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图学学报

图学学报 ›› 2022, Vol. 43 ›› Issue (6): 1018-1033.DOI: 10.11996/JG.j.2095-302X.2022061018

• 综述 • 上一篇    下一篇

T 样条用于计算机辅助设计、分析和制造的 新型表示方法 

  

  1. 1. 中国科学技术大学数学科学学院，安徽 合肥 230000；  2. 中国科学院大学数学科学学院，北京 100049；  3. 北京航空航天大学航空发动机研究院，北京 102206；  4. 上海交通大学密西根学院，上海 200240；  5. 北京航空航天大学机械工程及自动化学院，北京 100083
  • 出版日期:2022-12-30 发布日期:2023-01-11
  • 基金资助:
    国家自然科学基金项目(62102011，52175213，61872328)；北京市重点专项课题(Z190004)；国家重点研发计划课题(2020YFA0713703) 

T-splines a new representation for CAD, CAE and CAM

  1. 1. School of Mathematical Sciences, University of Science and Technology of China, Hefei Anhui 230000, China;  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;  3. Research Institute of Aero-Engine, Beihang University, Beijing 102206, China;  4. University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai 200240, China;  5. School of Mechanical Engineering and Automation, Beihang University, Beijing 100083, China
  • Online:2022-12-30 Published:2023-01-11
  • Supported by:
    National Natural Science Foundation of China (62102011, 52175213, 61872328); The Key Project of Beijing (Z190004), National Key R&D Program of China (2020YFA0713703) 

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摘要：

几何造型主要研究在计算机环境下几何模型的表示与设计，其是计算机辅助设计、工程和制造领 域中重要的基础研究方向。当前工业制造中几何模型表示的标准是非均匀有理 B 样条(NURBS)。然而，由于张量 积拓扑结构，NURBS 在表示复杂几何模型时具有难以克服的局限性。T 样条是一种新型兼容 NURBS 的自由曲面 造型表示技术。由于克服了 NURBS 的多个重要的局限，T 样条自提出后引起了学术界和工业界的极大关注。为 了使国内外同行对 T 样条的发展历程和研究现状有一个较为全面的了解，对其进行系统综述。在广泛文献调研的 基础上，对 T 样条的定义、基础算法，以及在计算机辅助设计、工程和制造中的应用进行归纳总结和详细分析， 重点分析了这些算法的基本思想和原理，比较了其优点和不足。由于工业界对几何表示的精度和效率的要求越来 越高，导致 T 样条的研究仍然不完善，还存在大量亟待解决的问题和可能的发展方向。

关键词: T 样条, 非均匀有理 B 样条, 计算机辅助设计, 计算机辅助分析, 计算机辅助制造

Abstract:

Geometric modeling is the main research area in computer-aided design (CAD), computer-aided engineering (CAE), and computer-aided manufacturing (CAM), focusing on the representation and design of geometric models on computers. Currently, the standard representation is non-uniform rational B-splines (NURBS). However, due to the tensor-product structure, NURBS has several main limitations in terms of the representations of complex models. T-spline is a new NURBS compatible free-form surface representation technology. T-splines have drawn wide attention both from academia and industry, after solving several limitations of the standard NURBS representation. To enable a more comprehensive understanding of T-splines, a systematic review was conducted. Based on the extensive literature research, the definition and basic operations for T-splines and applications of T-splines in CAD, CAE and CAM were summarized and compared, which mainly focused on the basic ideas, theories, merits and demerits of various algorithms. Due to the high demand of accuracy and efficiency required by geometric representation in the industry, the research on T-spline remains imperfect, and a number of problems and possible prospects are in need of exploration. 

Key words: T-splines, non-uniform rational B-splines, computer-aided design, computer-aided engineering; computer-aided manufacturing

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