Research status and prospects of free-form surface modeling theory for CAD, CAE and CAM

面向CAD、CAE和CAM的自由曲面造型理论研究现状与展望

¹ School of Mechanical Engineering, Xi'an University of Science and Technology, Xi'an 710072, China
² Key Laboratory of High Performance Manufacturing for Aero Engine, Ministry of Industry and Information Technology, Northwestern Polytechnical University, Xi'an 710072, China

Received: 25 October 2024

Abstract

Free-form surface modelling theory is the study of how to describe and construct free-form surfaces in the computer, and how to interactively display, modify and control them. It is not only an important research content in the field of computer-aided geometric design, but also a key factor in promoting the development and deep integration of CAD/CAE/CAM technologies, achieving CAX integration, and is the key to support the transformation and upgrading of the manufacturing industry. In the current research of free-form surface modelling theory oriented towards CAD, CAE, and CAM, parametric surface modelling and discrete surface modelling constitute two relatively complete system frameworks, which are interrelated and have complementary advantages, and have become the main branches of research in this field, as well as the most widely used and far-reaching theories. Based on the above two branches as the entry point, the current research and application status of free-form surface modelling theory for CAD, CAE and CAM is comprehensively analysed from the three levels of theoretical methods, commercial software and engineering applications, and the characteristics of different modelling methods are compared and summarized in terms of surface modelling capability and modelling quality, and finally the future development trend of free-form surface modelling theory is looked forward.

摘要

自由曲面造型理论是研究如何在计算机中描述和构造自由曲面, 以及如何对其进行交互式显示、修改和控制的理论体系与方法。它既是计算机辅助几何设计领域的重要研究内容, 也是促进CAD/CAE/CAM技术发展与深度融合、实现CAX一体化, 并支撑制造业转型升级的关键。在当前面向CAD、CAE和CAM的自由曲面造型理论研究中, 参数曲面造型和离散曲面造型构成了2个相对完整的体系框架, 它们相互关联且相互补充, 成为了该领域研究的主要分支, 并且也是应用最广泛、影响最为深远的理论。基于此, 以上述2个分支为切入点, 从理论方法、商用软件和工程应用3个层面, 综合分析了面向CAD、CAE和CAM的自由曲面造型理论研究与应用现状, 并从曲面造型能力和造型质量等方面对比总结了不同造型方法的特点, 展望了自由曲面造型理论的未来发展趋势。