Finding best-fit polyhedral rotations with geometric algebra
Finding best-fit polyhedral rotations with geometric algebra
复制标题
用几何代数寻找最合适的多面体旋转
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
M. Tucker
中科院分区：
文献类型：
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作者：
S. Wells;M. Dove;M. Tucker
有许多矿物的结构被很好地描述为连接的SiO4四面体框架。由于拉伸Si-O键的能量成本远远大于改变桥接Si-O- si键角的成本，这些结构可以使用刚性单元图进行初步近似分析，其中多面体被视为完全刚性。为了将刚性单元理论的预测与其他形式的模拟结果进行比较，我们希望确定用刚性单元运动来描述给定的一组原子运动的效果如何。我们提出了一套技术来寻找最接近于一组给定原子运动的多面体旋转，并用于量化多面体的残余畸变。几何（Clifford）代数的形式证明了处理任意旋转非常方便，我们在转子拟合分析中使用了这种形式。
There are many minerals whose structure is well described as a framework of linked SiO4 tetrahedra. Since the energy cost of stretching the Si-O bond is much greater than the cost of changing the bridging Si-O-Si bond angle, these structures may to a first approximation be analysed using the rigid-unit picture, in which the polyhedra are treated as completely rigid. In order to compare the predictions of rigid-unit theory with the results of other forms of simulation, we wish to determine how well a given set of atomic motions can be described in terms of rigid-unit motion. We present a set of techniques for finding the polyhedral rotations that most closely fit a given set of atomic motions, and for quantifying the residual distortion of the polyhedra. The formalism of geometric (Clifford) algebra proved very convenient for handling arbitrary rotations, and we use this formalism in our rotor-fitting analysis.