期刊
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING
卷 22, 期 7, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/0965-0393/22/7/075013
关键词
rotations; equal-area mapping; texture analysis; quaternions; homochoric
资金
- Air Force Office of Scientific Research, MURI [FA9550-12-1-0458]
In computational work, data sets must often be represented on the surface of a sphere or inside a ball, requiring uniform grids. We construct a new volume-preserving projection between a cube and the set of unit quaternions. The projection consists of two steps: an equal-volume mapping from the cube to the unit ball, followed by an inverse generalized Lambert projection to either of the two unit quaternion hemispheres. The new projection provides a one-to-one mapping between a grid in the cube and elements of the special orthogonal group SO(3), i.e., 3D rotations. We provide connections to other rotation representation schemes, including the Rodrigues-Frank vector and the homochoric parameterizations, and illustrate the new mapping through example applications relevant to texture analysis.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据