Work

An explicit and rapid intersection algorithm of plane and NURBS surface in CNC surface machining

Year: 2025

Type: article

Abstract: To address the challenge of plane-surface intersection in toolpath planning for CNC surface machining, a rapid intersection algorithm between a plane and a NURBS surface is proposed, which can provide an explicit Non-Uniform Rational B-Spline (NURBS) description of the intersection curve. By leveraging the dual-parameter property of NURBS surfaces, a series of fixed parameter values (usually values in the knot vector of this parameter) in one parametric direction are selected to generate NURBS curves in the other parametric direction. The bisection method is employed to compute the intersection points of these curves and the plane. Subsequently, the reverse engineering algorithm is applied to construct a NURBS curve that passes through these points, representing the desired intersection curve. The proposed algorithm significantly improves computational efficiency by reducing the problem to one of calculating the intersections of multiple NURBS curves and the plane. Furthermore, the explicit NURBS representation of the intersection curve facilitates subsequent NURBS interpolation. Simulations and experimental results validate the algorithm's effectiveness and accuracy, demonstrating its capability of deriving the intersection expression.

Source: Scientific Reports

DOI: 10.1038/s41598-025-25765-z

Authors: Shengli Wei, Kai Zhao, Huaiping Yan, Yuan Li

Institution: Anyang Institute of Technology

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,690

Funders: Anyang Institute of Technology, Henan Provincial Science and Technology Research Project