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画法几何新解

  

  1. 上海交通大学计算机系,上海 200240
  • 出版日期:2018-02-28 发布日期:2018-02-06

Interpretation of Descriptive Geometry

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
  • Online:2018-02-28 Published:2018-02-06

摘要: 从几何学的角度重新认识画法几何,结合计算化需求,梳理画法几何的理论体系。
首先,以新的视角,分析画法几何教材在表述上的一些问题;其次,揭示了投影、2D/3D 对应
和尺规作图以及轴测图、阴影与透视等理论的本质;并讨论上述理论的计算化问题,给出了画
法几何在理论与应用方面进一步发展的设想。

关键词: 几何, 图学, 画法几何, 投影

Abstract: From the aspect of geometry, this paper gives new understandings on descriptive geometry.
Combined with the demand for computerization, the theory system of descriptive geometry is
clarified. On this basis, some expressions in some textbooks of descriptive geometry are first
reframed. Then the essences of theories on projection, 2D/3D corresponding, drawing by ruler and
compass, as well as isometric drawing, shadow and perspective are revealed. Problems related to
computerize these theories are further discussed. In the end, some assumptions are proposed to the
development of descriptive geometry both in theory and in application.

Key words: geometry, graphics, descriptive geometry, projection