Carrier Method for the General Evaluation and Control of Pose, Molecular Conformation, Tracking, and the Like
Carrier Method for the General Evaluation and Control of Pose, Molecular Conformation, Tracking, and the Like
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DOI：
10.1007/s00006-009-0160-9
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发表时间：
2009-02
影响因子：
1.5
通讯作者：
E. Hitzer;K. Tachibana;S. Buchholz;I. Yu
中科院分区：
文献类型：
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作者：
E. Hitzer;K. Tachibana;S. Buchholz;I. Yu
点、点对、圆和球面这四种基本几何对象对应于共形几何代数中由共形点构成的外积零空间。与无穷远点楔入，我们得到四个平面对象：有限-无穷远点对，直线，平面和整个5D空间。我们证明了所有这些基本几何对象都具有相同的代数结构。然后，我们开发了一个单一的一般代数方法来量化和插值的八个不同类别的对象的相对姿态。作为一个明确的例子，我们最后applylyour框架的有机大分子的构象。
The four basic geometric objects of points, point pairs, circles and spheres correspond to outer product null-spaces constructed by conformal points in conformal geometric algebra. Wedging with the infinity point we get four flat objects: finite-infinity point pairs, lines, planes and the whole 5D space. We show that all these basic geometric objects have thesame algebraic structure. We then develop a single general algebraic method to quantify and interpolate therelative poseof the eight different classes of objects. As an explicit example we finallyapplyour framework to the conformation of organic macromolecules.