| 球极投影中关于透视的两个推论及其应用 |
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| 引用本文： | 李耀.球极投影中关于透视的两个推论及其应用[J].湖南科技大学学报(自然科学版),1996(2). |
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| 作者姓名： | 李耀 |
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| 摘 要： | 本文提出了以投影圆球之赤道平面为投影平面的一种球极投影，首次引入了射影几何理论中关于平面场透视变换的双旋法则，并得到了两个关于球极投影的推论。从而在工程技术界广泛使用球极投影图的应用中，完全可以据此推论来精确地绘制空间直线和平面的球极投影图以及分析解决各种工程实际问题。同时也为使用计算机绘制球极投影图提供了一种简单而实用的数学模型，因此就避免了以往那种繁琐的球面三角学解析运算处理方法。图８、参４。
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| 关 键 词： | 球极投影 赤平面 透视 计算机绘图 |
TWO COROLLARIES OF PERSPECTIVE IN STEREOGRAPHIC PROJECTION AND THEIR APPLICATIONS |
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| Li Yao.TWO COROLLARIES OF PERSPECTIVE IN STEREOGRAPHIC PROJECTION AND THEIR APPLICATIONS[J].Journal of Hunan University of Science & Technology(Natural Science Editon),1996(2). |
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| Authors: | Li Yao |
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| Institution: | Dept.of Mechanical Engineering |
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| Abstract: | In this paper the auther puts forward the stereographic projection in which the projection plane is the equatorial plane of projection-sphere, recommends the rules about perspective mapping of plane field in projective geometry and reveals two corollaries in stereographic projection. Therefore in broad application of stereographic projection to engineering practice the stereographic projection of straight line and plane can be accurately drawn and various problems analyzed by use of the two corollaries. What is more, by applying them, simple mathematical models for drawing the stereographic projection in computer drafting can be set up without complicated spherical trigeometry calculation,8figs., 4refs. |
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| Keywords: | stereographic projection equatorial plane perspective computer drafting |
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