北京航空航天大学学报 ›› 2001, Vol. 27 ›› Issue (3): 348-350.

• 论文 • 上一篇    下一篇

应用最优化理论中的投影定理计算平行正投影

郑国磊1, 朱心雄1, 许德2   

  1. 1. 北京航空航天大学 机械工程及自动化学院;
    2. 成都飞机工业公司总师办
  • 收稿日期:2000-01-11 出版日期:2001-03-31 发布日期:2010-09-27
  • 作者简介:郑国磊(1964-),男,福建莆田人,副教授,100083,北京.

Calculation of an Orthographic Projection with the Projection Theorem

ZHENG Guo-lei1, ZHU Xin-xiong1, XU De2   

  1. 1. Beijing University of Aeronautics and Astronautics, School of Mechanical Engineering and Automation;
    2. Chengdu Aircraft Corporation, Office of Chief Engineers
  • Received:2000-01-11 Online:2001-03-31 Published:2010-09-27

摘要: 拟应用最优化理论中的投影定理,从理论上严格证明物体平行正投影的存在和唯一性,并在此基础上建立一个全新的平行正投影计算方法.内容包括:①应用数学语言阐明三维物体平行正投影的含义;②应用最优化理论中的相关理论依次论证与投影定理有关的几个命题,并在此基础上严格证明物体平行正投影的存在和唯一性,以及利用傅里叶级数形式建立平行正投影计算式;③简要分析这种计算方法的特点.

Abstract: This paper describes the process of proving the sole existence of an orthographic projection for a 3-dimentional geometry based on the projection theorem in the optimal theory, and proposes a new method of calculating the orthographically projective transformation of an object. It includes: ①An orthographic projection of a 3-dimentional geometry is defined again with the mathematical concepts; ②In order to apply the projection theorem, a series of propositions related to the orthographic projection are proved sequentially, and then the sole existence of an orthographic projection for a 3-dimentional object is strictly testified and the orthographically projective transformation of an object is found with respect to the Fourier series; ③The advantages of the method of calculating the orthographically projective transformation are concluded.

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