| 关于椭圆抛物面与一般二次曲面相交的研究 |
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| 引用本文： | 周良德 江立芬. 关于椭圆抛物面与一般二次曲面相交的研究[J]. 湘潭大学自然科学学报, 1997, 19(2): 100-104 |
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| 作者姓名： | 周良德 江立芬 |
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| 作者单位： | 湘潭大学机械工程系!湘潭，411105 |
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| 摘 要： | 本文通过对椭圆抛物面与其一般形式的二次曲面相交的研究，得出了求交线的一种方法．该方法的关键在于借助作辅助柱面定出交已知曲面于相似和位似椭圆的平面方向，然后根据情况或采用正、斜投影法，或采用空间亲似变换的方法，将平行于上述平面方向的辅助平面截已知两曲面所得的椭圆变成圆，从而准确求得交线上的各点．
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| 关 键 词： | 椭圆抛物面 二次曲面 交线 位似椭圆 渐近柱面 |
THE STUDY ON THE CROSS OF ELLIPTIC PARABOLOID WITH THE GENERAL SECOND ORDER QUARDRIC SURFACES |
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| Zhou liangde, Jiang Lifen. THE STUDY ON THE CROSS OF ELLIPTIC PARABOLOID WITH THE GENERAL SECOND ORDER QUARDRIC SURFACES[J]. Natural Science Journal of Xiangtan University, 1997, 19(2): 100-104 |
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| Authors: | Zhou liangde Jiang Lifen |
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| Affiliation: | Department of Mechanical engineering of Xiangtan University |
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| Abstract: | The author has got a method in solving the line of intersection through studing the cross of elliptic paraboloid with the general second order quadric surfaces. The key to the method lies in defining the direction of similar ellipse and similar desposed ellipse crossing with the known quadric surfaces by maens of doing auxiliary cy tinder. Then according to the condition or adopting right and oblique protection or adopting the way of three-dimensional kindred transformation,turn the ellipse that was got by auxiliary plane that parralled to the ahead plane the known two quadric surfaces into a circle. Then accurately solve all the dots in the lines of intersection. |
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| Keywords: | elliptic paraboloid the second order quadric surfaces the lines of intersection similar disposed ellpse asymptote cylinder |
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