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对偶曲线和直线轨迹 被引量:2
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作者 华宣积 《数学年刊(A辑)》 CSCD 北大核心 1991年第5期595-602,共8页
本文介绍了拟合或设计三维空间中直线轨迹的一种新方法,利用对偶数和对偶向量,我们把直纹面对应到单位对偶球面上的曲线。证明了这种曲线的Frenet公式。在引进对偶球面坐标之后,把直纹面对应到四维空间中的一条曲线,于是Bézier曲... 本文介绍了拟合或设计三维空间中直线轨迹的一种新方法,利用对偶数和对偶向量,我们把直纹面对应到单位对偶球面上的曲线。证明了这种曲线的Frenet公式。在引进对偶球面坐标之后,把直纹面对应到四维空间中的一条曲线,于是Bézier曲线,B样条曲线和累加弦长参数曲线成为拟合或设计直纹面的重要手段。 展开更多
关键词 对偶曲线 直线轨迹 拟合 frenet式
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Symplectic invariants for curves and integrable systems in similarity symplectic geometry 被引量:2
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作者 LI YanYan QU ChangZheng 《Science China Mathematics》 SCIE CSCD 2015年第7期1415-1432,共18页
In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Prenet formulae for curves in similarity symplectic geometry are ob... In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Prenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations. 展开更多
关键词 similarity symplectic geometry integrable system symplectic invariant moving frame method matrix Burgers equation
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