Study二次曲面周围空间的运动学解释
Kinematic interpretation of the Study quadric's ambient space
摘要：
众所周知，Study二次曲面的实点（沿三维生成空间切片）对应于欧几里得三维空间的位移。但我们仍然缺乏周围7维射影空间$P^7$上的点的运动学意义。本文用欧氏四维空间的位移给出了一种可能的解释。从这一观点出发，我们还讨论了广义逆运动映射、$P^7$中直线对应的运动以及SE（3）-位移的线性复形。此外，我们提出了一个应用程序的交互式运动设计的背景下，这种解释。
英文摘要：
It is well known that real points of the Study quadric (sliced along a 3-dimensional generator space) correspond to displacements of the Euclidean 3-space. But we still lack of a kinematic meaning for the points of the ambient 7-dimensional projective space $P^7$. This paper gives one possible interpretation in terms of displacements of the Euclidean 4-space. From this point of view we also discuss the extended inverse kinematic map, motions corresponding to straight lines in $P^7$ and linear complexes of SE(3)-displacements. Moreover we present an application of this interpretation in the context of interactive motion design.
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