thank Professor Jun Zou (Chinese University of Hong Kong) for his careful and fruitful guidance.

Notes

The work of this author was supported by China Postdoctoral Science Foundation (Grant no. 2012M521444) and National Natural Science Foundation of China (Nos 91130022, 11161130003 and 11101317).