An algorithm for determining the inner and outer loops of arbitrary parametric surfaces

Abstract

Purpose

The purpose of this paper is to present an algorithm for determining the inner and outer loops of arbitrary parametric surfaces.

Design/methodology/approach

The algorithm considers two sub-algorithms: one for non-closed surfaces and another one for closed surfaces. The first sub-algorithm named by area positive and negative method (APNM), combines a curve discretization algorithm with the polygon direction judgment algorithm to judge the inner and outer loops of non-closed surfaces. The second sub-algorithm, called by cross-period number method (CPNM), combines a curve discretization algorithm with the periodicity of closed surfaces to judge the type of boundary loops.

Findings

The APNM can use less CPU time to determining the inner and outer loops of the non-closed parametric surfaces. The CPNM can also determine the inner and outer loops of closed parametric surfaces effectively. The judgment results of loops can ensure that the direction of meshes generated on these surfaces is right. And finally ensure the correctness of the numerical simulation results.

Originality/value

Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the APNM saves in the process of determining the inner and outer loops for non-closed surfaces. The CPNM is also a new method to determining the inner and outer loops for closed parametric surfaces. The single run-time of CPNM is very small and can reach the level of microseconds.

Citation

Ju, C., Zhang, J., Zhang, Y., Du, X., Yuan, Z. and Liu, T. (2023), "An algorithm for determining the inner and outer loops of arbitrary parametric surfaces", Engineering Computations, Vol. 40 No. 1, pp. 296-310. https://doi.org/10.1108/EC-01-2022-0036