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

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.