Fast closest logarithm algorithm in the special orthogonal group
Fast closest logarithm algorithm in the special orthogonal group
复制标题
特殊正交群中的快速最接近对数算法
DOI：
10.1093/imanum/drv027
复制
发表时间：
2016
影响因子：
2.1
通讯作者：
Adrien Escande
中科院分区：
文献类型：
--
作者：
Adrien Escande
对于的元素之间的内插，通过指数映射从一个空间传递到另一个空间的工作是有吸引力的。然而，对数是一个多值映射，特定图像的选择会影响内插的质量。在这篇文章中，我们提出了一种快速而准确的算法来计算似乎最适合于内插的图像：给定和，我们的算法在最小条件下返回最接近的对数。我们仔细研究了问题的数学性质，建立了算法，讨论了算法的实现，并证明了算法的有效性。
For interpolating between elements of, it is attractive to work in, passing from one space to the other via the exponential map. However, the logarithm is a multi-valued map and the choice of a particular image affects the quality of the interpolation. In this paper, we propose a fast and accurate algorithm to compute the image that seems the most appropriate for interpolation: givenand, our algorithm returns the logarithm ofwhich is the closest to, under minimal conditions on. We carefully study the mathematical properties of our problem to establish the algorithm, discuss its implementation and demonstrate its efficiency.