Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibration
نویسندگان
چکیده
منابع مشابه
Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibration
The problem of generating uniform deterministic samples over the rotation group, SO(3), is fundamental to computational biology, chemistry, physics, and numerous branches of computer science. We present the best-known method to date for constructing incremental, deterministic grids on SO(3); it provides: 1) the lowest metric distortion for grid neighbor edges, 2) optimal dispersion-reduction wi...
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The Hopf fibration is an example of a texture: a topologically stable, smooth, global configuration of a field. Here we demonstrate the controlled sculpting of the Hopf fibration in nematic liquid crystals through the control of point defects. We demonstrate how these are related to torons by use of a topological visualization technique derived from the Pontryagin-Thom construction.
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Among the most important topological constructions are Hopf fibrations. That they both play an important role in topology itself and have numerous physical applications lends credence to this statement. In this paper, I will discuss some of these applications as motivation for mathematicians to learn about the physical significance of the Hopf fibration in greater detail than that presented her...
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ژورنال
عنوان ژورنال: The International Journal of Robotics Research
سال: 2009
ISSN: 0278-3649,1741-3176
DOI: 10.1177/0278364909352700