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| 用圆锥曲面求解几何约束问题 |
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蒋鲲1,2, 高小山1
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1.中国科学院,数学与系统科学研究院,北京,100080;2.黑龙江大学,理学院,黑龙江,哈尔滨,150080
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| 摘要: |
| 通常大多数三维参数化CAD系统都只用平面和球面作为最基本的作图工具,这在某种程度上限制了三维参数化CAD系统的作图范围.通过引进一类新的作图工具,使得三维参数化CAD系统的作图范围得到扩大. 同时证明了一个三维几何图形可以用平面、球面和圆锥曲面构造出来的充分必要条件是这个三维几何图形可以用一个三角化的次数小于9的代数方程组来描述.通过引进圆锥曲面作为新的作图工具,著名的三维Appolonius作图问题可以被完全求解. |
| 关键词: 几何约束求解 圆锥曲面 参数化CAD |
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| 基金项目:Supported by the National Grand Fundamental Research 973 Program of China under Grant No.G1998030600 (国家重点基础研究发展规划973项目基金); the Chinese National Science Fundation under an Outstanding Youth Grant No.69725002 (国家基金委杰出青年基金) |
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| 3D Geometric Constraint Solving with Conicoid |
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JIANG Kun,GAO Xiao-shan
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| Abstract: |
| In general, most 3D parametric design systems use plane and sphere as basic tools to draw a three-dimensional diagram. In this paper, we introduce a class of new drawing tools: conicoid. The scope of three-dimensional diagram that can be drawn with conicoid is strictly larger than that with plane and sphere only. We prove that a diagram can be drawn with conicoid sequentially if and only if it can be described by a set of triangular equations of degree less than nine. Spatial Appolonius drawing problems can be completely solved with conicoid. |
| Key words: geometric constraint solving conicoid parametric CAD |
